Peer Reviewed Papers
Does the black hole shadow probe the event horizon geometry?
There is an exciting prospect of obtaining the shadow of
astrophysical black holes (BHs) in the near future with
the Event Horizon Telescope. As a matter of principle,
this justifies asking how much one can learn about the
BH horizon itself from such a measurement. Since the
shadow is determined by a set of special photon orbits,
rather than horizon properties, it is possible that
different horizon geometries yield similar shadows. One
may then ask how sensitive is the shadow to details of
the horizon geometry? As a case study, we consider the
double Schwarzschild BH and analyse the impact on the
lensing and shadows of the conical singularity that holds
the two BHs in equilibrium -- herein taken to be a strut
along the symmetry axis in between the two BHs. Whereas
the conical singularity induces a discontinuity of the
scattering angle of photons, clearly visible in the lensing
patterns along the direction of the strut's location, it
produces no observable effect on the shadows, whose edges
remain everywhere smooth. The latter feature is illustrated
by examples including both equal and unequal mass BHs.
This smoothness contrasts with the intrinsic geometry of
the (spatial sections of the) horizon of these BHs, which
is not smooth, and provides a sharp example on how BH
shadows are insensitive to some horizon geometry details.
This observation, moreover, suggests that for the study
of their shadows, this static double BH system may be an
informative proxy for a dynamical binary.
Deliverable D2.3 (Shadows of single black holes)
Constraining the mass of dark photons and axion-like particles
through black-hole superradiance
Ultralight bosons and axion-like particles appear naturally
in different scenarios and could solve some long-standing
puzzles. Their detection is challenging, and all direct
methods hinge on unknown couplings to the Standard Model
of particle physics. However, the universal coupling to
gravity provides model-independent signatures for these
fields. We explore here the superradiant instability of
spinning black holes triggered in the presence of such
fields. The instability taps angular momentum from and
limits the maximum spin of astrophysical black holes. We
compute, for the first time, the spectrum of the most
unstable modes of a massive vector (Proca) field for
generic black-hole spin and Proca mass. The observed
stability of the inner disk of stellar-mass black holes
can be used to derive direct constraints on the
mass of dark photons in the mass range 10^{−13}
eV ≲ m_{V} ≲ 3 ×
10^{−12} eV. By including also higher azimuthal
modes, similar constraints apply to axion-like particles
in the mass range 6 × 10^{−13} eV ≲
m_{ALP} ≲ 10^{−11} eV.
Likewise, mass and spin distributions of supermassive BHs
-- as measured through continuum fitting, Kα iron line,
or with the future space-based gravitational-wave detector
LISA -- imply indirect bounds in the mass range approximately
10^{−19} eV ≲ m_{V},
m_{ALP} ≲ 10^{−13} eV, for
both axion-like particles and dark photons. Overall,
superradiance allows to explore a region of approximately
8 orders of magnitude in the mass of ultralight bosons.
Deliverable D1.1 (Non-linear superradiant instability)
Deliverable D2.2 (Black holes with gauge fields)
Probing the universality of synchronised hair around rotating
black holes with Q-clouds
Recently, various families of black holes (BHs) with
synchronised hair have been constructed. These are rotating
BHs surrounded, as fully non-linear solutions of the
appropriate Einstein-matter model, by a non-trivial bosonic
field in synchronised rotation with the BH horizon. Some
families bifurcate globally from a bald BH (e.g. the Kerr
BH), whereas others bifurcate only locally from a bald
BH (e.g. the D = 5 Myers–Perry BH). It would be
desirable to understand how generically synchronisation
allows hairy BHs to bifurcate from bald ones. However,
the construction and scanning of the domain of existence
of the former families of BHs can be a difficult and time
consuming (numerical) task. Here, we first provide a
simple perturbative argument to understand the generality
of the synchronisation condition. Then, we observe that
the study of Q-clouds is a generic tool to establish the
existence of BHs with synchronised hair bifurcating
(globally or locally) from a given bald BH without having
to solve the fully non-linear coupled system of Einstein-matter
equations. As examples, we apply this tool to establish
the existence of synchronised hair around D = 6
Myers–Perry BHs, D = 5 black rings and D =
4 Kerr-AdS BHs, where D is the spacetime dimension.
The black rings case provides an example of BHs with
synchronised hair beyond spherical horizon topology,
further establishing the generality of the mechanism.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D2.2 (Black holes with gauge fields)
Ultra-High Energy Cosmic Rays and Neutrinos from Tidal
Disruptions by Massive Black Holes
Tidal disruptions are extremely powerful phenomena, which
have been candidate sources of ultra-high energy cosmic
rays. The disruption of a star by a black hole can naturally
provide protons but also heavier nuclei, which can be
injected and accelerated to ultra-high energies within a
jet. Inside the jet, accelerated nuclei are likely to
interact with a dense photon field, leading to a significant
production of neutrinos and secondary particles. We model
numerically the propagation and interactions of high
energy nuclei in jetted tidal disruption events, in order
to evaluate consistently their signatures in cosmic rays
and neutrinos. We propose a simple model of the light
curve of tidal distruption events, consisting of two
stages: a high state with bright luminosity and short
duration and a medium state, less bright and lasting
longer. These two states have different impacts on the
production of cosmic rays and neutrinos. In order to
calculate the diffuse fluxes of cosmic rays and neutrinos,
we model the luminosity function and redshift evolution
of jetted tidal disruption events. We find that we can
fit the latest ultra-high energy cosmic ray spectrum and
composition results of the Auger experiment for a range
of reasonable parameters. The diffuse neutrino flux
associated to this scenario is found to be sub-dominant,
but nearby events can be detected by IceCube or next-generation
detectors such as IceCube-Gen2.
Deliverable D3.2 (Astrophysical Observables)
Shadows and strong gravitational lensing: a brief review
For ultra compact objects (UCOs), Light Rings (LRs) and
Fundamental Photon Orbits (FPOs) play a pivotal role in
the theoretical analysis of strong gravitational lensing
effects, and of BH shadows in particular. In this short
review, specific models are considered to illustrate how
FPOs can be useful in order to understand some non-trivial
gravitational lensing effects. This paper aims at briefly
overviewing the theoretical foundations of these effects,
touching also some of the related phenomenology, both in
General Relativity (GR) and alternative theories of
gravity, hopefully providing some intuition and new
insights for the underlying physics, which might be
critical when testing the Kerr black hole hypothesis.
Deliverable D2.3 (Shadows of single black holes)
Deliverable D2.4 (Shadows of black-hole binaries)
Ultra-High Energy Cosmic Rays and Neutrinos from Tidal
Disruptions by Massive Black Holes
Tidal disruptions are extremely powerful phenomena, which
have been candidate sources of ultra-high energy cosmic
rays. The disruption of a star by a black hole can naturally
provide protons but also heavier nuclei, which can be
injected and accelerated to ultra-high energies within a
jet. Inside the jet, accelerated nuclei are likely to
interact with a dense photon field, leading to a significant
production of neutrinos and secondary particles. We model
numerically the propagation and interactions of high
energy nuclei in jetted tidal disruption events, in order
to evaluate consistently their signatures in cosmic rays
and neutrinos. We propose a simple model of the light
curve of tidal distruption events, consisting of two
stages: a high state with bright luminosity and short
duration and a medium state, less bright and lasting
longer. These two states have different impacts on the
production of cosmic rays and neutrinos. In order to
calculate the diffuse fluxes of cosmic rays and neutrinos,
we model the luminosity function and redshift evolution
of jetted tidal disruption events. We find that we can
fit the latest ultra-high energy cosmic ray spectrum and
composition results of the Auger experiment for a range
of reasonable parameters. The diffuse neutrino flux
associated to this scenario is found to be sub-dominant,
but nearby events can be detected by IceCube or next-generation
detectors such as IceCube-Gen2.
Deliverable D3.2 (Astrophysical Observables)
Quasinormal modes and Strong Cosmic Censorship
The fate of Cauchy horizons, such as those found inside
charged black holes, is intrinsically connected to the
decay of small perturbations exterior to the event horizon.
As such, the validity of the strong cosmic censorship
(SCC) conjecture is tied to how effectively the exterior
damps fluctuations. Here, we study massless scalar fields
in the exterior of Reissner--Nordstrom--de Sitter black
holes. Their decay rates are governed by quasinormal modes
of the black hole. We identify three families of modes
in these spacetimes: one directly linked to the photon
sphere, well described by standard WKB-type tools; another
family whose existence and timescale is closely related
to the de Sitter horizon. Finally, a third family which
dominates for near-extremally-charged black holes and
which is also present in asymptotically flat spacetimes.
The last two families of modes seem to have gone unnoticed
in the literature. We give a detailed description of
linear scalar perturbations of such black holes, and
conjecture that SCC is violated in the near extremal
regime.
Deliverable D1.1 (Non-linear superradiant instability)
Deliverable D2.1 (Black holes with scalar fields)
ENIGMA: Eccentric, Non-spinning, Inspiral Gaussian-process
Merger Approximant for the characterization of eccentric
binary black hole mergers
We present 𝙴𝙽𝙸𝙶𝙼𝙰, a time domain, inspiral-merger-ringdown
waveform model that describes non-spinning binary black
holes systems that evolve on moderately eccentric orbits.
The inspiral evolution is described using a consistent
combination of post-Newtonian theory, self-force and black
hole perturbation theory. Assuming moderately eccentric
binaries that circularize prior to coalescence, we smoothly
match the eccentric inspiral with a stand-alone,
quasi-circular merger, which is constructed using machine
learning algorithms that are trained with quasi-circular
numerical relativity waveforms. We show that 𝙴𝙽𝙸𝙶𝙼𝙰
reproduces with excellent accuracy the dynamics of
quasi-circular compact binaries. We validate 𝙴𝙽𝙸𝙶𝙼𝙰 using
a set of 𝙴𝚒𝚗𝚜𝚝𝚎𝚒𝚗 𝚃𝚘𝚘𝚕𝚔𝚒𝚝 eccentric numerical relativity
waveforms, which describe eccentric binary black hole
mergers with mass-ratios between 1 ≤ q ≤
5.5, and eccentricities e_{0} ≲
0.2 ten orbits before merger. We use this model to explore
in detail the physics that can be extracted with moderately
eccentric, non-spinning binary black hole mergers. In
particular, we use 𝙴𝙽𝙸𝙶𝙼𝙰 to show that the gravitational
wave transients GW150914, GW151226, GW170104 and GW170814
can be effectively recovered with spinning, quasi-circular
templates if the eccentricity of these events at a
gravitational wave frequency of 10Hz satisfies
e_{0} ≤ {0.175,0.125,0.175,0.175},
respectively. We show that if these systems have
eccentricities e_{0} ∼ 0.1 at a
gravitational wave frequency of 10Hz, they can be
misclassified as quasi-circular binaries due to parameter
space degeneracies between eccentricity and spin corrections.
Deliverable D3.1 (Compact binary waveform)
Spontaneous scalarization of black holes and compact stars from
a Gauss-Bonnet coupling
We identify a class of scalar-tensor theories with coupling
between the scalar and the Gauss-Bonnet invariant that
exhibit spontaneous scalarization for both black holes
and compact stars. In particular, these theories formally
admit all of the stationary solutions of general relativity,
but these are not dynamically preferred if certain
conditions are satisfied. Remarkably, black holes exhibit
scalarization if their mass lies within one of many narrow
bands. We find evidence that scalarization can occur in
neutron stars as well.
Deliverable D3.3 (Smoking Guns)
Dirac perturbations on Schwarzschild–anti–de Sitter spacetimes:
Generic boundary conditions and new quasinormal modes
We study Dirac quasinormal modes of Schwarzschild–anti–de
Sitter (Schwarzschild-AdS) black holes, following the
generic principle for allowed boundary conditions proposed
in [M. Wang, C. Herdeiro, and M. O. P. Sampaio, Phys.
Rev. D 92, 124006 (2015).]. After deriving the
equations of motion for Dirac fields on the aforementioned
background, we impose vanishing energy flux boundary
conditions to solve these equations. We find a set of two
Robin boundary conditions are allowed. These two boundary
conditions are used to calculate Dirac normal modes on
empty AdS and quasinormal modes on Schwarzschild-AdS black
holes. In the former case, we recover the known normal
modes of empty AdS; in the latter case, the two sets of
Robin boundary conditions lead to two different branches
of quasinormal modes. The impact on these modes of the
black hole size, the angular momentum quantum number and
the overtone number are discussed. Our results show that
vanishing energy flux boundary conditions are a robust
principle, applicable not only to bosonic fields but also
to fermionic fields.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D2.2 (Black holes with gauge fields)
Gravitational wave signatures of highly compact boson star
binaries
Solitonic boson stars are stable objects made of a complex
scalar field with a compactness that can reach values
comparable to that of neutron stars. A recent study of
the collision of identical boson stars produced only
nonrotating boson stars or black holes, suggesting that
rotating boson stars may not form from binary mergers.
Here we extend this study to include an analysis of the
gravitational waves radiated during the coalescence of
such a binary, which is crucial to distinguish these
events from other binaries with LIGO and Virgo observations.
Our studies reveal that the remnant’s gravitational wave
signature is mainly governed by its fundamental frequency
as it settles down to a nonrotating boson star, emitting
significant gravitational radiation during this post-merger
state. We calculate how the waveforms and their post-merger
frequencies depend on the compactness of the initial boson
stars and estimate analytically the amount of energy
radiated after the merger.
Deliverable D1.2 (Structure of stars with dark cores
Deliverable D2.3 (Shadows of single black holes)
Superradiance in the BTZ black hole with Robin boundary
conditions
We show the existence of superradiant modes of massive
scalar fields propagating in BTZ black holes when certain
Robin boundary conditions, which never include the commonly
considered Dirichlet boundary conditions, are imposed at
spatial infinity. These superradiant modes are defined
as those solutions whose energy flux across the horizon
is towards the exterior region. Differently from rotating,
asymptotically flat black holes, we obtain that not all
modes which grow up exponentially in time are superradiant;
for some of these, the growth is sourced by a bulk
instability of AdS3, triggered by the scalar field with
Robin boundary conditions, rather than by energy extraction
from the BTZ black hole. Thus, this setup provides an
example wherein Bosonic modes with low frequency are
pumping energy into, rather than extracting energy from,
a rotating black hole.
Deliverable D1.1 (Non-linear superradiant instability)
Skyrmions, Skyrme stars and black holes with Skyrme hair in five
spacetime dimension
We consider a class of generalizations of the Skyrme model
to five spacetime dimensions (d = 5), which is
defined in terms of an O(5) sigma model. A special
ansatz for the Skyrme field allows angular momentum to
be present and equations of motion with a radial dependence
only. Using it, we obtain: 1) everywhere regular solutions
describing localised energy lumps (Skyrmions), 2)
Self-gravitating, asymptotically flat, everywhere
non-singular solitonic solutions (Skyrme stars), upon
minimally coupling the model to Einstein’s gravity, 3)
both static and spinning black holes with Skyrme hair,
the latter with rotation in two orthogonal planes, with
both angular momenta of equal magnitude. In the absence
of gravity we present an analytic solution that satisfies
a BPS-type bound and explore numerically some of the
non-BPS solutions. In the presence of gravity, we contrast
the solutions to this model with solutions to a complex
scalar field model, namely boson stars and black holes
with synchronised hair. Remarkably, even though the two
models present key differences, and in particular the
Skyrme model allows static hairy black holes, when
introducing rotation, the synchronisation condition becomes
mandatory, providing further evidence for its generality
in obtaining rotating hairy black holes.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D2.2 (Black holes with gauge fields)
Black Hole Spectroscopy: Systematic Errors and Ringdown Energy
Estimates
The relaxation of a distorted black hole to its final
state provides important tests of general relativity
within the reach of current and upcoming gravitational
wave facilities. In black hole perturbation theory, this
phase consists of a simple linear superposition of
exponentially damped sinusoids (the quasinormal modes)
and of a power-law tail. How many quasinormal modes are
necessary to describe waveforms with a prescribed precision?
What error do we incur by only including quasinormal
modes, and not tails? What other systematic effects are
present in current state-of-the-art numerical waveforms?
These issues, which are basic to testing fundamental
physics with distorted black holes, have hardly been
addressed in the literature. We use numerical relativity
waveforms and accurate evolutions within black hole
perturbation theory to provide some answers. We show that
(i) a determination of the fundamental l = m
= 2 quasinormal mode to within 1% or better requires the
inclusion of at least the first overtone, and preferably
of the first two or three overtones; (ii) a determination
of the black hole mass and spin with precision better
than 1% requires the inclusion of at least two quasinormal
modes for any given angular harmonic mode (ℓ,m).
We also improve on previous estimates and fits for the
ringdown energy radiated in the various multipoles. These
results are important to quantify theoretical (as opposed
to instrumental) limits in parameter estimation accuracy
and tests of general relativity allowed by ringdown
measurements with high signal-to-noise ratio gravitational
wave detectors.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D3.2 (Astrophysical Observables)
Orbital fingerprints of ultralight scalar fields around black
holes
Ultralight scalars have been predicted in a variety of
scenarios and advocated as a possible component of dark
matter. These fields can form compact regular structures
known as boson stars, or—in the presence of horizons—give
rise to nontrivial time-dependent scalar hair and a
stationary geometry. Because these fields can be coherent
over large spatial extents, their interaction with “regular”
matter can lead to very peculiar effects, most notably
resonances. Here we study the motion of stars in a
background describing black holes surrounded by nonaxially
symmetric scalar field profiles. By analyzing the system
in a weak-field approach, we find that the presence of a
scalar field gives rise to secular effects akin to ones
existing in planetary and accretion disks. Particularly,
the existence of resonances between the orbiting stars
and the scalar field may enable angular momentum exchange
between them, providing mechanisms similar to planetary
migration. Additionally, these mechanisms may allow
floating orbits, which are stable radiating orbits. We
also show, in the full relativistic case, that these
effects also appear when there is a direct coupling between
the scalar field and the stellar matter, which can arise
due to the presence of a scalar core in the star or in
alternative theories of gravity.
Deliverable D1.2 (Structure of stars with dark cores
Black-hole head-on collisions in higher dimensions
The collision of black holes and the emission of gravitational
radiation in higher dimensional spacetimes are of interest
in various research areas, including the gauge-gravity
duality, the TeV gravity scenarios evoked for the explanation
of the hierarchy problem, and the large-dimensionality
limit of general relativity. We present numerical simulations
of head-on collisions of nonspinning, unequal-mass black
holes starting from rest in general relativity with 4
≤ D ≤ 10 spacetime dimensions. We compare
the energy and linear momentum radiated in gravitational
waves with perturbative predictions in the extreme mass
ratio limit, demonstrating the strength and limitations
of black hole perturbation theory in this context.
Deliverable D4.1 (Wave extraction in axisymmetry)
Deliverable D4.2 (Black-hole head-on collisions)
Evidence for a maximum mass cut-off in the neutron star mass
distribution and constraints on the equation of state
We infer the mass distribution of neutron stars in binary
systems using a flexible Gaussian mixture model and use
Bayesian model selection to explore evidence for
multi-modality and a sharp cut-off in the mass distribution.
We find overwhelming evidence for a bimodal distribution,
in agreement with previous literature, and report for the
first time positive evidence for a sharp cut-off at a
maximum neutron star mass. We measure the maximum mass
to be 2.06 M_{⊙} < m_{max}
< 2.24M_{⊙} (68%), 2.0
M_{⊙} < m_{max} <
2.5M_{⊙} (90%), where this constraint
is robust against the choice of model for the mass
distribution and to removing the most extreme (highest
mass) neutron stars from the dataset. If this sharp cut-off
is interpreted as the maximum stable neutron star mass
allowed by the equation of state of dense matter, our
measurement puts tight constraints on the equation of
state. For a set of realistic equations of state that
support > 2 M_{⊙} neutron stars, our
inference of mmax is able to distinguish between models
at odds ratios of up to 15:1, whilst under a flexible
piecewise polytropic equation of state model our maximum
mass measurement improves constraints on the pressure at
3−7 × the nuclear saturation density by ∼35−50%
compared to simply requiring m_{max} >
2M_{⊙}. We obtain a lower bound on
the maximum sound speed attained inside the neutron star
of c^{max}_{s} > 0.64c (99.8%),
ruling out c_{s}^{max} < c
/ √3 at high significance.Our constraints on the
equation of state strengthen the case for neutron
star-neutron star mergers as the primary source of short
gamma-ray bursts.
Deliverable D1.2 (Structure of stars with dark cores)
Deliverable D3.2 (Astrophysical Observables)
Gravitational waves from single neutron stars: an advanced
detector era survey
With the doors beginning to swing open on the new
gravitational wave astronomy, this review provides an
up-to-date survey of the most important physical mechanisms
that could lead to emission of potentially detectable
gravitational radiation from isolated and accreting neutron
stars. In particular we discuss the gravitational wave-driven
instability and asteroseismology formalism of the f- and
r-modes, the different ways that a neutron star could
form and sustain a non-axisymmetric quadrupolar "mountain"
deformation, the excitation of oscillations during magnetar
flares and the possible gravitational wave signature of
pulsar glitches. We focus on progress made in the recent
years in each topic, make a fresh assessment of the
gravitational wave detectability of each mechanism and,
finally, highlight key problems and desiderata for future
work.
Deliverable D3.1 (Compact binary waveform)
Lensing and dynamics of ultra-compact bosonic stars
Spherically symmetric bosonic stars are one of the few
examples of gravitating solitons that are known to form
dynamically, via a classical process of (incomplete)
gravitational collapse. As stationary solutions of the
Einstein--Klein-Gordon or the Einstein--Proca theory,
bosonic stars may also become sufficiently compact to
develop light rings and hence mimic, in principle,
gravitational-wave observational signatures of black holes
(BHs). In this paper, we discuss how these horizonless
ultra-compact objects (UCOs) are actually distinct from
BHs, both phenomenologically and dynamically. In the
electromagnetic channel, the light ring associated
phenomenology reveals remarkable lensing patterns, quite
distinct from a standard BH shadow, with an infinite
number of Einstein rings accumulating in the vicinity of
the light ring, both inside and outside the latter. The
strong lensing region, moreover, can be considerably
smaller than the shadow of a BH with a comparable mass.
Dynamically, we investigate the fate of such UCOs under
perturbations, via fully non-linear numerical simulations
and observe that, in all cases, they decay into a
Schwarzschild BH within a time scale of O(M),
where M is the mass of the bosonic star. Both these
studies reinforce how difficult it is for horizonless
UCOs to mimic BH phenomenology and dynamics, in all its
aspects.
Deliverable D1.2 (Structure of stars with dark cores)
Post-Newtonian evolution of massive black hole triplets in
galactic nuclei -- III. A robust lower limit to the
nHz stochastic background of gravitational waves
Inspiraling massive black-hole binaries (MBHBs) forming
in the aftermath of galaxy mergers are expected to be the
loudest gravitational-wave (GW) sources relevant for
pulsar-timing arrays (PTAs) at nHz frequencies. The
incoherent overlap of signals from a cosmic population
of MBHBs gives rise to a stochastic GW background (GWB)
with characteristic strain around h_{c}
∼ 10^{−15} at a reference frequency of 1
yr^{−1}, although uncertainties around this value
are large. Current PTAs are piercing into the GW amplitude
range predicted by state-of-the-art MBHB-population models,
but no detection has been reported so far. To assess the
future success prospects of PTA experiments, it is therefore
important to estimate the minimum GWB level consistent
with our current understanding of the formation and
evolution of galaxies and massive black holes (MBHs). To
this purpose, we couple a state-of-the-art semianalytic
model of galaxy evolution and an extensive study of the
statistical outcome of triple MBH interactions. We show
that even in the most pessimistic scenario where all MBHBs
stall before entering the GW-dominated regime, triple
interactions resulting from subsequent galaxy mergers
inevitably drive a considerable fraction of the MBHB
population to coalescence. In the nHz frequency range
relevant for PTA, the resulting GWB is only a factor of
2-to-3 suppressed compared to a fiducial model where
binaries are allowed to merge over Gyr timescales after
their host galaxies merge. Coupled with current estimates
of the expected GWB amplitude range, our findings suggest
that the minimum GWB from cosmic MBHBs is unlikely to be
lower than h_{c} ∼ 10^{−16}
(at f = 1 yr^{−1}), well within the expected
sensitivity of projected PTAs based on future observations
with FAST, MeerKAT and SKA.
Deliverable D3.1 (Compact binary waveform)
Post-Newtonian evolution of massive black hole triplets in
galactic nuclei -- II. Survey of the parameter space
Massive black hole binaries (MBHBs) are expected to form
at the centre of merging galaxies during the hierarchical
assembly of the cosmic large scale structure, and are
therefore expected to be the loudest sources of gravitational
waves (GWs) in the frequency window from nHz to tens of
mHz. However, because of the dearth of relevant energy
exchanges with background stars and gas, many of these
MBHBs may stall at separations too large for GW emission
to drive them to coalescence in less than a Hubble time.
Triple MBH systems are then bound to form after a further
galaxy merger, triggering a complex and rich dynamics
that can eventually lead to MBH coalescence. Here we
report on the results of a large set of numerical simulations
performed with the code presented in Bonetti et al. (2016)
where MBH triplets are set in spherical stellar potentials
and MBH dynamics is followed through 2.5 post-Newtonian
order in the equations of motion. We characterise each
simulated system by the mass of the heavier MBH, the inner
and outer mass ratios, the initial eccentricities of the
inner and outer binaries, and the relative inclination,
running a total of about 15k simulations. From our full
suite of simulated systems we find that a fraction 20-30%
of the MBH binaries that would otherwise stall are led
to coalesce within a Hubble time. The corresponding
coalescence timescale has a log-normal distribution, with
a mean value around 250 Myr, while the eccentricity close
to the plunge, albeit small, is non-negligible (∼0.1).
We construct and discuss marginalised probability
distributions of the main parameters involved and, in a
companion paper, we will use the results presented here
to forecast the contribution of MBH triplets to the GW
signal in the nHz regime probed by PTA experiments. In a
follow-up paper, we will perform a similar exercise for
MBHBs in the mHz regime targeted by LISA.
Deliverable D3.1 (Compact binary waveform)
Tests for the existence of horizons through gravitational wave
echoes
The existence of black holes and of spacetime singularities
is a fundamental issue in science. Despite this, observations
supporting their existence are scarce, and their
interpretation unclear. We overview how strong a case for
black holes has been made in the last few decades, and
how well observations adjust to this paradigm. Unsurprisingly,
we conclude that observational proof for black holes is
impossible to come by. However, just like Popper's black
swan, alternatives can be ruled out or confirmed to exist
with a single observation. These observations are within
reach. In the next few years and decades, we will enter
the era of precision gravitational-wave physics with more
sensitive detectors. Just as accelerators require larger
and larger energies to probe smaller and smaller scales,
more sensitive gravitational-wave detectors will be probing
regions closer and closer to the horizon, potentially
reaching Planck scales and beyond. What may be there,
lurking?
Deliverable D1.2 (Structure of stars with dark cores)
Asymptotically flat scalar, Dirac and Proca stars: discrete vs.
continuous families of solutions
The existence of localized, approximately stationary,
lumps of the classical gravitational and electromagnetic
field - geons - was conjectured more than half a
century ago. If one insists on exact stationarity,
topologically trivial configurations in electro-vacuum
are ruled out by no-go theorems for solitons. But stationary,
asymptotically flat geons found a realization in
scalar-vacuum, where everywhere non-singular, localized
field lumps exist, known as (scalar) boson stars. Similar
geons have subsequently been found in Einstein-Dirac
theory and, more recently, in Einstein-Proca theory. We
identify the common conditions that allow these solutions,
which may also exist for other spin fields. Moreover, we
present a comparison of spherically symmetric geons for
the spin 0,1/2 and 1, emphasising the mathematical
similarities and clarifying the physical differences,
particularly between the bosonic and fermonic cases. We
clarify that for the fermionic case, Pauli's exclusion
principle prevents a continuous family of solutions for
a fixed field mass; rather only a discrete set exists,
in contrast with the bosonic case.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D2.2 (Black holes with gauge fields)
Light ring stability in ultra-compact objects
We prove the following theorem: axisymmetric, stationary
solutions of the Einstein field equations formed from
classical gravitational collapse of matter obeying the
null energy condition, that are everywhere smooth and
ultracompact (i.e., they have a light ring) must have at
least two light rings, and one of them is stable. It has
been argued that stable light rings generally lead to
nonlinear spacetime instabilities. Our result implies
that smooth, physically and dynamically reasonable
ultracompact objects are not viable as observational
alternatives to black holes whenever these instabilities
occur on astrophysically short time scales. The proof of
the theorem has two parts: (i) We show that light rings
always come in pairs, one being a saddle point and the
other a local extremum of an effective potential. This
result follows from a topological argument based on the
Brouwer degree of a continuous map, with no assumptions
on the spacetime dynamics, and hence it is applicable to
any metric gravity theory where photons follow null
geodesics. (ii) Assuming Einstein's equations, we show
that the extremum is a local minimum of the potential
(i.e., a stable light ring) if the energy-momentum tensor
satisfies the null energy condition.
Deliverable D1.2 (Structure of stars with dark cores)
Long-lived inverse chirp signals from core collapse in massive
scalar-tensor gravity
This letter considers stellar core collapse in massive
scalar-tensor theories of gravity. The presence of a
mass term for the scalar field allows for dramatic increases
in the radiated gravitational wave signal. There are
several potential smoking gun signatures of a departure
from general relativity associated with this process.
These signatures could show up within existing LIGO-Virgo
searches.
Deliverable D3.3 (Smoking Guns)
Self-gravitating oscillons and new critical behavior
The dynamical evolution of self-interacting scalars is
of paramount importance in cosmological settings, and can
teach us about the content of Einstein's equations. In
flat space, nonlinear scalar field theories can give rise
to localized, non-singular, time-dependent, long-lived
solutions called oscillons. Here, we discuss the
effects of gravity on the properties and formation of
these structures, described by a scalar field with a
double well potential. We show that oscillons continue
to exist even when gravity is turned on, and we conjecture
that there exists a sequence of critical solutions with
infinite lifetime. Our results suggest that a new type
of critical behavior appears in this theory, characterized
by modulations of the lifetime of the oscillon around the
scaling law and the modulations of the amplitude of the
critical solutions.
Deliverable D1.2 (Structure of stars with dark cores)
General first-order mass ladder operators for Klein-Gordon
fields
We study the ladder operator on scalar fields, mapping a
solution of the Klein-Gordon equation onto another solution
with a different mass, when the operator is at most first
order in derivatives. Imposing the commutation relation
between d'Alembertian, we obtain the general condition
for the ladder operator. The general condition contains
a non-trivial case which was not discussed in previous
work [V. Cardoso, T. Houri and M. Kimura, Phys.Rev.D
96, 024044 (2017), arXiv:1706.07339].
Deliverable D1.1 (Non-linear superradiant instability)
Deliverable D2.1 (Black holes with scalar fields)
Stationary scalar clouds around a BTZ black hole
We establish the existence of stationary clouds of massive
test scalar fields around BTZ black holes. These clouds
are zero-modes of the superradiant instability and are
possible when Robin boundary conditions (RBCs) are
considered at the AdS boundary. These boundary conditions
are the most general ones that ensure the AdS space is
an isolated system, and include, as a particular case,
the commonly considered Dirichlet or Neumann-type boundary
conditions (DBCs or NBCs). We obtain an explicit, closed
form, resonance condition, relating the RBCs that allow
the existence of normalizable (and regular on and outside
the horizon) clouds to the system's parameters. Such RBCs
never include pure DBCs or NBCs. We illustrate the spatial
distribution of these clouds, their energy and angular
momentum density for some cases. Our results show that
BTZ black holes with scalar hair can be constructed, as
the non-linear realization of these clouds.
Deliverable D2.1 (Black holes with scalar fields)
An astrometric search method for individually resolvable
gravitational wave sources with Gaia
Gravitational waves (GWs) cause the apparent position of
distant stars to oscillate with a characteristic pattern
on the sky. Astrometric measurements (e.g. those made by
Gaia) therefore provide a new way to search for GWs. The
main difficulty facing such a search is the large size
of the data set; Gaia observes more than one billion
stars. In this letter the problem of searching for GWs
from individually resolvable supermassive black hole
binaries using astrometry is addressed for the first time;
it is demonstrated how the data set can be compressed by
a factor of more than 10^{6}, with a loss of sensitivity of
less than 1%. This technique is successfully used to
recover artificially injected GWs from mock Gaia data.
Repeated injections are used to calculate the sensitivity
of Gaia as a function of frequency, and Gaia's directional
sensitivity variation, or antenna pattern. Throughout
the letter the complementarity of Gaia and pulsar timing
searches for GWs is highlighted.
Physics Focus Story
Deliverable D3.2 (Astrophysical Observables)
About gravitational-wave generation by a three-body system
We highlight some subtleties that affect naive implementations
of quadrupolar and octupolar gravitational waveforms from
numerically-integrated trajectories of three-body systems.
We show that some of these subtleties were occasionally
overlooked in the literature, with consequences for
published results. We also provide prescriptions that
lead to correct and robust predictions for the waveforms
computed from numerically-integrated orbits.
Deliverable D3.1 (Compact binary waveform)
The observational evidence for horizons: from echoes to
precision gravitational-wave physics
The existence of black holes and of spacetime singularities
is a fundamental issue in science. Despite this, observations
supporting their existence are scarce, and their
interpretation unclear. We overview how strong a case for
black holes has been made in the last few decades, and
how well observations adjust to this paradigm. Unsurprisingly,
we conclude that observational evidence for black holes
is impossible to come by. However, just like Popper's
black swan, alternatives can be ruled out or confirmed
to exist with a single observation. These observations
are within reach. In the next few years and decades, we
will enter the era of precision gravitational-wave physics
with more sensitive detectors. Just as accelerators require
larger and larger energies to probe smaller and smaller
scales, more sensitive gravitational-wave detectors will
be probing regions closer and closer to the horizon,
potentially reaching Planck scales and beyond. What may
be there, lurking?
Deliverable D1.2 (Structure of stars with dark cores)
Post-Kerr black hole spectroscopy
One of the central goals of the newborn field of gravitational
wave astronomy is to test gravity in the highly nonlinear,
strong field regime characterizing the spacetime of black
holes. In particular, "black hole spectroscopy" (the
observation and identification of black hole quasinormal
mode frequencies in the gravitational wave signal) is
expected to become one of the main tools for probing the
structure and dynamics of Kerr black holes. In this paper
we take a significant step towards that goal by constructing
a "post-Kerr" quasinormal mode formalism. The formalism
incorporates a parametrized but general perturbative
deviation from the Kerr metric and exploits the
well-established connection between the properties of the
spacetime's circular null geodesics and the fundamental
quasinormal mode to provide approximate, eikonal limit
formulae for the modes' complex frequencies. The resulting
algebraic toolkit can be used in waveform templates for
ringing black holes with the purpose of measuring deviations
from the Kerr metric. As a first illustrative application
of our framework, we consider the Johannsen-Psaltis
deformed Kerr metric and compute the resulting deviation
in the quasinormal mode frequency relative to the known
Kerr result.
Deliverable D1.2 (Structure of stars with dark cores)
Deliverable D3.1 (Compact binary waveform)
Mass ladder operators from spacetime conformal symmetry
Ladder operators can be useful constructs, allowing for
unique insight and intuition. In fact, they have played
a special role in the development of quantum mechanics
and field theory. Here, we introduce a novel type of
ladder operators, which map a scalar field onto another
massive scalar field. We construct such operators, in
arbitrary dimensions, from closed conformal Killing vector
fields, eigenvectors of the Ricci tensor. As an example,
we explicitly construct these objects in anti–de Sitter
(AdS) spacetime and show that they exist for masses
above the Breitenlohner-Freedman bound. Starting from a
regular seed solution of the massive Klein-Gordon equation,
mass ladder operators in AdS allow one to build a variety
of regular solutions with varying boundary condition at
spatial infinity. We also discuss mass ladder operator
in the context of spherical harmonics, and the relation
between supersymmetric quantum mechanics and so-called
Aretakis constants in an extremal black hole.
Deliverable D1.1 (Non-linear superradiant instability)
Deliverable D2.1 (Black holes with scalar fields)
Kerr black holes with synchronised hair: an analytic model and
dynamical formation
East and Pretorius (arXiv:1704.04791) have successfully
evolved, using fully non-linear numerical simulations,
the superradiant instability of the Kerr black hole (BH)
triggered by a massive, complex vector field. Evolutions
terminate in stationary states of a vector field condensate
synchronised with a rotating BH horizon. We show these
end points are fundamental states of Kerr BHs with
synchronised Proca hair. Motivated by the "experimental
data" from these simulations we suggest a universal (i.e.
field-spin independent), analytic model for the subset
of BHs with sychronised hair that possess a quasi-Kerr
horizon, applicable in the weak hair regime. Comparing
this model with fully non-linear numerical solutions of
BHs with synchronised scalar or Proca hair, we show the
model is accurate for hairy BHs that may emerge dynamically
from superradiance, whose domain we identify.
Deliverable D2.2 (Black holes with gauge fields)
Gravitational wave searches for ultralight bosons with LIGO and
LISA
Ultralight bosons can induce superradiant instabilities
in spinning black holes, tapping their rotational energy
to trigger the growth of a bosonic condensate. Possible
observational imprints of these boson clouds include (i)
direct detection of the nearly monochromatic (resolvable
or stochastic) gravitational waves emitted by the condensate,
and (ii) statistically significant evidence for the
formation of "holes" at large spins in the spin versus
mass plane (sometimes also referred to as "Regge plane")
of astrophysical black holes. In this work, we focus on
the prospects of LISA and LIGO detecting or constraining
scalars with mass in the range m_{s} ∈
[10^{−19},10^{−15}] eV and m_{s}
∈ [10^{−14},10^{−11}] eV, respectively.
Using astrophysical models of black-hole populations and
black-hole perturbation theory calculations of the
gravitational emission, we find that LIGO could observe
a stochastic background of gravitational radiation in the
range m_{s} ∈
[2&yimes;10^{−13},10^{−12}] eV, and up
to ∼10^{4} resolvable events in a 4-year
search if m_{s} ∼ 3×10^{−13}
eV. LISA could observe a stochastic background for boson
masses in the range m_{s} ∈
[5×10^{−19},5×10^{−16}], and
up to ∼10^{3} resolvable events in a 4-year
search if ms ∼ 10^{−17}
eV. LISA could further measure spins for black-hole
binaries with component masses in the range
[10^{3},10^{7}] M_{⊙},
which is not probed by traditional spin-measurement
techniques. A statistical analysis of the spin distribution
of these binaries could either rule out scalar fields in
the mass range [4×10^{−18},10^{−14}]
eV, or measure ms with ten percent accuracy if light
scalars in the mass range [10^{−17},10^{−13}]
eV exist.
Deliverable D1.1 (Non-linear superradiant instability)
Deliverable D3.1 (Compact binary waveform)
Stochastic and resolvable gravitational waves from ultralight
bosons
Ultralight scalar fields around spinning black holes can
trigger superradiant instabilities, forming a long-lived
bosonic condensate outside the horizon. We use numerical
solutions of the perturbed field equations and astrophysical
models of massive and stellar-mass black hole populations
to compute, for the first time, the stochastic
gravitational-wave background from these sources. The
background is observable by Advanced LIGO and LISA for
field masses ms in the range
[2×10^{−13},10^{−12}]eV and
[5×10^{−19},5×10^{−16}] eV,
respectively, and it can affect the detectability of
resolvable sources. Our estimates suggest that current
constraints on the stochastic background from LIGO O1 may
already exclude masses in the Advanced LIGO window.
Semicoherent searches with Advanced LIGO (LISA) should
detect ∼ 15 (5) to 200 (40) resolvable sources for
scalar field masses 3×10^{−13} (10^{−17})
eV. LISA measurements of massive BH spins could either
rule out bosons in the range
[10^{−18},1.6×10^{−13}] eV, or
measure ms with ten percent accuracy in the range
[10^{−17},10^{−13}] eV.
Deliverable D1.1 (Non-linear superradiant instability)
Deliverable D3.1 (Compact binary waveform)
Scattering of point particles by black holes: gravitational
radiation
Gravitational waves can teach us not only about sources
and the environment where they were generated, but also
about the gravitational interaction itself. Here we study
the features of gravitational radiation produced during
the scattering of a point-like mass by a black hole. Our
results are exact (to numerical error) at any order in a
velocity expansion, and are compared against various
approximations. At large impact parameter and relatively
small velocities our results agree to within percent level
with various post-Newtonian and weak-field results.
Further, we find good agreement with scaling predictions
in the weak-field/high-energy regime. Lastly, we achieve
striking agreement with zero-frequency estimates.
Deliverable D3.1 (Compact binary waveform)
Synchronous frequencies of extremal Kerr black holes:
resonances, scattering and stability
The characteristic damping times of the natural oscillations
of a Kerr black hole become arbitrarily large as the
extremal limit is approached. This behavior is associated
with the so-called zero damped modes (ZDMs), and suggests
that extremal black holes are characterized by quasinormal
modes whose frequencies are purely real. Since these
frequencies correspond to oscillations whose angular phase
velocity matches the horizon angular velocity of the black
hole, they are sometimes called "synchronous frequencies".
Several authors have studied the ZDMs for near-extremal
black holes. Recently, their correspondence to branch
points of the Green's function of the wave equation was
linked to the Aretakis instability of extremal black
holes. Here we investigate the existence of ZDMs for
extremal black holes, showing that these real-axis
resonances of the field are unphysical as natural black
hole oscillations: the corresponding frequency is always
associated with a scattering mode. By analyzing the
behavior of these modes near the event horizon we obtain
new insight into the transition to extremality, including
a simple way to understand the Aretakis instability.
Deliverable D2.3 (Shadows of single black holes)
Reissner-Nordström black holes with non-Abelian hair
We consider d ≥ 4 Einstein--(extended-)Yang-Mills
theory, where the gauge sector is augmented by higher
order terms. Linearizing the (extended) Yang-Mills equations
on the background of the electric Reissner-Nordström
(RN) black hole, we show the existence of normalizable
zero modes, dubbed non-Abelian magnetic stationary clouds.
The non-linear realization of these clouds bifurcates the
RN family into a branch of static, spherically symmetric,
electrically charged and asymptotically flat black holes
with non-Abelian hair. Generically, the hairy black holes
are thermodynamically preferred over the RN solution,
which, in this model, becomes unstable against the formation
of non-Abelian hair, for sufficiently large values of the
electric charge.
Deliverable D2.2 (Black holes with gauge fields)
Fundamental photon orbits: black hole shadows and spacetime
instabilities
The standard Black Holes (BHs) in General Relativity, as
well as other ultra-compact objects (with or without an
event horizon) admit planar circular photon orbits. These
light rings (LRs) determine several spacetime properties.
For instance, stable LRs trigger instabilities and, in
spherical symmetry, (unstable) LRs completely determine
BH shadows. In generic stationary, axi-symmetric spacetimes,
non-planar bound photon orbits may also exist, regardless
of the integrability properties of the photon motion. We
suggest a classification of these fundamental photon
orbits (FPOs) and, using Poincaré maps, determine
a criterion for their stability. For the Kerr BH, all
FPOs are unstable (similarly to its LRs) and completely
determine the Kerr shadow. But in non-Kerr spacetimes,
stable FPOs may also exist, even when all LRs are unstable,
triggering new instabilities. We illustrate this for the
case of Kerr BHs with Proca hair, wherein, moreover,
qualitatively novel shadows with a cuspy edge exist, a
feature that can be understood from the interplay between
stable and unstable FPOs. FPOs are the natural generalisation
of LRs beyond spherical symmetry and should generalise
the LRs key role in different spacetime properties.
Deliverable D2.3 (Shadows of single black holes)
The Fast and the Fiducial: Augmented kludge waveforms for
detecting extreme-mass-ratio inspirals
The extreme-mass-ratio inspirals (EMRIs) of stellar-mass
compact objects into massive black holes are an important
class of source for the future space-based gravitational-wave
detector LISA. Detecting signals from EMRIs will require
waveform models that are both accurate and computationally
efficient. In this paper, we present the latest implementation
of an augmented analytic kludge (AAK) model, publicly
available at github.com/alvincjk/EMRI_Kludge_Suite as
part of an EMRI waveform software suite. This version of
the AAK model has improved accuracy compared to its
predecessors, with two-month waveform overlaps against a
more accurate fiducial model exceeding 0.97 for a generic
range of sources; it also generates waveforms 5-15 times
faster than the fiducial model. The AAK model is well
suited for scoping out data analysis issues in the upcoming
round of mock LISA data challenges. A simple analytic
argument shows that it might even be viable for detecting
EMRIs with LISA through a semi-coherent template bank
method, while the use of the original analytic kludge in
the same approach will result in around 90% fewer detections.
Deliverable D3.1 (Compact binary waveform)
Gravitational Waves from Binary Black Hole Mergers Inside of Stars
We present results from a controlled numerical experiment
investigating the effect of stellar density gas on the
coalescence of binary black holes (BBHs) and the resulting
gravitational waves (GWs). This investigation is motivated
by the proposed stellar core fragmentation scenario for
BBH formation and the associated possibility of an
electromagnetic counterpart to a BBH GW event. We employ
full numerical relativity coupled with general-relativistic
hydrodynamics and set up a 30+30 M_{⊙}
BBH (motivated by GW150914) inside gas with realistic
stellar densities. Our results show that at densities
ρ ≳ 10^{6} - 10^{7}g cm^{-3}
dynamical friction between the BHs and gas changes the
coalescence dynamics and the GW signal in an unmistakable
way. We show that for GW150914, LIGO observations
conclusively rule out BBH coalescence inside stellar gas
of ρ ≳ 10^{7} g cm^{-3}. Typical
densities in the collapsing cores of massive stars are
in excess of this density. This excludes the fragmentation
scenario for the formation of GW150914.
Deliverable D3.1 (Compact binary waveform)
Deliverable D3.2 (Astrophysical Observables)
Superradiance in rotating stars and pulsar-timing constraints on
dark photons
In the presence of massive bosonic degrees of freedom,
rotational superradiance can trigger an instability that
spins down black holes. This leads to peculiar
gravitational-wave signatures and distribution in the
spin-mass plane, which in turn can impose stringent
constraints on ultralight fields. Here, we demonstrate
that there is an analogous spindown effect for conducting
stars. We show that rotating stars amplify low frequency
electromagnetic waves, and that this effect is largest
when the time scale for conduction within the star is of
the order of a light crossing time. This has interesting
consequences for dark photons, as massive dark photons
would cause stars to spin down due to superradiant
instabilities. The time scale of the spindown depends on
the mass of the dark photon, and on the rotation rate,
compactness, and conductivity of the star. Existing
measurements of the spindown rate of pulsars place direct
constraints on models of dark sectors. Our analysis
suggests that dark photons of mass m_{V}
∼ 10^{-12} eV are excluded by pulsar-timing
observations. These constraints also exclude superradiant
instabilities triggered by dark photons as an explanation
for the spin limit of observed pulsars.
Deliverable D1.1 (Non-linear superradiant instability)
Deliverable D1.4 (Bounds on particle masses using gravity)
Evolution of a proto-neutron star with a nuclear many-body
equation of state: neutrino luminosity and gravitational
wave frequencies
In a core-collapse supernova, a huge amount of energy is
released in the Kelvin-Helmholtz phase subsequent to the
explosion, when the proto-neutron star cools and deleptonizes
as it loses neutrinos. Most of this energy is emitted
through neutrinos, but a fraction of it can be released
through gravitational waves. We model the evolution of a
proto-neutron star in the Kelvin-Helmholtz phase using a
general relativistic numerical code, and a recently
proposed finite temperature, many-body equation of state;
from this we consistently compute the diffusion coefficients
driving the evolution. To include the many-body equation
of state, we develop a new fitting formula for the high
density baryon free energy at finite temperature and
intermediate proton fraction. We estimate the emitted
neutrino signal, assessing its detectability by present
terrestrial detectors, and we determine the frequencies
and damping times of the quasi-normal modes which would
characterize the gravitational wave signal emitted in
this stage.
Deliverable D3.2 (Astrophysical Observables)
Prospects for observing extreme-mass-ratio inspirals with LISA
One of the key astrophysical sources for the Laser
Interferometer Space Antenna (LISA) are the inspirals of
stellar-origin compact objects into massive black holes
in the centres of galaxies. These extreme-mass-ratio
inspirals (EMRIs) have great potential for astrophysics,
cosmology and fundamental physics. In this paper we
describe the likely numbers and properties of EMRI events
that LISA will observe. We present the first results
computed for the 2.5 Gm interferometer that was the new
baseline mission submitted in January 2017 in response
to the ESA L3 mission call. In addition, we attempt to
quantify the astrophysical uncertainties in EMRI event
rate estimates by considering a range of different models
for the astrophysical population. We present both likely
event rates and estimates for the precision with which
the parameters of the observed sources could be measured.
We finish by discussing the implications of these results
for science using EMRIs.
Deliverable D3.1 (Compact binary waveform)
Deliverable D3.2 (Astrophysical Observables)
Geodesic Models of Quasi-periodic-oscillations as Probes of
Quadratic Gravity
Future very-large-area X-ray instruments (for which the
effective area is larger than > 3 m^{2}) will
be able to measure the frequencies of quasi-periodic
oscillations (QPOs) observed in the X-ray flux from
accreting compact objects with sub-percent precision. If
correctly modeled, QPOs can provide a novel way to test
the strong-field regime of gravity. By using the relativistic
precession model and a modified version of the epicyclic
resonance model, we develop a method to test general
relativity against a generic class of theories with
quadratic curvature corrections. With the instrumentation
being studied for future missions such as eXTP, LOFT, or
STROBE-X, a measurement of at least two QPO triplets from
a stellar mass black hole can set stringent constraints
on the coupling parameters of quadratic gravity.
Deliverable D3.2 (Astrophysical Observables)
Probing Planckian corrections at the horizon scale with LISA
binaries
Several quantum-gravity models of exotic compact objects
predict microscopic or even Planckian corrections at the
horizon scale. We discuss two model-independent, smoking-gun
effects of these corrections in the gravitational waveform
of a compact binary, namely the absence of tidal heating
and the presence of tidal deformability. For events
detectable by the future space-based interferometer LISA,
we show that the effect of tidal heating dominates and
allows one to constrain putative corrections near the
horizon down to the Planck scale, even for binaries up
to redshift ∼ 9. Furthermore, the measurement
of the tidal Love numbers with LISA can constrain the
compactness of an exotic compact object down to microscopic
scales in conservative scenarios, and down to the Planck
scale in the case of a highly spinning binary at 1-10 Gpc
for dimensionless spin 0.9-0.99. Our analysis suggests
that highly spinning, supermassive binaries provide
unparalleled tests of quantum-gravity effects at the
horizon scale.
Deliverable D1.2 (Structure of stars with dark cores)
Science with the space-based interferometer LISA. V: Extreme
mass-ratio inspirals
The space-based Laser Interferometer Space Antenna (LISA)
will be able to observe the gravitational-wave signals
from systems comprised of a massive black hole and a
stellar-mass compact object. These systems are known as
extreme-mass-ratio inspirals (EMRIs) and are expected to
complete ∼ 104 - 105 cycles in band, thus allowing
exquisite measurements of their parameters. In this work,
we attempt to quantify the astrophysical uncertainties
affecting the predictions for the number of EMRIs detectable
by LISA, and find that competing astrophysical assumptions
produce a variance of about three orders of magnitude in
the expected intrinsic EMRI rate. However, we find that
irrespective of the astrophysical model, at least a few
EMRIs per year should be detectable by the LISA mission,
with up to a few thousands per year under the most
optimistic astrophysical assumptions. We also investigate
the precision with which LISA will be able to extract the
parameters of these sources. We find that typical fractional
statistical errors with which the intrinsic parameters
(redshifted masses, massive black hole spin and orbital
eccentricity) can be recovered are ∼ 10^{−6}
- 10^{−4}. Luminosity distance (which is required
to infer true masses) is inferred to about 10% precision
and sky position is localized to a few square degrees,
while tests of the multipolar structure of the Kerr metric
can be performed to percent-level precision or better.
Deliverable D3.1 (Compact binary waveform)
Deliverable D3.2 (Astrophysical Observables)
Iron Kα line of Kerr black holes with Proca hair
We continue our study on the capabilities of present and
future X-ray missions to test the nature of astrophysical
black hole candidates via X-ray reflection spectroscopy
and distinguish Kerr black holes from other solutions of
4-dimensional Einstein's gravity in the presence of a
matter field. Here we investigate the case of Kerr black
holes with Proca hair [1]. The analysis of a sample of
these configurations suggests that even extremely hairy
black holes can mimic the iron line profile of the standard
Kerr black holes, and, at least for the configurations
of our study, we find that current X-ray missions cannot
distinguish these objects from Kerr black holes. This
contrasts with our previous findings for the case of Kerr
black holes with scalar (rather than Proca) hair [2],
even though such comparison may be biased by the limited
sample. Future X-ray missions can detect the presence of
Proca hair, but a theoretical knowledge of the expected
intensity profile (currently missing) can be crucial to
obtain strong constraints.
Deliverable D2.2 (Black holes with gauge fields)
Are merging black holes born from stellar collapse or previous
mergers?
Advanced LIGO detectors at Hanford and Livingston made
two confirmed and one marginal detection of binary black
holes during their first observing run. The first event,
GW150914, was from the merger of two black holes much
heavier that those whose masses have been estimated so
far, indicating a formation scenario that might differ
from "ordinary" stellar evolution. One possibility is
that these heavy black holes resulted from a previous
merger. When the progenitors of a black hole binary
merger result from previous mergers, they should (on
average) merge later, be more massive, and have spin
magnitudes clustered around a dimensionless spin ∼
0.7. Here we ask the following question: can gravitational-wave
observations determine whether merging black holes were
born from the collapse of massive stars ("first generation"),
rather than being the end product of earlier mergers
("second generation")? We construct simple, observationally
motivated populations of black hole binaries and we use
Bayesian model selection to show that measurements of the
masses, luminosity distance (or redshift) and "effective
spin" of black hole binaries can indeed distinguish between
these different formation scenarios.
Deliverable D3.1 (Compact binary waveform)
Deliverable D3.2 (Astrophysical Observables)
The nightmare scenario: measuring the stochastic
gravitational-wave background from stalling massive black-hole
binaries with pulsar-timing arrays
Massive black-hole binaries, formed when galaxies merge,
are among the primary sources of gravitational waves
targeted by ongoing Pulsar Timing Array (PTA) experiments
and the upcoming space-based LISA interferometer. However,
their formation and merger rates are still highly uncertain.
Recent upper limits on the stochastic gravitational-wave
background obtained by PTAs are starting being in marginal
tension with theoretical models for the pairing and orbital
evolution of these systems. This tension can be resolved
by assuming that these binaries are more eccentric or
interact more strongly with the environment (gas and
stars) than expected, or by accounting for possible
selection biases in the construction of the theoretical
models. However, another (pessimistic) possibility is
that these binaries do not merge at all, but stall at
large (∼ pc) separations. We explore this extreme
scenario by using a galaxy-formation semi-analytic model
including massive black holes (isolated and in binaries),
and show that future generations of PTAs will detect the
stochastic gravitational-wave background from the massive
black-hole binary population within 10−15 years of
observations, even in the "nightmare scenario" in which
all binaries stall at the hardening radius. Moreover,
we argue that this scenario is too pessimistic, because
our model predicts the existence of a sub-population of
binaries with small mass ratios (q ≲
10^{−3}) that should merge within a Hubble time
simply as a result of gravitational-wave emission. This
sub-population will be observable with large signal-to-noise
ratios by future PTAs thanks to next-generation radiotelescopes
such as SKA or FAST, and possibly by LISA.
Deliverable D3.1 (Compact binary waveform)
Deliverable D3.2 (Astrophysical Observables)
Numerical evolutions of spherical Proca stars
Vector boson stars, or Proca stars, have been recently
obtained as fully non-linear numerical solutions of the
Einstein-(complex)-Proca system. These are self-gravitating,
everywhere non-singular, horizonless Bose-Einstein
condensates of a massive vector field, which resemble in
many ways, but not all, their scalar cousins, the well-known
(scalar) boson stars. In this paper we report fully-non
linear numerical evolutions of Proca stars, focusing on
the spherically symmetric case, with the goal of assessing
their stability and the end-point of the evolution of the
unstable stars. Previous results from linear perturbation
theory indicate the separation between stable and unstable
configurations occurs at the solution with maximal ADM
mass. Our simulations confirm this result. Evolving
numerically unstable solutions, we find, depending on the
sign of the binding energy of the solution and on the
perturbation, three different outcomes: (i) migration to
the stable branch, (ii) total dispersion of the scalar
field, or (iii) collapse to a Schwarzschild black hole.
In the latter case, a long lived Proca field remnant --
a Proca wig -- composed by quasi-bound states, may be
seen outside the horizon after its formation, with a
life-time that scales inversely with the Proca mass. We
comment on the similarities/differences with the scalar
case as well as with neutron stars.
Deliverable D2.2 (Black holes with gauge fields)
Selection bias in dynamically-measured supermassive black hole
samples: Scaling relations and correlations between residuals in
semi-analytic galaxy formation models
Recent work has confirmed that the masses of supermassive
black holes, estimated from scaling relations with global
properties such as the stellar masses of their host
galaxies, may be biased high. Much of this may be caused
by the requirement that the gravitational sphere of
influence of the black hole must be resolved for the
black-hole mass to be reliably estimated. We revisit
this issue by using a comprehensive galaxy evolution
semi-analytic model, which self-consistently evolves
supermassive black holes from high-redshift seeds via gas
accretion and mergers, and also includes AGN feedback.
Once tuned to reproduce the (mean) correlation of black-hole
mass with velocity dispersion, the model is unable to
also account for the correlation with stellar mass. This
behaviour is independent of the model's parameters, thus
suggesting an internal inconsistency in the data. The
predicted distributions, especially at the low-mass end,
are also much broader than observed. However, if selection
effects are included, the model's predictions tend to
align with the observations. We also demonstrate that the
correlations between the residuals of the local scaling
relations are more effective than the scaling relations
themselves at constraining AGN feedback models. In fact,
we find that our semi-analytic model, while in apparent
broad agreement with the scaling relations when accounting
for selection biases, yields very weak correlations between
their residuals at fixed stellar mass, in stark contrast
with observations. This problem persists when changing
the AGN feedback strength, and is also present in the
z ∼ 0 outputs of the hydrodynamic cosmological
simulation Horizon-AGN, which includes state-of-the-art
treatments of AGN feedback. This suggests that current
AGN feedback models may be too weak or are simply not
capturing the effect of the black hole on the stellar
velocity dispersion.
Deliverable D3.1 (Compact binary waveform)
Deliverable D3.2 (Astrophysical Observables)
End Point of the Ultraspinning Instability and Violation of
Cosmic Censorship
We determine the end point of the axisymmetric ultraspinning
instability of asymptotically flat Myers-Perry black holes
in D = 6 spacetime dimensions. In the nonlinear
regime, this instability gives rise to a sequence of
concentric rings connected by segments of black membrane
on the rotation plane. The latter become thinner over
time, resulting in the formation of a naked singularity
in finite asymptotic time and hence a violation of the
weak cosmic censorship conjecture in asymptotically flat
higher-dimensional spaces.
Deliverable D4.4 (Black-hole grazing collisions)
Radionovas: can black hole superradiance power Fast Radio
Bursts?
Highly spinning Kerr black holes with masses M =
1 - 100 M_{⊙} are subject to an
efficient superradiant instability in the presence of
bosons with masses μ ∼ 10^{−10} −
10^{−12} eV. We observe that this precisely matches
the effective plasma-induced photon mass in diffuse
galactic or intracluster environments (ω_{pl}
∼ 10^{−10} − 10^{−12} eV). This
suggests that bare Kerr black holes within galactic or
intracluster environments, possibly even including the
one produced in GW150914, are unstable to formation of a
photon cloud that may contain a significant fraction of
the mass of the original black hole. At maximal efficiency,
the instability timescale for a massive vector is
milliseconds, potentially leading to a transient rate of
energy extraction from a black hole as large as
∼10^{55} erg s^{−1}. We discuss
mechanisms for releasing the energy in the photon cloud,
including a possible connection to Fast Radio Bursts.
Deliverable D1.1 (Non-linear superradiant instability)
Deliverable D2.1 (Black holes with scalar fields)
Testing strong-field gravity with tidal Love numbers
The tidal Love numbers (TLNs) encode the deformability
of a self-gravitating object immersed in a tidal environment
and depend significantly both on the object's internal
structure and on the dynamics of the gravitational field.
An intriguing result in classical general relativity is
the vanishing of the TLNs of black holes. We extend this
result in three ways, aiming at testing the nature of
compact objects: (i) we compute the TLNs of exotic compact
objects, including different families of boson stars,
gravastars, wormholes, and other toy models for quantum
corrections at the horizon scale. In the black-hole limit,
we find a universal logarithmic dependence of the TLNs
on the location of the surface; (ii) we compute the TLNs
of black holes beyond vacuum general relativity, including
Einstein-Maxwell, Brans-Dicke and Chern-Simons gravity;
(iii) We assess the ability of present and future
gravitational-wave detectors to measure the TLNs of these
objects, including the first analysis of TLNs with LISA.
Both LIGO, ET and LISA can impose interesting constraints
on boson stars, while LISA is able to probe even extremely
compact objects. We argue that the TLNs provide a smoking
gun of new physics at the horizon scale, and that future
gravitational-wave measurements of the TLNs in a binary
inspiral provide a novel way to test black holes and
general relativity in the strong-field regime.
Deliverable D1.2 (Structure of stars with dark cores)
Deliverable D1.4 (Bounds on particle masses using gravity)
Iron Kα line of Proca stars
X-ray reflection spectroscopy can be a powerful tool to
test the nature of astrophysical black holes. Extending
previous work on Kerr black holes with scalar hair [1]
and on boson stars [2], here we study whether astrophysical
black hole candidates may be horizonless, self-gravitating,
vector Bose-Einstein condensates, known as Proca stars
[3]. We find that observations with current X-ray missions
can only provide weak constraints and rule out solely
Proca stars with low compactness. There are two reasons.
First, at the moment we do not know the geometry of the
corona, and therefore the uncertainty in the emissivity
profile limits the ability to constrain the background
metric. Second, the photon number count is low even in
the case of a bright black hole binary, and we cannot
have a precise measurement of the spectrum.
Deliverable D2.2 (Black holes with gauge fields)
Shadows of Einstein-dilaton-Gauss-Bonnet black holes
We study the shadows of the fully non-linear, asymptotically
flat Einstein-dilaton-Gauss-Bonnet (EdGB) black holes
(BHs), for both static and rotating solutions. We find
that, in all cases, these shadows are smaller than for
comparable Kerr BHs, i.e. with the same total mass and
angular momentum. In order to compare both cases we
provide quantitative shadow parameters, observing in
particular that the differences in the shadows mean radii
are never larger than the percent level. Therefore,
generically, EdGB BHs cannot be excluded by (near future)
shadow observations alone. On the theoretical side, we
find no clear signature of some exotic features of EdGB
BHs on the corresponding shadows, such as the regions of
negative (Komar, say) energy density outside the horizon.
We speculate that this is due to the fact that the Komar
energy interior to the light rings (or more precisely,
the surfaces of constant radial coordinate that intersect
the light rings in the equatorial plane) is always smaller
than the ADM mass, and consequently the corresponding
shadows are smaller than those of comparable Kerr BHs.
The analysis herein provides a clear example that it is
the light ring impact parameter, rather than its "size",
that determines a BH shadow.
Deliverable D2.3 (Shadows of single black holes)
On the equal-mass limit of precessing black-hole binaries
We analyze the inspiral dynamics of equal-mass precessing
black-hole binaries using multi-timescale techniques. The
orbit-averaged post-Newtonian evolutionary equations admit
two constants of motion in the equal-mass limit, namely
the magnitude of the total spin S and the effective spin
ξ. This feature makes the entire dynamics qualitatively
different compared to the generic unequal-mass case, where
only ξ is constant while the variable S
parametrizes the precession dynamics. For fixed individual
masses and spin magnitudes, an equal-mass black-hole
inspiral is uniquely characterized by the two parameters
(S,ξ): these two numbers completely determine
the entire evolution under the effect of radiation reaction.
In particular, for equal-mass binaries we find that (i)
the black-hole binary spin morphology is constant throughout
the inspiral, and that (ii) the precessional motion of
the two black-hole spins about the total spin takes place
on a longer timescale than the precession of the total
spin and the orbital plane about the total angular momentum.
Deliverable D3.1 (Compact binary waveform)
Ultralight scalars and resonances in black-hole physics
We study the contribution of binary black hole (BH-BH)
mergers from the first, metal-free stars in the Universe
(Pop III) to gravitational wave detection rates. Our study
combines initial conditions for the formation of Pop III
stars based on N-body simulations of binary formation
(including rates, binary fraction, initial mass function,
orbital separation and eccentricity distributions) with
an updated model of stellar evolution specific for Pop
III stars. We find that the merger rate of these Pop III
BH-BH systems is relatively small (< 0.1 Gpc^{-3}
yr^{-1}) at low redshifts (z < 2), where
it can be compared with the LIGO empirical estimate of
9-240 Gpc^{-3} yr^{-1} (Abbott et al.
2016). The predicted rates are even smaller for Pop III
double neutron star and black hole neutron star mergers.
Our rates are compatible with those of Hartwig et al.
(2016), but significantly smaller than those found in
previous work (Bond & Carr 1984; Belczynski et al.
2004; Kinugawa et al. 2014, 2016). We explain the reasons
for this discrepancy by means of detailed model comparisons
and point out that (i) identification of Pop III BH-BH
mergers may not be possible by advanced LIGO, and (ii)
the level of stochastic gravitational wave background
from Pop III mergers may be lower than recently estimated
(Kowalska et al. 2012; Inayoshi et al. 2016; Dvorkin et
al. 2016). We further estimate gravitational wave detection
rates for third-generation interferometric detectors. Our
calculations are relevant for low to moderately rotating
Pop III stars. We can now exclude significant (> 1 per
cent) contribution of these stars to low-redshift BH-BH
mergers. However, it remains to be tested whether (and
at what level) rapidly spinning Pop III stars (homogeneous
evolution) can contribute to BH-BH mergers in the local
Universe.
Deliverable D3.1 (Compact binary waveform)
Deliverable D3.2 (Astrophysical Observables)
Ultralight scalars and resonances in black-hole physics
Ultralight degrees of freedom coupled to matter lead to
resonances, which can be excited when the Compton wavelength
of the field equals a dynamical scale in the problem. For
binaries composed of a star orbiting a supermassive black
hole, these resonances lead to a smoking-gun effect: a
periastron distance which stalls, even in the
presence of gravitational-wave dissipation. This effect,
also called a floating orbit}, occurs for generic
equatorial but eccentric orbits and we argue that finite-size
effects are not enough to suppress it.
Deliverable D1.4 (Bounds on particle masses using gravity)
Deliverable D3.3 (Smoking Guns)
Constraining Black Holes with Light Boson Hair and Boson
Stars using Quasi Periodic Oscillations
Light bosonic fields are ubiquitous in extensions of the
Standard Model. Even when minimally coupled to gravity,
these fields might evade the assumptions of the black-hole
no-hair theorems and give rise to spinning black holes
which can be drastically different from the Kerr metric.
Furthermore, they allow for self-gravitating compact
solitons, known as (scalar or Proca) boson stars. The
quasi-periodic oscillations (QPOs) observed in the X-ray
flux emitted by accreting compact objects carry information
about the strong-field region, thus providing a powerful
tool to constrain deviations from Kerr's geometry and to
search for exotic compact objects. By using the relativistic
precession model, we investigate how the QPO frequencies
could be used to test the no-hair theorem and the existence
of light bosonic fields near accreting compact objects.
We show that a detection of two QPO triplets with current
sensitivity can already constrain these models, and that
the future eXTP mission or a LOFT-like mission can set
very stringent constraints on black holes with bosonic
hair and on (scalar or Proca) boson stars. The peculiar
geodesic structure of compact scalar/Proca boson stars
implies that these objects can easily be ruled out as
alternative models for X-ray source GRO J1655-40.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D3.2 (Astrophysical Observables)
Dynamical formation of a hairy black hole in a cavity from the
decay of unstable solitons
Recent numerical relativity simulations within the
Einstein--Maxwell--(charged-)Klein-Gordon (EMcKG) system
have shown that the non-linear evolution of a superradiantly
unstable Reissner-Nordström black hole (BH) enclosed
in a cavity, leads to the formation of a BH with scalar
hair. Perturbative evidence for the stability of such
hairy BHs has been independently established, confirming
they are the true endpoints of the superradiant instability.
The same EMcKG system admits also charged scalar soliton-type
solutions, which can be either stable or unstable. Using
numerical relativity techniques, we provide evidence that
the time evolution of some of these unstable
solitons leads, again, to the formation of a hairy BH.
In some other cases, unstable solitons evolve into a
(bald) Reissner-Nordström BH. These results establish
that the system admits two distinct channels to form hairy
BHs at the threshold of superradiance: growing hair from
an unstable (bald) BH, or growing a horizon from an
unstable (horizonless) soliton. Some parallelism with the
case of asymptotically flat boson stars and Kerr BHs with
scalar hair is drawn.
Deliverable D2.2 (Black holes with gauge fields)
Chaotic lensing around boson stars and Kerr black holes
with scalar hair
In a recent letter, arXiv:1509.00021, it was shown that
the lensing of light around rotating boson stars and Kerr
black holes with scalar hair can exhibit chaotic patterns.
Since no separation of variables is known (or expected)
for geodesic motion on these backgrounds, we examine the
2D effective potentials for photon trajectories,
to obtain a deeper understanding of this phenomenon. We
find that the emergence of stable light rings on the
background spacetimes, allows the formation of "pockets"
in one of the effective potentials, for open sets of
impact parameters, leading to an effective trapping of
some trajectories, dubbed quasi-bound orbits. We conclude
that pocket formation induces chaotic scattering, although
not all chaotic orbits are associated to pockets. These
and other features are illustrated in a gallery of examples,
obtained with a new ray-tracing code, PYHOLE, which
includes tools for a simple, simultaneous visualization
of the effective potential together with the spacetime
trajectory, for any given point in a lensing image. An
analysis of photon orbits allows us to further establish
a positive correlation between photon orbits in chaotic
regions and those with more than one turning point in the
radial direction; we recall that the latter is not possible
around Kerr black holes. Moreover, we observe that the
existence of several light rings around a horizon (several
fundamental orbits, including a stable one), is a central
ingredient for the existence of multiple shadows of a
single hairy black hole. We also exhibit the lensing and
shadows by Kerr black holes with scalar hair, observed
away from the equatorial plane, obtained with PYHOLE.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D2.3 (Shadows of single black holes)
Extraction of gravitational-wave energy in higher dimensional
numerical relativity using the Weyl tensor
Gravitational waves are one of the most important diagnostic
tools in the analysis of strong-gravity dynamics and have
been turned into an observational channel with LIGO's
detection of GW150914. Aside from their importance in
astrophysics, black holes and compact matter distributions
have also assumed a central role in many other branches
of physics. These applications often involve spacetimes
with D > 4 dimensions where the calculation of
gravitational waves is more involved than in the four
dimensional case, but has now become possible thanks to
substantial progress in the theoretical study of general
relativity in D > 4. Here, we develop a numerical
implementation of the formalism by Godazgar and Reall [1]
-- based on projections of the Weyl tensor analogous to
the Newman–Penrose scalars -- that allows for the calculation
of gravitational waves in higher dimensional spacetimes
with rotational symmetry. We apply and test this method
in black-hole head-on collisions from rest in D =
6 spacetime dimensions and find that a fraction (8.19
± 0.05) × 10^{−4} of the Arnowitt–Deser–Misner
mass is radiated away from the system, in excellent
agreement with literature results based on the Kodama–Ishibashi
perturbation technique. The method presented here complements
the perturbative approach by automatically including
contributions from all multipoles rather than computing
the energy content of individual multipoles.
Deliverable D4.1 (Wave extraction in axisymmetry)
Deliverable D4.3 (Wave extraction, initial data)
Perturbed black holes in Einstein-dilaton-Gauss-Bonnet gravity:
stability, ringdown, and gravitational-wave emission
Gravitational waves emitted by distorted black holes---such
as those arising from the coalescence of two neutron stars
or black holes---carry not only information about the
corresponding spacetime but also about the underlying
theory of gravity. Although general relativity remains
the simplest, most elegant and viable theory of gravitation,
there are generic and robust arguments indicating that
it is not the ultimate description of the gravitational
universe. Here we focus on a particularly appealing
extension of general relativity, which corrects Einstein's
theory through the addition of terms which are second
order in curvature: the topological Gauss-Bonnet invariant
coupled to a dilaton. We study gravitational-wave emission
from black holes in this theory, and (i) find strong
evidence that black holes are linearly (mode) stable
against both axial and polar perturbations; (ii) discuss
how the quasinormal modes of black holes can be excited
during collisions involving black holes, and finally (iii)
show that future ringdown detections with large signal-to-noise
ratio would improve current constraints on the coupling
parameter of the theory.
Deliverable D3.3 (Smoking Guns)
Iron Kα line of boson stars
The present paper is a sequel to our previous work [Y.
Ni et al., JCAP 1607, 049 (2016)] in which we studied the
iron Kα line expected in the reflection spectrum
of Kerr black holes with scalar hair. These metrics are
solutions of Einstein's gravity minimally coupled to a
massive, complex scalar field. They form a continuous
bridge between a subset of Kerr black holes and a family
of rotating boson stars depending on one extra parameter,
the dimensionless scalar hair parameter q, ranging
from 0 (Kerr black holes) to 1 (boson stars). Here we
study the limiting case q = 1, corresponding to
rotating boson stars. For comparison, spherical boson
stars are also considered. We simulate observations with
XIS/Suzaku. Using the fact that current observations are
well fit by the Kerr solution and thus requiring that
acceptable alternative compact objects must be compatible
with a Kerr fit, we find that some boson star solutions
are relatively easy to rule out as potential candidates
to explain astrophysical black holes, while other solutions,
which are neither too dilute nor too compact are more
elusive and we argue that they cannot be distinguished
from Kerr black holes by the analysis of the iron line
with current X-ray facilities.
Deliverable D2.1 (Black holes with scalar fields)
Echoes of ECOs: gravitational-wave signatures of exotic
compact objects and of quantum corrections at the horizon
Gravitational waves from binary coalescences provide one
of the cleanest signatures of the nature of compact
objects. It has been recently argued that the post-merger
ringdown waveform of exotic ultracompact objects is
initially identical to that of a black-hole, and that
putative corrections at the horizon scale will appear as
secondary pulses after the main burst of radiation. Here
we extend this analysis in three important directions:
(i) we show that this result applies to a large class of
exotic compact objects with a photon sphere for generic
orbits in the test-particle limit; (ii) we investigate
the late-time ringdown in more detail, showing that it
is universally characterized by a modulated and distorted
train of "echoes" of the modes of vibration associated
with the photon sphere; (iii) we study for the first time
equal-mass, head-on collisions of two ultracompact boson
stars and compare their gravitational-wave signal to that
produced by a pair of black-holes. If the initial objects
are compact enough as to mimic a binary black-hole collision
up to the merger, the final object exceeds the maximum
mass for boson stars and collapses to a black-hole. This
suggests that -- in some configurations -- the coalescence
of compact boson stars might be almost indistinguishable
from that of black-holes. On the other hand, generic
configurations display peculiar signatures that can be
searched for in gravitational-wave data as smoking guns
of exotic compact objects.
Deliverable D1.2 (Structure of stars with dark cores)
Deliverable D2.1 (Black holes with scalar fields)
Kerr–Newman black holes with scalar hair
We construct electrically charged Kerr black holes (BHs)
with scalar hair. Firstly, we take an uncharged scalar
field, interacting with the electromagnetic field only
indirectly, via the background metric. The corresponding
family of solutions, dubbed Kerr–Newman BHs with ungauged
scalar hair, reduces to (a sub-family of) Kerr–Newman BHs
in the limit of vanishing scalar hair and to uncharged
rotating boson stars in the limit of vanishing horizon.
It adds one extra parameter to the uncharged solutions:
the total electric charge. This leading electromagnetic
multipole moment is unaffected by the scalar hair and can
be computed by using Gauss's law on any closed 2-surface
surrounding (a spatial section of) the event horizon. By
contrast, the first sub-leading electromagnetic multipole
– the magnetic dipole moment –, gets suppressed by the
scalar hair, such that the gyromagnetic ratio is always
smaller than the Kerr–Newman value ( g=2 ). Secondly, we
consider a gauged scalar field and obtain a family of
Kerr–Newman BHs with gauged scalar hair. The electrically
charged scalar field now stores a part of the total
electric charge, which can only be computed by applying
Gauss' law at spatial infinity and introduces a new
solitonic limit – electrically charged rotating boson
stars. In both cases, we analyze some physical properties
of the solutions.
Deliverable D2.1 (Black holes with scalar fields)
The Effect of Cosmological Evolution on Solar System
Constraints and on the Scalarization of Neutron Stars
in Massless Scalar-Tensor Theories
Certain scalar-tensor theories of gravity that generalize
Jordan-Fierz-Brans-Dicke theory are known to predict
nontrivial phenomenology for neutron stars. In these
theories, first proposed by Damour and Esposito-Farèse,
the scalar field has a standard kinetic term and couples
conformally to the matter fields. The weak equivalence
principle is therefore satisfied, but scalar effects may
arise in strong-field regimes, e.g., allowing for violations
of the strong equivalence principle in neutron stars
("spontaneous scalarization") or in sufficiently tight
binary neutron-star systems ("dynamical/induced
scalarization"). The original scalar-tensor theory proposed
by Damour and Esposito-Farèse is in tension with Solar
System constraints (for couplings that lead to scalarization),
if one accounts for cosmological evolution of the scalar
field and no mass term is included in the action. We
extend here the conformal coupling of that theory, in
order to ascertain if, in this way, Solar System tests
can be passed, while retaining a nontrivial phenomenology
for neutron stars. We find that, even with this generalized
conformal coupling, it is impossible to construct a theory
that passes both big bang nucleosynthesis and Solar System
constraints, while simultaneously allowing for scalarization
in isolated/binary neutron stars.
Deliverable D3.2 (Astrophysical Observables)
Dynamical formation of a Reissner-Nordström black hole
with scalar hair in a cavity
In a recent Letter [Sanchis-Gual et al., Phys. Rev. Lett.
116, 141101 (2016)], we presented numerical relativity
simulations, solving the full Einstein–Maxwell–Klein-Gordon
equations, of superradiantly unstable Reissner-Nordström
black holes (BHs), enclosed in a cavity. Low frequency,
spherical perturbations of a charged scalar field trigger
this instability. The system’s evolution was followed
into the nonlinear regime, until it relaxed into an
equilibrium configuration, found to be a hairy BH: a
charged horizon in equilibrium with a scalar field
condensate, whose phase is oscillating at the (final)
critical frequency. Here, we investigate the impact of
adding self-interactions to the scalar field. In particular,
we find sufficiently large self-interactions suppress the
exponential growth phase, known from linear theory, and
promote a nonmonotonic behavior of the scalar field energy.
Furthermore, we discuss in detail the influence of the
various parameters in this model: the initial BH charge,
the initial scalar perturbation, the scalar field charge,
the mass, and the position of the cavity’s boundary
(mirror). We also investigate the “explosive” nonlinear
regime previously reported to be akin to a bosenova. A
mode analysis shows that the “explosions” can be interpreted
as the decay into the BH of modes that exit the superradiant
regime.
Deliverable D2.1 (Black holes with scalar fields)
Testing the black hole "no-hair" hypothesis
Black holes in General Relativity are very simple objects.
This property, that goes under the name of "no-hair," has
been refined in the last few decades and admits several
versions. The simplicity of black holes makes them ideal
testbeds of fundamental physics and of General Relativity
itself. Here we discuss the no-hair property of black
holes, how it can be measured in the electromagnetic or
gravitational window, and what it can possibly tell us
about our universe.
Deliverable D1.3 (Collisions of hairy BHs)
The Effect of Pair-Instability Mass Loss on Black Hole
Mergers
Context. Mergers of two stellar-origin black holes are a
prime source of gravitational waves and are under intensive
investigation. One crucial ingredient in their modeling
has been neglected: pair-instability pulsation supernovae
with associated severe mass loss may suppress the formation
of massive black holes, decreasing black-hole-merger rates
for the highest black-hole masses.
Deliverable D3.1 (Compact binary waveform)
Deliverable D3.2 (Astrophysical Observables)
Rotational superradiance in fluid laboratories
Rotational superradiance has been predicted theoretically
decades ago, and is the chief responsible for a number
of important effects and phenomenology in black hole
physics. However, rotational superradiance has never been
observed experimentally. Here, with the aim of probing
superradiance in the lab, we investigate the behaviour
of sound and surface waves in fluids resting in a circular
basin at the center of which a rotating cylinder is placed.
We show that with a suitable choice for the material of
the cylinder, surface and sound waves are amplified. By
confining the superradiant modes near the rotating cylinder,
an instability sets in. Our findings are experimentally
testable in existing fluid laboratories and hence offer
experimental exploration and comparison of dynamical
instabilities arising from rapidly rotating boundary
layers in astrophysical as well as in fluid dynamical
systems.
Deliverable D1.1 (Non-linear superradiant instability)
Constraining stellar binary black hole formation scenarios with
eLISA eccentricity measurements
A space-based interferometer such as the evolved Laser
Interferometer Space Antenna (eLISA) could observe a few
to a few thousands of progenitors of black hole binaries
(BHBs) similar to those recently detected by Advanced
LIGO. Gravitational radiation circularizes the orbit
during inspiral, but some BHBs retain a measurable
eccentricity at the low frequencies where eLISA is the
most sensitive. The eccentricity of a BHB carries precious
information about its formation channel: BHBs formed in
the field, in globular clusters, or close to a massive
black hole (MBH) have distinct eccentricity distributions
in the eLISA band. We generate mock eLISA observations,
folding in measurement errors, and using a Bayesian model
selection, we study whether eLISA measurements can identify
the BHB formation channel. We find that a handful of
observations would suffice to tell whether BHBs were
formed in the gravitational field of an MBH. Conversely,
several tens of observations are needed to tell apart
field formation from globular cluster formation. A 5-yr
eLISA mission with the longest possible armlength is
desirable to shed light on BHB formation scenarios.
Deliverable D3.2 (Astrophysical Observables)
Violations of the Kerr and Reissner-Nordström bounds: Horizon
versus asymptotic quantities
A central feature of the most elementary rotating black
hole (BH) solution in general relativity is the Kerr bound
which, for vacuum Kerr BHs, can be expressed either in
terms of the Arnowitt-Deser-Misner (ADM) or horizon
“charges.” However, this bound is not a fundamental
property of general relativity and stationary, asymptotically
flat, and regular (on and outside an event horizon) BHs
are known to violate the Kerr bound, in terms of both
their ADM and horizon quantities. Examples include the
recently discovered Kerr BHs with scalar [C. A. R. Herdeiro
and E. Radu, Phys. Rev. Lett. 112, 221101 (2014)] or Proca
hair [C. Herdeiro, E. Radu, and H. Runarsson, arXiv:1603.02687].
Here, we point out the fact that the Kerr bound in terms
of horizon quantities is also violated by well-known
rotating and charged solutions which are known in closed
form, such as the Kerr-Newman and Kerr-Sen BHs. Moreover,
for the former we observe that the Reissner-Nordström
(RN) bound is also violated in terms of horizon quantities,
even in the static (i.e., RN) limit. By contrast, for the
latter the existence of charged matter outside the horizon
allows for a curious invariance of the charge-to-mass
ratio between the ADM and horizon quantities. Regardless
of the Kerr bound violation, we show that in all cases
the event horizon linear velocity [C. A. R. Herdeiro and
E. Radu, Int. J. Mod. Phys. D 24, 1544022 (2015)] never
exceeds the speed of light. Finally, we suggest a new
type of informative parametrization for BH spacetimes
where part of the asymptotic charge is supported outside
the horizon.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D2.2 (Black holes with gauge fields)
Astrophysical applications of the
post-Tolman-Oppenheimer-Volkoff formalism
The bulk properties of spherically symmetric stars in general
relativity can be obtained by integrating the Tolman-Oppenheimer-Volkoff (TOV)
equations. In previous work [K. Glampedakis, G. Pappas, H. O. Silva, and E.
Berti, Phys. Rev. D 92, 024056 (2015)], we developed a "post-TOV"
formalism—inspired by parametrized post-Newtonian theory—which allows us to
classify in a parametrized, phenomenological form all possible perturbative
deviations from the structure of compact stars in general relativity that may
be induced by modified gravity at second post-Newtonian order. In this paper
we extend the formalism to deal with the stellar exterior, and we compute
several potential astrophysical observables within the post-TOV formalism: the
surface redshift zs, the apparent radius Rapp, the Eddington luminosity at
infinity L^{∞}_{E} and the orbital frequencies. We show that, at leading order, all
of these quantities depend on just two post-TOV parameters μ_{1} and χ, and we
discuss the possibility to measure (or set upper bounds on) these parameters.
Deliverable D3.3 (Smoking Guns)
Post-Newtonian Evolution of Massive Black Hole Triplets in
Galactic Nuclei: I. Numerical Implementation and Tests
Massive black-hole binaries (MBHBs) are thought to be the
main source of gravitational waves (GWs) in the low-frequency
domain surveyed by ongoing and forthcoming Pulsar Timing
Array campaigns and future space-borne missions, such as
eLISA. However, many low-redshift MBHBs in realistic
astrophysical environments may not reach separations small
enough to allow significant GW emission, but rather stall
on (sub)pc-scale orbits. This "last-parsec problem" can
be eased by the appearance of a third massive black hole
(MBH) -- the "intruder" -- whose action can force, under
certain conditions, the inner MBHB on a very eccentric
orbit, hence allowing intense GW emission eventually
leading to coalescence. A detailed assessment of the
process, ultimately driven by the induced Kozai-Lidov
oscillations of the MBHB orbit, requires a general
relativistic treatment and the inclusion of external
factors, such as the Newtonian precession of the intruder
orbit in the galactic potential and its hardening by
scattering off background stars. In order to tackle this
problem, we developed a three-body Post-Newtonian (PN)
code framed in a realistic galactic potential, including
both non-dissipative 1PN and 2PN terms, and dissipative
terms such as 2.5PN effects, orbital hardening of the
outer binary, and the effect of the dynamical friction
on the early stages of the intruder dynamics. In this
first paper of a series devoted at studing the dynamics
of MBH triplets from a cosmological perspective, we
describe, test and validate our code.
Deliverable D3.2 (Astrophysical Observables)
Astrophysical imaging of Kerr black holes with scalar hair
We address the astrophysical imaging of a family of
deformed Kerr black holes (BHs). These are stationary,
asymptotically flat black hole (BH) spacetimes, that are
solutions of General Relativity minimally coupled to a
massive, complex scalar field: Kerr BHs with scalar hair
(KBHsSH). Such BHs bifurcate from the vacuum Kerr solution
and can be regarded as a horizon within a rotating boson
star. In a recent letter, it was shown that KBHsSH can
exhibit very distinct shadows from the ones of their
vacuum counterparts. The setup therein, however, considered
the light source to be a celestial sphere sufficiently
far away from the BH. Here, we analyse KBHsSH surrounded
by an emitting torus of matter, simulating a more realistic
astrophysical environment, and study the corresponding
lensing of light as seen by a very far away observer, to
appropriately model ground-based observations of Sgr A*.
We find that the differences in imaging between KBHsSH
and comparable vacuum Kerr BHs remain, albeit less dramatic
than those observed for the corresponding shadows in the
previous setup. In particular, we highlight two observables
that might allow differentiating KBHsSH and Kerr BHs. The
first is the angular size of the photon ring (in a Kerr
spacetime) or lensing ring (in a KBHSH spacetime), the
latter being significantly smaller for sufficiently
non-Kerr-like spacetimes. The second is the existence of
an edge in the intensity distribution (the photon ring
in Kerr spacetime). This edge can disappear for very
non-Kerr-like KBHsSH. It is plausible, therefore, that
sufficiently precise Very Long Baseline Interferometric
observations of BH candidates can constrain this model.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D2.3 (Shadows of single black holes)
Black Hole Kicks as New Gravitational Wave Observables
Generic black hole binaries radiate gravitational waves
anisotropically, imparting a recoil, or kick, velocity
to the merger remnant. If a component of the kick along
the line of sight is present, gravitational waves emitted
during the final orbits and merger will be gradually
Doppler shifted as the kick builds up. We develop a simple
prescription to capture this effect in existing waveform
models, showing that future gravitational wave experiments
will be able to perform direct measurements, not only of
the black hole kick velocity, but also of its accumulation
profile. In particular, the eLISA space mission will
measure supermassive black hole kick velocities as low
as ∼500 km s^{−1}, which are expected to be
a common outcome of black hole binary coalescence following
galaxy mergers. Black hole kicks thus constitute a promising
new observable in the growing field of gravitational wave
astronomy.
Deliverable D3.1 (Compact binary waveform)
Static black holes with no spatial isometries in
AdS-electrovacuum
We explicitly construct static black hole solutions to
the fully non-linear, D = 4, Einstein-Maxwell-AdS
equations that have no continuous spatial symmetries.
These black holes have a smooth, topologically spherical
horizon (section), but without isometries, and approach,
asymptotically, global AdS spacetime. They are interpreted
as bound states of a horizon with the Einstein-Maxwell-AdS
solitons recently discovered, for appropriate boundary
data. In sharp contrast with the uniqueness results for
Minkowski electrovacuum, the existence of these black
holes shows that single, equilibrium, BH solutions in
AdS-electrovacuum admit an arbitrary multipole structure.
Deliverable D2.2 (Black holes with gauge fields)
Spectroscopy of Kerr black holes with Earth- and space-based
interferometers
We estimate the potential of present and future interferometric
gravitational-wave detectors to test the Kerr nature of
black holes through "gravitational spectroscopy," i.e.
the measurement of multiple quasinormal mode frequencies
from the remnant of a black hole merger. Using population
synthesis models of the formation and evolution of
stellar-mass black hole binaries, we find that Voyager-class
interferometers will be necessary to perform these tests.
Gravitational spectroscopy in the local Universe may
become routine with the Einstein Telescope, but a 40-km
facility like Cosmic Explorer is necessary to go beyond
z ∼ 3. In contrast, eLISA-like detectors should
carry out a few - or even hundreds - of these tests every
year, depending on uncertainties in massive black hole
formation models. Many space-based spectroscopical
measurements will occur at high redshift, testing the
strong gravity dynamics of Kerr black holes in domains
where cosmological corrections to general relativity (if
they occur in nature) must be significant.
Deliverable D3.2 (Astrophysical Observables)
Inside black holes with synchronized hair
Recently, various examples of asymptotically flat, rotating
black holes (BHs) with synchronized hair have been
explicitly constructed, including Kerr BHs with scalar
or Proca hair, and Myers-Perry BHs with scalar hair and
a mass gap, showing there is a general mechanism at work.
All these solutions have been found numerically, integrating
the fully non-linear field equations of motion from the
event horizon outwards. Here, we address the spacetime
geometry of these solutions inside the event horizon.
Firstly, we provide arguments, within linear theory, that
there is no regular inner horizon for these solutions.
Then, we address this question fully non-linearly, using
as a tractable model five dimensional, equal spinning,
Myers-Perry hairy BHs. We find that, for non-extremal
solutions: (1) the inside spacetime geometry in the
vicinity of the event horizon is smooth and the equations
of motion can be integrated inwards; (2) before an inner
horizon is reached, the spacetime curvature grows
(apparently) without bound. In all cases, our results
suggest the absence of a smooth Cauchy horizon, beyond
which the metric can be extended, for hairy BHs with
synchronized hair.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D2.2 (Black holes with gauge fields)
Shadows of Kerr black holes with and without scalar hair
For an observer, the Black Hole (BH) shadow is the BH's
apparent image in the sky due to the gravitational lensing
of nearby radiation, emitted by an external source. A
recent class of solutions dubbed Kerr BHs with scalar
hair possess smaller shadows than the corresponding Kerr
BHs and, under some conditions, novel exotic shadow shapes
can arise. Thus, these hairy BHs could potentially provide
new shadow templates for future experiments such as the
Event Horizon Telescope. In order to obtain the shadows,
the backward ray-tracing algorithm is briefly introduced,
followed by numerical examples of shadows of Kerr BHs
with scalar hair contrasting with the Kerr analogues.
Additionally, an analytical solution for the Kerr shadow
is derived in closed form for a ZAMO observer at an
arbitrary position.
Deliverable D2.1 (Black holes with scalar fields)
Deliverable D2.3 (Shadows of single black holes)
The final spin from binary black holes in quasi-circular
orbits
We revisit the problem of predicting the spin magnitude
and direction of the black hole (BH) resulting from the
merger of two BHs with arbitrary masses and spins inspiraling
in quasi-circular orbits. We do this by analyzing a catalog
of 619 recent numerical-relativity simulations collected
from the literature and spanning a large variety of initial
conditions. By combining information from the post-Newtonian
approximation, the extreme mass-ratio limit, and perturbative
calculations, we improve our previously proposed
phenomenological formulae for the final remnant spin. In
contrast with alternative suggestions in the literature,
and in analogy with our previous expressions, the new
formula is a simple algebraic function of the initial
system parameters and is not restricted to binaries with
spins aligned/anti-aligned with the orbital angular
momentum but can be employed for fully generic binaries.
The accuracy of the new expression is significantly
improved, especially for almost extremal progenitor spins
and for small mass ratios, yielding an rms error σ
≈ 0.002 for aligned/anti-aligned binaries and
σ ≈ 0.006 for generic binaries. Our new
formula is suitable for cosmological applications and can
be employed robustly in the analysis of the gravitational
waveforms from advanced interferometric detectors.
Deliverable D3.1 (Compact binary waveform)
eLISA eccentricity measurements as tracers of binary black hole
formation
Up to hundreds of black hole binaries individually
resolvable by eLISA will coalesce in the Advanced LIGO
and Virgo band within 10 yr, allowing for multiband
gravitational wave observations. Binaries formed via
dynamical interactions in dense star clusters are expected
to have eccentricities e_{0} ∼ 10^{−3}
− 10^{−1} at the frequencies f_{0} =
10^{−2} Hz where eLISA is most sensitive, while
binaries formed in the field should have negligible
eccentricity in both frequency bands. We estimate that
eLISA should always be able to detect a nonzero e0 whenever
e_{0} ≳ 10^{−2}; if e_{0}
∼ 10^{−3}, eLISA should detect nonzero
eccentricity for a fraction ∼ 90% (∼ 25%) of
binaries when the observation time is T_{obs} =
5 (2) yr, respectively. Therefore eLISA observations of
black hole binaries have the potential to distinguish
between field and cluster formation scenarios.
Deliverable D3.2 (Astrophysical Observables)
PRECESSION. Dynamics of spinning black-hole binaries with
python
We present the numerical code PRECESSION: a new open-source
python module to study the dynamics of precessing black-hole
binaries in the post-Newtonian regime. The code provides
a comprehensive toolbox to (i) study the evolution of the
black-hole spins along their precession cycles, (ii)
perform gravitational-wave driven binary inspirals using
both orbit-averaged and precession-averaged integrations,
and (iii) predict the properties of the merger remnant
through fitting formulae obtained from numerical-relativity
simulations. PRECESSION is a ready-to-use tool to add the
black-hole spin dynamics to larger-scale numerical studies
such as gravitational-wave parameter estimation codes,
population synthesis models to predict gravitational-wave
event rates, galaxy merger trees and cosmological simulations
of structure formation. PRECESSION provides fast and
reliable integration methods to propagate statistical
samples of black-hole binaries from/to large separations
where they form to/from small separations where they
become detectable, thus linking gravitational-wave
observations of spinning black-hole binaries to their
astrophysical formation history. The code is also a useful
tool to compute initial parameters for numerical-relativity
simulations targeting specific precessing systems.
PRECESSION can be installed from the Python Package Index
and it is freely distributed under version control on
Github, where further documentation is provided.
Deliverable D3.1 (Compact binary waveform)
Post-Newtonian Evolution of Massive Black Hole Triplets in
Galactic Nuclei: I. Numerical Implementation and Tests
Massive black-hole binaries (MBHBs) are thought to be the
main source of gravitational waves (GWs) in the low-frequency
domain surveyed by ongoing and forthcoming Pulsar Timing
Array campaigns and future space-borne missions, such as
eLISA. However, many low-redshift MBHBs in realistic
astrophysical environments may not reach separations small
enough to allow significant GW emission, but rather stall
on (sub)pc-scale orbits. This "last-parsec problem" can
be eased by the appearance of a third massive black hole
(MBH) -- the "intruder" -- whose action can force, under
certain conditions, the inner MBHB on a very eccentric
orbit, hence allowing intense GW emission eventually
leading to coalescence. A detailed assessment of the
process, ultimately driven by the induced Kozai-Lidov
oscillations of the MBHB orbit, requires a general
relativistic treatment and the inclusion of external
factors, such as the Newtonian precession of the intruder
orbit in the galactic potential and its hardening by
scattering off background stars. In order to tackle this
problem, we developed a three-body Post-Newtonian (PN)
code framed in a realistic galactic potential, including
both non-dissipative 1PN and 2PN terms, and dissipative
terms such as 2.5PN effects, orbital hardening of the
outer binary, and the effect of the dynamical friction
on the early stages of the intruder dynamics. In this
first paper of a series devoted at studing the dynamics
of MBH triplets from a cosmological perspective, we
describe, test and validate our code.
Deliverable D3.2 (Astrophysical Observables)
Black holes and gravitational waves in models of minicharged
dark matter
In viable models of minicharged dark matter, astrophysical
black holes might be charged under a hidden U(1)
symmetry and are formally described by the same Kerr-Newman
solution of Einstein-Maxwell theory. These objects are
unique probes of minicharged dark matter and dark photons.
We show that the recent gravitational-wave detection of
a binary black-hole coalescence by aLIGO provides various
observational bounds on the black hole's charge, regardless
of its nature. The pre-merger inspiral phase can be used
to constrain the dipolar emission of (ordinary and dark)
photons, whereas the detection of the quasinormal modes
set an upper limit on the final black hole's charge. By
using a toy model of a point charge plunging into a
Reissner-Nordstrom black hole, we also show that in
dynamical processes the (hidden) electromagnetic quasinormal
modes of the final object are excited to considerable
amplitude in the gravitational-wave spectrum only when
the black hole is nearly extremal. The coalescence produces
a burst of low-frequency dark photons which might provide
a possible electromagnetic counterpart to black-hole
mergers in these scenarios.
Deliverable D1.3 (Collisions of hairy BHs)
Deliverable D2.2 (Black holes with gauge fields)
Spinning boson stars and Kerr black holes with scalar hair: the
effect of self-interactions
Self-interacting boson stars have been shown to alleviate
the astrophysically low maximal mass of their
non-self-interacting counterparts. We report some physical
features of spinning self-interacting boson stars, namely
their compactness, the occurence of ergo-regions and the
scalar field profiles, for a sample of values of the
coupling parameter. The results agree with the general
picture that these boson stars are comparatively less
compact than the non-self-interacting ones. We also briefly
discuss the effect of scalar self-interactions on the
properties of Kerr black holes with scalar hair.
Deliverable D2.1 (Black holes with scalar fields)
Scalar field dark matter and the Higgs field
We discuss the possibility that dark matter corresponds to
an oscillating scalar field coupled to the Higgs boson. We
argue that the initial field amplitude should generically
be of the order of the Hubble parameter during inflation,
as a result of its quasi-de Sitter fluctuations. This implies
that such a field may account for the present dark matter
abundance for masses in the range 10^{-6}-10^{-4} eV,
if the tensor-to-scalar ratio is within the range of planned CMB
experiments. We show that such mass values can naturally
be obtained through either Planck-suppressed non-renormalizable
interactions with the Higgs boson or, alternatively, through
renormalizable interactions within the Randall–Sundrum
scenario, where the dark matter scalar resides in the bulk
of the warped extra-dimension and the Higgs is confined to
the infrared brane.
Deliverable D1.4 (Bounds on particle masses using gravity)
Numerical Relativity and High Energy Physics: Recent
Developments
We review recent progress in the application of numerical
relativity techniques to astrophysics and high-energy
physics. We focus on some developments that took place
within the "Numerical Relativity and High Energy Physics"
network, a Marie Curie IRSES action that we coordinated,
namely: spin evolution in black hole binaries, high-energy
black hole collisions, compact object solutions in scalar-tensor
gravity, superradiant instabilities and hairy black hole
solutions in Einstein's gravity coupled to fundamental
fields, and the possibility to gain insight into these
phenomena using analog gravity models.
submitted to Int.Jour.Mod.Phys.D
Deliverable D1.1 (Non-linear superradiant instability)
Gravitational Waves from the Remnants of the First Stars
Gravitational waves (GWs) provide a revolutionary tool
to investigate yet unobserved astrophysical objects.
Especially the first stars, which are believed to be more
massive than present-day stars, might be indirectly
observable via the merger of their compact remnants. We
develop a self-consistent, cosmologically representative,
semi-analytical model to simulate the formation of the
first stars and track the binary stellar evolution of the
individual systems until the coalescence of the compact
remnants. We estimate the contribution of primordial stars
to the intrinsic merger rate density and to the detection
rate of the Advanced Laser Interferometer Gravitational-Wave
Observatory (aLIGO). Owing to their higher masses, the
remnants of primordial stars produce strong GW signals,
even if their contribution in number is relatively small.
We find a probability of ∼1% that the current detection
GW150914 is of primordial origin. We estimate that aLIGO
will detect roughly 1 primordial BH-BH merger per year
for the final design sensitivity, although this rate
depends sensitively on the primordial initial mass function.
Turning this around, the detection of black hole mergers
with a total binary mass of ∼300M_{⊙}
would enable us to constrain the primordial initial mass
function.
Deliverable D3.2 (Astrophysical Observables)
Neutron stars in Horndeski gravity
Horndeski’s theory of gravity is the most general
scalar-tensor theory with a single scalar whose equations
of motion contain at most second-order derivatives. A
subsector of Horndeski’s theory known as "Fab Four" gravity
allows for dynamical self-tuning of the quantum vacuum
energy, and therefore it has received particular attention
in cosmology as a possible alternative to the ΛCDM model.
Here we study compact stars in Fab Four gravity, which
includes as special cases general relativity ("George"),
Einstein-dilaton-Gauss-Bonnet gravity ("Ringo"), theories
with a nonminimal coupling with the Einstein tensor
("John"), and theories involving the double-dual of the
Riemann tensor ("Paul"). We generalize and extend previous
results in theories of the John class and were not able
to find realistic compact stars in theories involving the
Paul class.
Deliverable D3.3 (Smoking guns)
Theory-Agnostic Constraints on Black-Hole Dipole Radiation with
Multi-Band Gravitational-Wave Astrophysics
The aLIGO detection of the black-hole binary GW150914 opened
a new era for probing extreme gravity. Many gravity theories
predict the emission of dipole gravitational radiation by
binaries. This is excluded to high accuracy in binary
pulsars, but entire classes of theories predict this effect
predominantly (or only) in binaries involving black holes.
Joint observations of GW150914-like systems by aLIGO and
eLISA will improve bounds on dipole emission from black-hole
binaries by five orders of magnitude relative to current
constraints, probing extreme gravity with unprecedented
accuracy.
Deliverable D1.3 (Collisions of hairy BHs)
Deliverable D3.1 (Compact binary waveform)
Deliverable D3.3 (Smoking guns)
Kerr black holes with Proca hair
Bekenstein proved that in Einstein's gravity minimally
coupled to one (or many) real, Abelian, Proca field,
stationary black holes (BHs) cannot have Proca hair. Dropping
Bekenstein's assumption that matter inherits spacetime
symmetries, we show this model admits asymptotically flat,
stationary, axi-symmetric, regular on and outside an event
horizon BHs with Proca hair, for an even number of real (or
an arbitrary number of complex) Proca fields. To establish
it, we start by showing that a test, complex Proca field
can form bound states, with real frequency, around Kerr
BHs: stationary Proca clouds. These states exist at the
threshold of superradiance. It was conjectured in
arXiv:1403.2757, that the existence of such clouds at the
linear level implies the existence of a new family of BH
solutions at the non-linear level. We confirm this expectation
and explicitly construct examples of such Kerr black holes
with Proca hair (KBHsPH). For a single complex Proca field,
these BHs form a countable number of families with three
continuous parameters (ADM mass, ADM angular momentum and
Noether charge). They branch off from the Kerr solutions
that can support stationary Proca clouds and reduce to Proca
stars when the horizon size vanishes. We present the domain
of existence of one family of KBHsPH, as well as its phase
space in terms of ADM quantities. Some physical properties
of the solutions are discussed; in particular, and in
contrast with Kerr BHs with scalar hair, some spacetime
regions can be counter-rotating with respect to the horizon.
We further establish a no-Proca-hair theorem for static,
spherically symmetric BHs but allowing the complex Proca
field to have a harmonic time dependence, which shows BHs
with Proca hair in this model require rotation and have no
static limit. KBHsPH are also disconnected from Kerr-Newman
BHs with a real, massless vector field.
Deliverable D2.2 (Black holes with gauge fields)
Dimensional reduction in numerical relativity: Modified cartoon
formalism and regularization
We present in detail the Einstein equations in the
Baumgarte-Shapiro-Shibata-Nakamura formulation for the case
of D dimensional spacetimes with SO(D−d) isometry based on
a method originally introduced in Ref.1. Regularized
expressions are given for a numerical implementation of
this method on a vertex centered grid including the origin
of the quasi-radial coordinate that covers the extra
dimensions with rotational symmetry. Axisymmetry, corresponding
to the value d=D−2, represents a special case with fewer
constraints on the vanishing of tensor components and is
conveniently implemented in a variation of the general
method. The robustness of the scheme is demonstrated for
the case of a black-hole head-on collision in D=7 spacetime
dimensions with SO(4) symmetry.
submitted to Int.Jour.Mod.Phys.D
Deliverable D4.1 (Wave extraction in axisymmetry)
Deliverable D4.2 (Black-hole head-on collisions)
Is the gravitational-wave ringdown a probe of the event
horizon?
It is commonly believed that the ringdown signal from a
binary coalescence provides a conclusive proof for the
formation of an event horizon after the merger. This
expectation is based on the assumption that the ringdown
waveform at intermediate times is dominated by the quasinormal
modes of the final object. We point out that this assumption
should be taken with great care, and that basically any
compact object with a light ring will display a similar
ringdown stage, even when its quasinormal-mode spectrum is
completely different from that of a black hole. In other
words, universal ringdown waveforms indicate the presence
of light rings, rather than of horizons. Only precision
observations of the late-time ringdown signal, where the
differences in the quasinormal-mode spectrum eventually
show up, can be used to rule out exotic alternatives to
black holes and to test quantum effects at the horizon
scale.
6 pages, 4 figures.
PRL Editors' Suggestion
Deliverable D3.1 (Compact binary waveform)
Deliverable D3.2 (Astrophysical Observables)
Einstein-Maxwell-AdS spinning solitons
Electrostatics on global Anti-de-Sitter (AdS) spacetime is
sharply different from that on global Minkowski spacetime.
It admits a multipolar expansion with everywhere regular,
finite energy solutions, for every multipole moment except
the monopole (arXiv:1507.04370). A similar statement holds
for global AdS magnetostatics. We show that everywhere
regular, finite energy, electric plus magnetic fields exist
on AdS in three distinct classes: (I) with non-vanishing
total angular momentum J; (II) with vanishing J
but non-zero
angular momentum density, T^{t}_{φ};
(III) with vanishing J and
T^{t}_{φ}.
Considering backreaction, these configurations remain
everywhere smooth and finite energy, and we find, for
example, Einstein-Maxwell-AdS solitons that are globally -
Type I - or locally (but not globally) - Type II - spinning.
This backreaction is considered first perturbatively, using
analytical methods and then non-perturbatively, by constructing
numerical solutions of the fully non-linear Einstein-Maxwell-AdS
system. The variation of the energy and total angular
momentum with the boundary data is explicitly exhibited for
one example of a spinning soliton.
Deliverable D2.2 (Black holes with gauge fields)
Numerical simulations of stellar collapse in scalar-tensor
theories of gravity
We present numerical-relativity simulations of spherically
symmetric core collapse and compact-object formation in
scalar-tensor theories of gravity. The additional scalar
degree of freedom introduces a propagating monopole
gravitational-wave mode. Detection of monopole scalar waves
with current and future gravitational-wave experiments may
constitute smoking gun evidence for strong-field modifications
of General Relativity. We collapse both polytropic and more
realistic pre-supernova profiles using a high-resolution
shock-capturing scheme and an approximate prescription for
the nuclear equation of state. The most promising sources of
scalar radiation are protoneutron stars collapsing to black
holes. In case of a Galactic core collapse event forming a
black hole, Advanced LIGO may be able to place independent
constraints on the parameters of the theory at a level
comparable to current Solar-System and binary-pulsar measurements.
In the region of the parameter space admitting spontaneously
scalarised stars, transition to configurations with prominent
scalar hair before BH formation further enhances the emitted
signal. Although a more realistic treatment of the microphysics
is necessary to fully investigate the occurrence of spontaneous
scalarisation of neutron star remnants, we speculate that
formation of such objects could constrain the parameters of
the theory beyond the current bounds obtained with Solar-System
and binary-pulsar experiments.
Deliverable D3.2 (Astrophysical Observables)
Deliverable D3.3 (Smoking Guns)
Two worlds collide: Interacting shells in AdS spacetime
and chaos
We study the simplest two-body problem in asymptotically
anti-de Sitter spacetime: two, infinitely-thin, concentric
spherical shells of matter. We include only gravitational
interaction between the two shells, but we show that the
dynamics of this system is highly nontrivial. We observe
prompt collapse to a black hole, delayed collapse and even
perpetual oscillatory motion, depending on the initial
location of the shells (or their energy content). The system
exhibits critical behavior, and we show strong hints that
it is also chaotic.
Deliverable D2.1 (Black holes with scalar fields)
Collapsing shells, critical phenomena and black hole
formation
We study the gravitational collapse of two thin shells of
matter, in asymptotically flat spacetime or constrained to
move within a spherical box. We show that this simple
two-body system has surprisingly rich dynamics, which
includes prompt collapse to a black hole, perpetually
oscillating solutions or black hole formation at arbitrarily
large times. Collapse is induced by shell crossing and the
black hole mass depends sensitively on the number of shell
crossings. At certain critical points, the black hole mass
exhibits critical behavior, determined by the change in
parity (even or odd) of the number of crossings, with or
without mass-gap during the transition. Some of the features
we observe are reminiscent of confined scalars undergoing
"turbulent" dynamics.
Deliverable D2.1 (Black holes with scalar fields)
Science with the space-based interferometer eLISA. III: Probing
the expansion of the Universe using gravitational wave standard
sirens
We investigate the capability of various configurations of
the space interferometer eLISA to probe the late-time
background expansion of the universe using gravitational
wave standard sirens. We simulate catalogues of standard
sirens composed by massive black hole binaries whose
gravitational radiation is detectable by eLISA, and which
are likely to produce an electromagnetic counterpart
observable by future surveys. The main issue for the
identification of a counterpart resides in the capability
of obtaining an accurate enough sky localisation with eLISA.
This seriously challenges the capability of four-link (2
arm) configurations to successfully constrain the cosmological
parameters. Conversely, six-link (3 arm) configurations
have the potential to provide a test of the expansion of
the universe up to z∼8 which is complementary
to other cosmological probes based on electromagnetic
observations only. In particular, in the most favourable
scenarios, they can provide a significant constraint on
H_{0} at the level of 0.5%. Furthermore,
(Ω_{M},Ω_{Λ}) can
be constrained to a level competitive with present SNIa
results. On the other hand, the lack of massive black hole
binary standard sirens at low redshift allows to constrain
dark energy only at the level of few percent.
Deliverable D3.2 (Astrophysical Observables)
Spin evolution of a proto-neutron star
We study the evolution of the rotation rate of a proto-neutron
star, born in a core-collapse supernova, in the first
seconds of its life. During this phase, the star evolution
can be described as a sequence of stationary configurations,
which we determine by solving the neutrino transport and
the stellar structure equations in general relativity.
We include in our model the angular momentum loss due to
neutrino emission. We find that the requirement of a
rotation rate not exceeding the mass-shedding limit at
the beginning of the evolution implies a strict bound on
the rotation rate at later times. Moreover, assuming
that the proto-neutron star is born with a finite
ellipticity, we determine the emitted gravitational wave
signal and estimate its detectability by present and
future ground-based interferometric detectors.
Deliverable D3.2 (Astrophysical Observables)
Slowly rotating black holes in Einstein-æther theory
(23 pages, 10 figures)
We study slowly rotating, asymptotically flat black holes in
Einstein-aether theory and show that solutions that are free
from naked finite area singularities form a two-parameter
family. These parameters can be thought of as the mass and
angular momentum of the black hole, while there are no
independent aether charges. We also show that the aether has
non-vanishing vorticity throughout the spacetime, as a result
of which there is no hypersurface that resembles the universal
horizon found in static, spherically symmetric solutions.
Moreover, for experimentally viable choices of the coupling
constants, the frame-dragging potential of our solutions only
shows percent-level deviations from the corresponding quantities
in General Relativity and Horava gravity. Finally, we uncover
and discuss several subtleties in the correspondence between
Einstein-aether theory and Horava gravity solutions in the
c_{ω}→∞ limit.
23 pages, 10 figures.
Deliverable D1.3 (Collisions of hairy BHs)
Deliverable D2.2 (Black holes with gauge fields)
Explosion and Final State of an Unstable Reissner-Nordström
Black Hole
A Reissner-Nordström black hole (BH) is superradiantly
unstable against spherical perturbations of a charged scalar
field, enclosed in a cavity, with frequency lower than a
critical value. We use numerical relativity techniques to
follow the development of this unstable system -- dubbed
charged BH bomb -- into the non-linear regime, solving the
full Einstein--Maxwell--Klein-Gordon equations, in spherical
symmetry. We show that: i) the process stops before
all the charge is extracted from the BH; ii) the
system settles down into a hairy BH: a charged horizon in
equilibrium with a scalar field condensate, whose phase is
oscillating at the (final) critical frequency. For low
scalar field charge, q, the final state is approached
smoothly and monotonically. For large q, however,
the energy extraction overshoots and an explosive phenomenon,
akin to a bosenova, pushes some energy back into the BH.
The charge extraction, by contrast, does not reverse.
Deliverable D1.1 (Non-linear superradiant instability)
Maxwell perturbations on Kerr-Anti-de-Sitter: quasinormal modes
superradiant instabilities and vector clouds
Scalar and gravitational perturbations on Kerr-anti-de
Sitter (Kerr-AdS) black holes have been addressed in the
literature and have been shown to exhibit a rich phenomenology.
In this paper we complete the analysis of bosonic fields
on this background by studying Maxwell perturbations,
focusing on superradiant instabilities and vector clouds.
For this purpose, we solve the Teukolsky equations numerically,
imposing the boundary conditions we have proposed
in\cite{Wang:2015goa} for the radial Teukolsky equation.
As found therein, two Robin boundary conditions can be
imposed for Maxwell fields on Kerr-AdS black holes, one of
which produces a new set of quasinormal modes even for
Schwarzschild-AdS black holes. Here, we show these different
boundary conditions produce two different sets of superradiant
modes. Interestingly the "new modes" may be unstable in a
larger parameter space. We then study stationary Maxwell
clouds, that exist at the threshold of the superradiant
instability, with the two Robin boundary conditions. These
clouds, obtained at the linear level, indicate the existence
of a new family of black hole solutions at the nonlinear
level, within the Einstein-Maxwell-AdS system, branching
off from the Kerr-Newman-AdS family. As a comparison with
the Maxwell clouds, scalar clouds on Kerr-AdS black holes
are also studied, and it is shown there are Kerr-AdS black
holes that are stable against scalar, but not vector modes,
with the same "quantum numbers".
Deliverable D2.2 (Black holes with gauge fields)
Interaction between bosonic dark matter and stars
We provide a detailed analysis of how bosonic dark matter
“condensates” interact with compact stars, extending significantly
the results of a recent Letter [1]. We focus on bosonic fields
with mass mB, such as axions, axion-like candidates and hidden
photons. Self-gravitating bosonic fields generically form
“breathing” configurations, where both the spacetime geometry
and the field oscillate, and can interact and cluster at the
center of stars. We construct stellar configurations formed
by a perfect fluid and a bosonic condensate, and which may
describe the late stages of dark matter accretion onto stars,
in dark-matter-rich environments. These composite stars
oscillate at a frequency which is a multiple of
f=2.5×10^{14} (mBc^{2}/eV) Hz.
Using perturbative analysis and
numerical relativity techniques, we show that these stars are
generically stable, and we provide criteria for instability.
Our results also indicate that the growth of the dark matter
core is halted close to the Chandrasekhar limit. We thus
dispel a myth concerning dark matter accretion by stars: dark
matter accretion does not necessarily lead to the destruction
of the star, nor to collapse to a black hole. Finally, we
argue that stars with long-lived bosonic cores may also develop
in other theories with effective mass couplings, such as
(massless) scalar-tensor theories.
26 pages, 23 figures.
PRD Editors' Suggestion
Deliverable D1.2 (Structure of stars with dark cores)
Gravity-dominated unequal-mass black hole collisions
We continue our series of studies of high-energy collisions
of black holes investigating unequal-mass, boosted head-on
collisions in four dimensions. We show that the fraction of
the center-of-mass energy radiated as gravitational waves
becomes independent of mass ratio and approximately equal to
13% at large energies. We support this conclusion with
calculations using black hole perturbation theory and Smarr’s
zero-frequency limit approximation. These results lend strong
support to the conjecture that the detailed structure of the
colliding objects is irrelevant at high energies.
5 pages, 3 figures.
Deliverable D3.1 (Compact binary waveform)
Deliveravle D4.2 (Black-hole head-on collisions)
Science with the space-based interferometer eLISA:
Supermassive black hole binaries
We compare the science capabilities of different eLISA mission
designs, including four-link (two-arm) and six-link (three-arm)
configurations with different arm lengths, low-frequency noise
sensitivities and mission durations. For each of these
configurations we consider a few representative massive black
hole formation scenarios. These scenarios are chosen to explore
two physical mechanisms that greatly affect eLISA rates,
namely (i) black hole seeding, and (ii) the delays between
the merger of two galaxies and the merger of the black holes
hosted by those galaxies. We assess the eLISA parameter
estimation accuracy using a Fisher matrix analysis with
spin-precessing, inspiral-only waveforms. We quantify the
information present in the merger and ringdown by rescaling
the inspiral-only Fisher matrix estimates using the signal-to-noise
ratio from nonprecessing inspiral-merger-ringdown phenomenological
waveforms, and from a reduced set of precessing numerical
relativity/post-Newtonian hybrid waveforms. We find that all
of the eLISA configurations considered in our study should
detect some massive black hole binaries. However, configurations
with six links and better low-frequency noise will provide
much more information on the origin of black holes at high
redshifts and on their accretion history, and they may allow
the identification of electromagnetic counterparts to massive
black hole mergers.
28 pages, 13 figures, 7 tables.
Deliverable D3.2 (Astrophysical Observables)
Cosmic Censorship and parametrized spinning
black-hole geometries
The “cosmic censorship conjecture” asserts that all singularities
arising from gravitational collapse are hidden within black
holes. We investigate this conjecture in a setup of interest
for tests of general relativity: black hole solutions which
are parametrically small deviations away from the Kerr solution.
These solutions have an upper bound on rotation, beyond which
a naked singularity is visible to outside observers. We study
whether these (generic) spacetimes can be spun-up past
extremality with point particles or accretion disks. Our
results show that cosmic censorship is preserved for generic
parameterizations. We also present examples of special
geometries which can be spun-up past extremality.
9 pages
Deliverable D3.3 (Smoking Guns)
Gravitation-Wave Emission in Shift-Symmetric
Horndeski Theories
Gravity theories beyond general relativity typically predict
dipolar gravitational emission by compact-star binaries. This
emission is sourced by “sensitivity” parameters depending on
the stellar compactness. We introduce a general formalism to
calculate these parameters, and show that in shift-symmetric
Horndeski theories stellar sensitivities and dipolar radiation
vanish, provided that the binary’s dynamics is perturbative
(i.e., the post-Newtonian formalism is applicable) and
cosmological-expansion effects can be neglected. This allows
one to reproduce the binary-pulsar-observed orbital decay.
5 pages.
Deliverable D3.1 (Compact binary waveform)
Distinguishing black-hole spin-orbit resonances by their
gravitational wave signatures. II: Full parameter estimation
Gravitational waves from coalescing binary black holes encode
the evolution of their spins prior to merger. In the
post-Newtonian regime and on the precession time scale, this
evolution has one of three morphologies, with the spins either
librating around one of two fixed points ("resonances") or
circulating freely. In this paper we perform full parameter
estimation on resonant binaries with fixed masses and spin
magnitudes, changing three parameters: a conserved "projected
effective spin" ξ and resonant family ΔΦ=0,π
(which uniquely
label the source); the inclination θJN of the binary’s total
angular momentum with respect to the line of sight (which
determines the strength of precessional effects in the
waveform); and the signal amplitude. We demonstrate that
resonances can be distinguished for a wide range of binaries,
except for highly symmetric configurations where precessional
effects are suppressed. Motivated by new insight into double-spin
evolution, we introduce new variables to characterize precessing
black hole binaries which naturally reflects the time scale
separation of the system and therefore better encode the
dynamical information carried by gravitational waves.
23 pages, 14 figures, 2 tables
Deliverable D3.1 (Compact binary waveform)
Conference Proceedings
Testing the strong field gravity regime with QPO
observations
Keywords : Gravitation; black hole physics; accretion;
accretion disks; X-rays: binaries.
Deliverable D3.2 (Astrophysical Observables)
Testing the strong equivalence principle with gravitational-wave
observations of binary black holes
The recent LIGO detection of gravitational waves from black-hole
binaries offers the exciting possibility of testing gravitational
theories in the previously inaccessible strong-field, highly
relativistic regime. While the LIGO detections are so far
consistent with the predictions of General Relativity, future
gravitational-wave observations will allow us to explore this
regime to unprecedented accuracy. One of the generic predictions
of theories of gravity that extend General Relativity is the
violation of the strong equivalence principle, i.e. strongly
gravitating bodies such as neutron stars and black holes
follow trajectories that depend on their nature and composition.
This has deep consequences for gravitational-wave emission,
which takes place with additional degrees of freedom besides
the tensor polarizations of General Relativity. I will briefly
review the formalism needed to describe these extra emission
channels, and show that binary black-hole observations probe
a set of gravitational theories that are largely disjoint
from those that are testable with binary pulsars or neutron
stars.
Deliverable D3.1 (Compact binary waveform)