Peer Reviewed Papers
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.
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.
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.
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.
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.
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.
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
Precessional instability in binary black holes with
aligned spins
Binary black holes on quasicircular orbits with spins aligned
with their orbital angular momentum have been testbeds for
analytic and numerical relativity for decades, not least
because symmetry ensures that such configurations are equilibrium
solutions to the spin-precession equations. In this work, we
show that these solutions can be unstable when the spin of
the higher-mass black hole is aligned with the orbital angular
momentum and the spin of the lower-mass black hole is
anti-aligned. Spins in these configurations are unstable to
precession to large misalignment when the binary separation
r is between the values
r_{ud±}=(
√ χ1
±
√ q χ2
)^{4} (1-q)^{-2}M
, where
M is the total mass,
q≡m_{2}/m_{1} is the mass ratio,
and χ_{1} (χ_{2}) is the
dimensionless spin of the more (less) massive black hole.
This instability exists for a wide range of spin magnitudes
and mass ratios and can occur in the strong-field regime near
merger. We describe the origin and nature of the instability
using recently developed analytical techniques to characterize
fully generic spin precession. This instability provides a
channel to circumvent astrophysical spin alignment at large
binary separations, allowing significant spin precession prior
to merger affecting both gravitational-wave and electromagnetic
signatures of stellar-mass and supermassive binary black
holes.
5 pages, 4 figures.
PRL Editors' Suggestion
Multi-timescale analysis of phase transitions in precessing
black-hole binaries
The dynamics of precessing binary black holes (BBHs) in the
post-Newtonian regime has a strong timescale hierarchy: the
orbital timescale is very short compared to the spin-precession
timescale which, in turn, is much shorter than the
radiation-reaction timescale on which the orbit is shrinking
due to gravitational-wave emission. We exploit this timescale
hierarchy to develop a multiscale analysis of BBH dynamics
elaborating on the analysis of Kesden et al. [Phys. Rev. Lett.
114, 081103 (2015)]. We solve the spin-precession equations
analytically on the precession time and then implement a
quasiadiabatic approach to evolve these solutions on the
longer radiation-reaction time. This procedure leads to an
innovative “precession-averaged” post-Newtonian approach to
studying precessing BBHs. We use our new solutions to classify
BBH spin precession into three distinct morphologies, then
investigate phase transitions between these morphologies as
BBHs inspiral. These precession-averaged post-Newtonian
inspirals can be efficiently calculated from arbitrarily large
separations, thus making progress towards bridging the gap
between astrophysics and numerical relativity.
26 pages, 14 figures, 1 table.
Tensor-multi-scalar theories: relativistic stars and 3 + 1
decomposition
Gravitational theories with multiple scalar fields coupled
to the metric and each other—a natural extension of the well
studied single-scalar-tensor theories—are interesting
phenomenological frameworks to describe deviations from general
relativity in the strong-field regime. In these theories, the
N-tuple of scalar fields takes values in a coordinate patch
of an N-dimensional Riemannian target-space manifold whose
properties are poorly constrained by weak-field observations.
Here we introduce for simplicity a non-trivial model with two
scalar fields and a maximally symmetric target-space manifold.
Within this model we present a preliminary investigation of
spontaneous scalarization for relativistic, perfect fluid
stellar models in spherical symmetry. We find that the
scalarization threshold is determined by the eigenvalues of
a symmetric scalar-matter coupling matrix, and that the
properties of strongly scalarized stellar configurations
additionally depend on the target-space curvature radius. In
preparation for numerical relativity simulations, we also
write down the 3 + 1 decomposition of the field equations for
generic tensor-multi-scalar theories.
32 pages, 8 figures, 1 table. Invited contribution to the Classical and
Quantum Gravity Focus Issue "Black holes and fundamental fields".
See also CQG+
Testing General Relativity with Present and Future Astrophysical
Observations
One century after its formulation, Einstein's general relativity
(GR) has made remarkable predictions and turned out to be
compatible with all experimental tests. Most of these tests
probe the theory in the weak-field regime, and there are
theoretical and experimental reasons to believe that GR should
be modified when gravitational fields are strong and spacetime
curvature is large. The best astrophysical laboratories to
probe strong-field gravity are black holes and neutron stars,
whether isolated or in binary systems. We review the motivations
to consider extensions of GR. We present a (necessarily
incomplete) catalog of modified theories of gravity for which
strong-field predictions have been computed and contrasted
to Einstein's theory, and we summarize our current understanding
of the structure and dynamics of compact objects in these
theories. We discuss current bounds on modified gravity from
binary pulsar and cosmological observations, and we highlight
the potential of future gravitational wave measurements to
inform us on the behavior of gravity in the strong-field
regime.
188 pages, 46 figures, 6 tables.
The numerical relativity breakthrough for binary black holes
The evolution of black-hole (BH) binaries in vacuum spacetimes
constitutes the two-body problem in general relativity. The
solution of this problem in the framework of the Einstein
field equations is a substantially more complex exercise than
that of the dynamics of two point masses in Newtonian gravity,
but it also presents us with a wealth of new exciting physics.
Numerical methods are likely to be the only way to compute
the dynamics of BH systems in the fully nonlinear regime and
have been pursued since the 1960s, culminating in dramatic
breakthroughs in 2005. Here we review the methodology and the
developments that finally gave us a solution of this fundamental
problem of Einstein's theory and discuss the breakthroughs'
implications for the wide range of contemporary BH physics.
34 pages, 5 figures. Invited contribution to the Classical and
Quantum Gravity Focus Issue "Milestones of General Relativity".
Effective potentials and morphological transitions for binary
black-hole spin precession
We derive an effective potential for binary black hole (BBH)
spin precession at second post-Newtonian order. This effective
potential allows us to solve the orbit-averaged spin-precession
equations analytically for arbitrary mass ratios and spins.
These solutions are quasiperiodic functions of time: after a
fixed period, the BBH spins return to their initial relative
orientations and jointly precess about the total angular
momentum by a fixed angle. Using these solutions, we classify
BBH spin precession into three distinct morphologies between
which BBHs can transition during their inspiral. We also
derive a precession-averaged evolution equation for the total
angular momentum that can be integrated on the radiation-reaction
time and identify a new class of spin-orbit resonances that
can tilt the direction of the total angular momentum during
the inspiral. Our new results will help efforts to model and
interpret gravitational waves from generic BBH mergers and
predict the distributions of final spins and gravitational
recoils.
5 pages, 2 figures.
Testing the nonlinear stability of Kerr-Newman black holes
The nonlinear stability of Kerr-Newman black holes (KNBHs)
is investigated by performing numerical simulations within
the full Einstein-Maxwell theory. We take as initial data a
KNBH with mass M, angular momentum to mass ratio a and
charge Q. Evolutions are performed to scan this parameter
space within the intervals 0 ≤ a/M ≤ 0.994
and 0 ≤ Q/M ≤ 0.996, corresponding to an
extremality parameter a/a_{max}
(a_{max} ≡ M_{2} -
Q_{2}) ranging from 0 to 0.995. These KNBHs
are evolved, together with a small bar-mode perturbation, up
to a time of order 120M. Our results suggest that for
small Q/a, the quadrupolar oscillation modes
depend solely on a/amax, a universality also apparent in
previous perturbative studies in the regime of small rotation.
Using as a stability criterion the absence of significant
relative variations in the horizon areal radius and BH spin,
we find no evidence for any developing instability.
8 pages, 4 figures.
Exploring New Physics Frontiers Through Numerical Relativity
The demand to obtain answers to highly complex problems within
strong-field gravity has been met with significant progress
in the numerical solution of Einstein's equations - along
with some spectacular results - in various setups. We review
techniques for solving Einstein's equations in generic
spacetimes, focusing on fully nonlinear evolutions but also
on how to benchmark those results with perturbative approaches.
The results address problems in high-energy physics, holography,
mathematical physics, fundamental physics, astrophysics and
cosmology.
156 pages, 21 figures.
Higher dimensional Numerical Relativity: code comparison
The nonlinear behavior of higher dimensional black hole
spacetimes is of interest in several contexts, ranging from
an understanding of cosmic censorship to black hole production
in high-energy collisions. However, nonlinear numerical
evolutions of higher dimensional black hole spacetimes are
tremendously complex, involving different diagnostic tools
and "dimensional reduction methods." In this work we compare
two different successful codes to evolve Einstein’s equations
in higher dimensions, and show that the results of such
different procedures agree to numerical precision, when applied
to the collision from rest of two equal-mass black holes. We
calculate the total radiated energy to be
E_{rad}/M = (9.0 ± 0.5) ×
10^{-4} in five dimensions and
E_{rad}/M = (8.1 ± 0.4) ×
10^{-4} in six dimensions.
7 pages, 3 figures.
Numerical relativity: the role of black holes in gravitational wave
physics, astrophysics and high-energy physics
Black holes play an important role in many areas of physics.
Their modeling in the highly-dynamic, strong-field regime of
general relativity requires the use of computational methods.
We present a review of the main results obtained through
numerical relativity simulations of black-hole spacetimes
with a particular focus on the most recent developments in
the areas of gravitational-wave physics, astrophysics,
high-energy collisions, the gauge-gravity duality, and the
study of fundamental properties of black holes.
23 pages, 1 figure.
Distinguishing black-hole spin-orbit resonances by their
gravitational-wave signatures
If binary black holes form following the successive core
collapses of sufficiently massive binary stars, precessional
dynamics may align their spins, S_{1} and
S_{2}, and the orbital angular momentum L
into a plane in which they jointly precess about the total
angular momentum J. These spin orientations are known
as spin-orbit resonances since S_{1},
S_{2}, and L all precess at the same
frequency to maintain their planar configuration. Two families
of such spin-orbit resonances exist, differentiated by whether
the components of the two spins in the orbital plane are
either aligned or antialigned. The fraction of binary black
holes in each family is determined by the stellar evolution
of their progenitors, so if gravitational-wave detectors could
measure this fraction they could provide important insights
into astrophysical formation scenarios for binary black holes.
In this paper, we show that even under the conservative
assumption that binary black holes are observed along the
direction of J (where precession-induced modulations
to the gravitational waveforms are minimized), the waveforms
of many members of each resonant family can be distinguished
from all members of the other family in events with signal-to-noise
ratios ρ ≈ 10, typical of those expected for the
first detections with Advanced LIGO and Virgo. We hope that
our preliminary findings inspire a greater appreciation of
the capability of gravitational-wave detectors to constrain
stellar astrophysics and stimulate further studies of the
distinguishability of spin-orbit resonant families in more
expanded regions of binary black-hole parameter space
16 pages, 11 figures.
The NINJA-2 project: Detecting and characterizing gravitational
waveforms modelled using numerical binary black hole simulations
The Numerical INJection Analysis (NINJA) project is a collaborative
effort between members of the numerical relativity and gravitational-wave
astrophysics communities. The purpose of NINJA is to study the ability to
detect gravitational waves emitted from merging binary black holes and recover
their parameters with next-generation gravitational-wave observatories. We
report here on the results of the second NINJA project, NINJA-2, which employs
60 complete binary black hole hybrid waveforms consisting of a numerical
portion modelling the late inspiral, merger, and ringdown stitched to a
post-Newtonian portion modelling the early inspiral. In a "blind injection
challenge" similar to that conducted in recent LIGO and Virgo science runs, we
added 7 hybrid waveforms to two months of data recolored to predictions of
Advanced LIGO and Advanced Virgo sensitivity curves during their first
observing runs. The resulting data was analyzed by gravitational-wave
detection algorithms and 6 of the waveforms were recovered with false alarm
rates smaller than 1 in a thousand years. Parameter estimation algorithms were
run on each of these waveforms to explore the ability to constrain the masses,
component angular momenta and sky position of these waveforms. We also perform
a large-scale monte-carlo study to assess the ability to recover each of the
60 hybrid waveforms with early Advanced LIGO and Advanced Virgo sensitivity
curves. Our results predict that early Advanced LIGO and Advanced Virgo will
have a volume-weighted average sensitive distance of 300 Mpc (1 Gpc) for
10 M_{⊙} + 10 M_{⊙} (50 M_{⊙} + 50 M_{⊙}) binary black hole coalescences. We demonstrate that
neglecting the component angular momenta in the waveform models used in
matched-filtering will result in a reduction in sensitivity for systems with
large component angular momenta.
52 pages, 11 figures, 7 tables. Report number: LIGO-P1300199.
CQG Highlight 2014/15
Collisions of oppositely charged black holes
The first fully nonlinear numerical simulations of colliding
charged black holes in D=4 Einstein-Maxwell theory
were recently reported [Zilhão et al., Phys. Rev. D 85, 124062
(2012)]. These collisions were performed for black holes with
equal charge-to-mass ratio, for which initial data can be
found in closed analytic form. Here we generalize the study
of collisions of charged black holes to the case of unequal
charge-to-mass ratios. We focus on oppositely charged black
holes, as to maximize acceleration-dependent effects. As
|Q| / M increases from 0 to 0.99, we observe
that the gravitational radiation emitted increases by a factor
of ∼2.7; the electromagnetic radiation emission becomes
dominant for |Q| / M ≳ 0.37 and at
|Q| / M = 0.99 is larger, by a factor of ∼5.8,
than its gravitational counterpart. We observe that these
numerical results exhibit a precise and simple scaling with
the charge. Furthermore, we show that the results from the
numerical simulations are qualitatively captured by a simple
analytic model that computes the electromagnetic dipolar
radiation and the gravitational quadrupolar radiation of two
nonrelativistic interacting particles in Minkowski spacetime.
11 pages, 4 figures.
Error-analysis and comparison to analytical models of numerical
waveforms produced by the NRAR Collaboration
The Numerical–Relativity–Analytical–Relativity (NRAR)
collaboration is a joint effort between members of the numerical
relativity, analytical relativity and gravitational-wave data
analysis communities. The goal of the NRAR collaboration is
to produce numerical-relativity simulations of compact binaries
and use them to develop accurate analytical templates for the
LIGO/Virgo Collaboration to use in detecting gravitational-wave
signals and extracting astrophysical information from them.
We describe the results of the first stage of the NRAR project,
which focused on producing an initial set of numerical waveforms
from binary black holes with moderate mass ratios and spins,
as well as one non-spinning binary configuration which has a
mass ratio of 10. All of the numerical waveforms are analysed
in a uniform and consistent manner, with numerical errors
evaluated using an analysis code created by members of the
NRAR collaboration. We compare previously-calibrated,
non-precessing analytical waveforms, notably the effective-one-body
(EOB) and phenomenological template families, to the
newly-produced numerical waveforms. We find that when the
binary's total mass is ∼100–200 M_{⊙},
current EOB and phenomenological models of spinning,
non-precessing binary waveforms have overlaps above 99% (for
advanced LIGO) with all of the non-precessing-binary numerical
waveforms with mass ratios ≤4, when maximizing over binary
parameters. This implies that the loss of event rate due to
modelling error is below 3%. Moreover, the non-spinning EOB
waveforms previously calibrated to five non-spinning waveforms
with mass ratio smaller than 6 have overlaps above 99.7% with
the numerical waveform with a mass ratio of 10, without even
maximizing on the binary parameters.
51 pages, 10 figures.
CQG Highlight 2013/14
The Transient Gravitational-Wave Sky
Interferometric detectors will very soon give us an unprecedented
view of the gravitational-wave sky, and in particular of the
explosive and transient Universe. Now is the time to challenge
our theoretical understanding of short-duration gravitational-wave
signatures from cataclysmic events, their connection to more
traditional electromagnetic and particle astrophysics, and
the data analysis techniques that will make the observations
a reality. This paper summarizes the state of the art, future
science opportunities, and current challenges in understanding
gravitational-wave transients.
33 pages, 2 figures.
Numerical simulations of single and binary black holes in
scalar-tensor theories: circumventing the no-hair theorem
Scalar-tensor theories are a compelling alternative to general
relativity and one of the most accepted extensions of Einstein’s
theory. Black holes in these theories have no hair, but could
grow "wigs" supported by time-dependent boundary conditions
or spatial gradients. Time-dependent or spatially varying
fields lead in general to nontrivial black hole dynamics,
with potentially interesting experimental consequences. We
carry out a numerical investigation of the dynamics of single
and binary black holes in the presence of scalar fields. In
particular we study gravitational and scalar radiation from
black-hole binaries in a constant scalar-field gradient, and
we compare our numerical findings to analytical models. In
the single black hole case we find that, after a short
transient, the scalar field relaxes to static configurations,
in agreement with perturbative calculations. Furthermore we
predict analytically (and verify numerically) that accelerated
black holes in a scalar-field gradient emit scalar radiation.
For a quasicircular black-hole binary, our analytical and
numerical calculations show that the dominant component of
the scalar radiation is emitted at twice the binary’s orbital
frequency.
21 pages, 6 figures.
Resonant-plane locking and spin alignment in stellar-mass black-hole
binaries: a diagnostic of compact-binary formation
We study the influence of astrophysical formation scenarios on the
precessional dynamics of spinning black-hole binaries by the time they enter
the observational window of second- and third-generation gravitational-wave
detectors, such as Advanced LIGO/Virgo, LIGO-India, KAGRA, and the Einstein
Telescope. Under the plausible assumption that tidal interactions are
efficient at aligning the spins of few-solar mass black-hole progenitors with
the orbital angular momentum, we find that black-hole spins should be expected
to preferentially lie in a plane when they become detectable by
gravitational-wave interferometers. This “resonant plane” is identified by the
conditions Δφ = 0^{°} or Δφ = ±180^{°}, where Δφ is the angle between the components of
the black-hole spins in the plane orthogonal to the orbital angular momentum.
If the angles ΔΦ can be accurately measured for a large sample of
gravitational-wave detections, their distribution will constrain models of
compact binary formation. In particular, it will tell us whether tidal
interactions are efficient and whether a mechanism such as mass transfer,
stellar winds, or supernovae can induce a mass-ratio reversal (so that the
heavier black hole is produced by the initially lighter stellar progenitor).
Therefore, our model offers a concrete observational link between
gravitational-wave measurements and astrophysics. We also hope that it will
stimulate further studies of precessional dynamics, gravitational-wave
template placement, and parameter estimation for binaries locked in the
resonant plane.
26 pages, 11 figures, 3 tables.
Numerical relativity in higher dimensions
We present an overview of recent developments in numerical
relativity studies of higher dimensional spacetimes with a
focus on time evolutions of black hole (BH) systems. After a
brief review of the numerical techniques employed for these
studies, we summarize results grouped into the following three
areas: (i) numerical studies of fundamental properties of
BHs, (ii) applications of BH collisions to the modeling of
Trans-Planckian scattering and (iii) numerical studies of
asymptotically anti-de Sitter spacetimes in the context of
the gauge-gravity duality.
24 pages. Rapporteur article for the 13th Marcel Grossmann Meeting.
Superradiant instabilities in astrophysical systems
Light bosonic degrees of freedom have become a serious candidate
for dark matter, which seems to pervade our entire Universe.
The evolution of these fields around curved spacetimes is
poorly understood but is expected to display interesting
effects. In particular, the interaction of light bosonic
fields with supermassive black holes, key players in most
galaxies, could provide colorful examples of superradiance
and nonlinear bosenovalike collapse. In turn, the observation
of spinning black holes is expected to impose stringent bounds
on the mass of putative massive bosonic fields in our Universe.
Our purpose here is to present a comprehensive study of the
evolution of linearized massive scalar and vector fields in
the vicinities of rotating black holes. The evolution of
generic initial data has a very rich structure, depending on
the mass of the field and of the black hole. Quasinormal
ringdown or exponential decay followed by a power-law tail
at very late times is a generic feature of massless fields
at intermediate times. Massive fields generically show a
transition to power-law tails early on. For a certain boson
field mass range, the field can become trapped in a potential
barrier outside the horizon and transition to a bound state.
Because there are a number of such quasibound states, the
generic outcome is an amplitude modulated sinusoidal, or
beating, signal, whose envelope is well described by the two
lowest overtones. We believe that the appearance of such
beatings has gone unnoticed in the past, and in fact mistaken
for exponential growth. The amplitude modulation of the signal
depends strongly on the relative excitation of the overtones,
which in turn is strongly tied to the bound state geography.
A fine-tuning of the initial data allows one to see the
evolution of the nearly pure bound state mode that turns
unstable for sufficiently large black hole (BH) rotation. For
the first time we explore massive vector fields in a generic
black hole background that are difficult, if not impossible,
to separate in the Kerr background. Our results show that
spinning BHs are generically strongly unstable against massive
vector fields.
29 pages, 13 figures.
Universality, maximum radiation and absorption in high-energy
collisions of black holes with spin
We explore the impact of black hole spins on the dynamics of
high-energy black hole collisions. We report results from
numerical simulations with γ factors up to 2.49 and dimensionless
spin parameter χ = +0.85, +0.6, 0, -0.6, -0.85. We find
that the scattering threshold becomes independent of spin at
large center-of-mass energies, confirming previous conjectures
that structure does not matter in ultrarelativistic collisions.
It has further been argued that in this limit all of the
kinetic energy of the system may be radiated by fine tuning
the impact parameter to threshold. On the contrary, we find
that only about 60% of the kinetic energy is radiated for
γ = 2.49. By monitoring apparent horizons before and
after scattering events we show that the "missing energy" is
absorbed by the individual black holes in the encounter, and
moreover the individual black-hole spins change significantly.
We support this conclusion with perturbative calculations.
An extrapolation of our results to the limit γ → ∞
suggests that about half of the center-of-mass energy of the
system can be emitted in gravitational radiation, while the
rest must be converted into rest-mass and spin energy.
5 pages, 2 figures, 1 table.
Collisions of charged black holes
We perform fully non-linear numerical simulations of
charged-black-hole collisions, described by the Einstein-Maxwell
equations, and contrast the results against analytic expectations.
We focus on head-on collisions of non-spinning black holes,
starting from rest and with the same charge to mass ratio,
Q / M. The addition of charge to black holes
introduces a new interesting channel of radiation and dynamics,
most of which seem to be captured by Newtonian dynamics and
flat-space intuition. The waveforms can be qualitatively
described in terms of three stages: (i) an infall phase prior
to the formation of a common apparent horizon; (ii) a nonlinear
merger phase which corresponds to a peak in gravitational and
electromagnetic energy; (iii) the ringdown marked by an
oscillatory pattern with exponentially decaying amplitude and
characteristic frequencies that are in good agreement with
perturbative predictions. We observe that the amount of
gravitational-wave energy generated throughout the collision
decreases by about three orders of magnitude as the charge-to-mass
ratio Q / M is increased from 0 to 0.98. We
interpret this decrease as a consequence of the smaller
accelerations present for larger values of the charge. In
contrast, the ratio of energy carried by electromagnetic to
gravitational radiation increases, reaching about 22% for the
maximum Q / M ratio explored, which is in good
agreement with analytic predictions.
15 pages, 8 figures.
Dynamics of black holes in de Sitter spacetimes
Nonlinear dynamics in cosmological backgrounds has the potential
to teach us immensely about our universe, and also to serve
as prototype for nonlinear processes in generic curved
spacetimes. Here we report on dynamical evolutions of black
holes in asymptotically de Sitter spacetimes. We focus on the
head-on collision of equal mass binaries and for the first
time compare analytical and perturbative methods with full
blown nonlinear simulations. Our results include an accurate
determination of the merger/scatter transition (consequence
of an expanding background) for small mass binaries and a
test of the Cosmic Censorship conjecture, for large mass
binaries. We observe that, even starting from small separations,
black holes in large mass binaries eventually lose causal
contact, in agreement with the conjecture.
6 pages, 5 figures.
Effects of post-Newtonian Spin Alignment on the Distribution of
Black-Hole Recoils
Recent numerical relativity simulations have shown that the
final black hole produced in a binary merger can recoil with
a velocity as large as 5,000 km/s. Because of enhanced
gravitational-wave emission in the so-called 'hang-up'
configurations, this maximum recoil occurs when the black-hole
spins are partially aligned with the orbital angular momentum.
We revisit our previous statistical analysis of post-Newtonian
evolutions of black-hole binaries in the light of these new
findings. We demonstrate that despite these new configurations
with enhanced recoil velocities, spin alignment during the
post-Newtonian stage of the inspiral will still significantly
suppress (or enhance) kick magnitudes when the initial spin
of the more massive black hole is more (or less) closely
aligned with the orbital angular momentum than that of the
smaller hole. We present a preliminary study of how this
post-Newtonian spin alignment affects the ejection probabilities
of supermassive black holes from their host galaxies with
astrophysically motivated mass ratio and initial spin
distributions. We find that spin alignment suppresses (enhances)
ejection probabilities by ∼ 40% (20%) for an observationally
motivated mass-dependent galactic escape velocity, and by an
even greater amount for a constant escape velocity of 1,000
km/s. Kick suppression is thus at least a factor two more
efficient than enhancement.
12 pages, 4 figures, 1 table.
The NINJA-2 catalog of hybrid post-Newtonian/numerical-relativity
waveforms for non-precessing black-hole binaries
The numerical injection analysis (NINJA) project is a
collaborative effort between members of the numerical-relativity
and gravitational wave data-analysis communities. The purpose
of NINJA is to study the sensitivity of existing gravitational-wave
search and parameter-estimation algorithms using numerically
generated waveforms and to foster closer collaboration between
the numerical-relativity and data-analysis communities. The
first NINJA project used only a small number of injections
of short numerical-relativity waveforms, which limited its
ability to draw quantitative conclusions. The goal of the
NINJA-2 project is to overcome these limitations with long
post-Newtonian—numerical-relativity hybrid waveforms, large
numbers of injections and the use of real detector data. We
report on the submission requirements for the NINJA-2 project
and the construction of the waveform catalog. Eight
numerical-relativity groups have contributed 56 hybrid waveforms
consisting of a numerical portion modeling the late inspiral,
merger and ringdown stitched to a post-Newtonian portion
modeling the early inspiral. We summarize the techniques
used by each group in constructing their submissions. We also
report on the procedures used to validate these submissions,
including examination in the time and frequency domains and
comparisons of waveforms from different groups against each
other. These procedures have so far considered only the (ℓ,
m) = (2, 2) mode. Based on these studies, we judge
that the hybrid waveforms are suitable for NINJA-2 studies.
We note some of the plans for these investigations.
28 pages, 11 figures, 1 table.
NR/HEP: roadmap for the future
Physics in curved spacetime describes a multitude of phenomena,
ranging from astrophysics to high energy physics. The last
few years have witnessed further progress on several fronts,
including the accurate numerical evolution of the gravitational
field equations, which now allows highly nonlinear phenomena
to be tamed. Numerical relativity simulations, originally
developed to understand strong field astrophysical processes,
could prove extremely useful to understand high-energy physics
processes like trans-Planckian scattering and gauge-gravity
dualities. We present a concise and comprehensive overview
of the state-of-the-art and important open problems in the
field(s), along with guidelines for the next years. This
writeup is a summary of the "NR/HEP Workshop" held in Madeira,
Portugal from August 31st to September 3rd 2011.
68 pages, 4 figures.
Higher-dimensional puncture initial data
We calculate puncture initial data, corresponding to single
and binary black holes with linear momenta, which solve the
constraint equations of D dimensional vacuum gravity.
The data are generated by a modification of the pseudo-spectral
code presented in arXiv:gr-qc/0404056 and made available as
the TwoPunctures thorn inside the Cactus computational toolkit.
As examples, we exhibit convergence plots, the violation of
the Hamiltonian constraint as well as the initial data for
D = 4,5,6,7. These initial data are the starting point
to perform high energy collisions of black holes in D
dimensions.
11 pages, 3 figures, 1 table.
Numerical simulations of black-hole binaries and gravitational wave
emission
We review recent progress in numerical relativity simulations
of black-hole (BH) spacetimes. Following a brief summary of
the methods employed in the modeling, we summarize the key
results in three major areas of BH physics: (i) BHs as sources
of gravitational waves (GWs), (ii) astrophysical systems
involving BHs, and (iii) BHs in high-energy physics. We
conclude with a list of the most urgent tasks for numerical
relativity in these three areas.
Journal version: 12 pages, 1 figure. arXiv
version: 47 pages, 3 figures.
Extreme black hole simulations: collisions of unequal mass black
holes and the point particle limit
Numerical relativity has seen incredible progress in the last
years, and is being applied with success to a variety of
physical phenomena, from gravitational-wave research and
relativistic astrophysics to cosmology and high-energy physics.
Here we probe the limits of current numerical setups, by
studying collisions of unequal mass, non-rotating black holes
of mass-ratios up to 1:100 and making contact with a classical
calculation in General Relativity: the infall of a point-like
particle into a massive black hole. Our results agree well
with the predictions coming from linearized calculations of
the infall of point-like particles into non-rotating black
holes. In particular, in the limit that one hole is much
smaller than the other, and the infall starts from an infinite
initial separation, we recover the point-particle limit. Thus,
numerical relativity is able to bridge the gap between fully
non-linear dynamics and linearized approximations, which may
have important applications. Finally, we also comment on the
"spurious" radiation content in the initial data and the
linearized predictions.
8 pages, 2 figures, 1 table.
11-orbit inspiral of a mass ratio 4:1 black-hole binary
We analyse an eleven-orbit inspiral of a non-spinning black-hole
binary with mass ratio q = M_{1} /
M_{2} = 4. The numerically obtained gravitational
waveforms are compared with post-Newtonian (PN) predictions
including several sub-dominant multipoles up to multipolar
indices (l = 5,m = 5). We find that (i) numerical
and post-Newtonian predictions of the phase of the (2,2) mode
accumulate a phase difference of about 0.35 rad at the PN cut
off frequency 0.1 for the Taylor T1 approximant when numerical
and PN waveforms are matched over a window in the early
inspiral phase; (ii) in contrast to previous studies of
equal-mass and specific spinning binaries, we find the Taylor
T4 approximant to agree less well with numerical results,
provided the latter are extrapolated to infinite extraction
radius; (iii) extrapolation of gravitational waveforms to
infinite extraction radius is particularly important for
subdominant multipoles with l ≠ m; (iv)
3PN terms in post-Newtonian multipole expansions significantly
improve the agreement with numerical predictions for sub-dominant
multipoles.
15 pages, 8 figures, 2 tables.
Dynamics and Gravitational Wave Signature of Collapsar
Formation
We perform 3+1 general relativistic simulations of rotating
core collapse in the context of the collapsar model for long
gamma-ray bursts. We employ a realistic progenitor, rotation
based on results of stellar evolution calculations, and a
simplified equation of state. Our simulations track
self-consistently collapse, bounce, the postbounce phase,
black hole formation, and the subsequent early hyperaccretion
phase. We extract gravitational waves from the spacetime
curvature and identify a unique gravitational wave signature
associated with the early phase of collapsar formation.
4 pages, 4 figures, 1 table.
Gravitational Wave Extraction in Simulations of Rotating
Stellar Core Collapse
We perform simulations of general relativistic rotating stellar
core collapse and compute the gravitational waves (GWs) emitted
in the core bounce phase of three representative models via
multiple techniques. The simplest technique, the quadrupole
formula (QF), estimates the GW content in the spacetime from
the mass quadrupole tensor. It is strictly valid only in the
weak-field and slow-motion approximation. For the first time,
we apply GW extraction methods in core collapse that are fully
curvature-based and valid for strongly radiating and highly
relativistic sources. We employ three extraction methods
computing (i) the Newman-Penrose (NP) scalar Ψ_{4},
(ii) Regge-Wheeler-Zerilli-Moncrief (RWZM) master functions,
and (iii) Cauchy-Characteristic Extraction (CCE) allowing for
the extraction of GWs at future null infinity, where the
spacetime is asymptotically flat and the GW content is
unambiguously defined. The latter technique is the only one
not suffering from residual gauge and finite-radius effects.
All curvature-based methods suffer from strong non-linear
drifts. We employ the fixed-frequency integration technique
as a high-pass waveform filter. Using the CCE results as a
benchmark, we find that finite-radius NP extraction yields
results that agree nearly perfectly in phase, but differ in
amplitude by ∼ 1 - 7% at core bounce, depending on the
model. RWZM waveforms, while in general agreeing in phase,
contain spurious high-frequency noise of comparable amplitudes
to those of the relatively weak GWs emitted in core collapse.
We also find remarkably good agreement of the waveforms
obtained from the QF with those obtained from CCE. They agree
very well in phase but systematically underpredict peak
amplitudes by ∼ 5 - 11% which is comparable to the NP
results and is within the uncertainties associated with core
collapse physics.
26 pages, 10 figures, 5 tables.
Stability of the puncture method with a generalized BSSN
formulation
The puncture method for dealing with black holes in the
numerical simulation of vacuum spacetimes is remarkably
successful when combined with the BSSN formulation of the
Einstein equations. We examine a generalized class of
formulations modeled along the lines of the Laguna-Shoemaker
system, including BSSN as a special case. The formulation is
a two parameter generalization of the choice of variables
used in standard BSSN evolutions. Numerical stability of the
standard finite difference methods is proven for the formulation
in the linear regime around flat space, a special case of
which is the numerical stability of BSSN. Numerical evolutions
are presented and compared with a standard BSSN implementation.
We find that a significant portion of the parameter space
leads to stable evolutions and that standard BSSN is located
near the edge of the stability region. Non-standard parameter
choices typically result in smoother behaviour of the evolution
variables close to the puncture and thus hold promise for
improved accuracy in, e.g., long-term BH binary inspirals,
and for overcoming (numerical) stability problems still
encountered in some types of black-hole simulations, e.g.,
in D ≥ 6 dimensions.
16 pages, 7 figures, 3 tables.
Superkicks in ultrarelativistic encounters of spinning black
holes
We study ultrarelativistic encounters of two spinning,
equal-mass black holes through simulations in full numerical
relativity. Two initial data sequences are studied in detail:
one that leads to scattering and one that leads to a grazing
collision and merger. In all cases, the initial black hole
spins lie in the orbital plane, a configuration that leads
to the so-called "superkicks". In astrophysical, quasicircular
inspirals, such kicks can be as large as ∼ 3,000 km/s;
here, we find configurations that exceed ∼ 15,000 km/s.
We find that the maximum recoil is to a good approximation
proportional to the total amount of energy radiated in
gravitational waves, but largely independent of whether a
merger occurs or not. This shows that the mechanism predominantly
responsible for the superkick is not related to merger dynamics.
Rather, a consistent explanation is that the "bobbing" motion
of the orbit causes an asymmetric beaming of the radiation
produced by the in-plane orbital motion of the binary, and
the net asymmetry is balanced by a recoil. We use our results
to formulate some conjectures on the ultimate kick achievable
in any black hole encounter.
10 pages, 6 figures, 2 tables.
Head-on collisions of unequal mass black holes in D=5
dimensions
We study head-on collisions of unequal mass black hole binaries
in D = 5 space-time dimensions, with mass ratios between
1:1 and 1:4. Information about gravitational radiation is
extracted by using the Kodama-Ishibashi gauge-invariant
formalism and details of the apparent horizon of the final
black hole. For the first time, we present waveforms, total
integrated energy and momentum for this process. Our results
show surprisingly good agreement, within 5% or less, with
those extrapolated from linearized, point-particle calculations.
Our results also show that consistency with the area theorem
bound requires that the same process in a large number of
spacetime dimensions must display new features.
10 pages, 5 figures.
High-order perturbations of a spherical collapsing star
In Ref. [1, 2] a formalism to deal with high-order perturbations
of a general spherical background was developed. In this
article, we apply it to the particular case of a perfect fluid
background. We have expressed the perturbations of the
energy-momentum tensor at any order in terms of the perturbed
fluid's pressure, density and velocity. In general, these
expressions are not linear and have sources depending on lower
order perturbations. For the second-order case we make the
explicit decomposition of these sources in tensor spherical
harmonics. Then, a general procedure is given to evolve the
perturbative equations of motions of the perfect fluid for
any value of the harmonic label. Finally, with the problem
of a spherical collapsing star in mind, we discuss the
high-order perturbative matching conditions across a timelike
surface, in particular the surface separating the perfect
fluid interior from the exterior vacuum.
21 pages.
Numerical relativity for D dimensional space-times: head-on
collisions of black holes and gravitational wave extraction
Black objects in higher dimensional space-times have a
remarkably richer structure than their four dimensional
counterparts. They appear in a variety of configurations (e.g.
black holes, black branes, black rings, black Saturns), and
display complex stability phase diagrams. They might also
play a key role in high energy physics: for energies above
the fundamental Planck scale, gravity is the dominant interaction
which, together with the hoop-conjecture, implies that the
trans-Planckian scattering of point particles should be well
described by black hole scattering. Higher dimensional scenarios
with a fundamental Planck scale of the order of TeV predict,
therefore, black hole production at the LHC, as well as in
future colliders with yet higher energies. In this setting,
accurate predictions for the production cross-section and
energy loss (through gravitational radiation) in the formation
of black holes in parton-parton collisions is crucial for
accurate phenomenological modelling in Monte Carlo event
generators. In this paper, we use the formalism and numerical
code reported in arXiv:1001.2302 to study the head-on collision
of two black holes. For this purpose we provide a detailed
treatment of gravitational wave extraction in generic
D-dimensional space-times, which uses the Kodama-Ishibashi
formalism. For the first time, we present the results of
numerical simulations of the head-on collision in five
space-time dimensions, together with the relevant physical
quantities. We show that the total radiated energy, when two
black holes collide from rest at infinity, is approximately
(0.089 ± 0.006)% of the centre of mass energy, slightly
larger than the 0.055% obtained in the four dimensional case,
and that the ringdown signal at late time is in very good
agreement with perturbative calculations.
31 pages, 12 figures, 2 tables.
Black holes in a box: towards the numerical evolution of black holes
in AdS
The evolution of black holes in "confining boxes" is interesting
for a number of reasons, particularly because it mimics the
global structure of Anti-de Sitter geometries. These are
non-globally hyperbolic space-times and the Cauchy problem
may only be well defined if the initial data is supplemented
by boundary conditions at the time-like conformal boundary.
Here, we explore the active role that boundary conditions
play in the evolution of a bulk black hole system, by imprisoning
a black hole binary in a box with mirror-like boundary
conditions. We are able to follow the post-merger dynamics
for up to two reflections off the boundary of the gravitational
radiation produced in the merger. We estimate that about 15%
of the radiation energy is absorbed by the black hole per
interaction, whereas transfer of angular momentum from the
radiation to the black hole is only observed in the first
interaction. We discuss the possible role of superradiant
scattering for this result. Unlike the studies with outgoing
boundary conditions, both the Newman-Penrose scalars Ψ_{4}
and Ψ_{0} are non-trivial in our setup, and we show
that the numerical data verifies the expected relations between
them.
17 pages, 12 figures, 2 tables.
Relativistic Suppression of Black Hole Recoils
Numerical-relativity simulations indicate that the black hole
produced in a binary merger can recoil with a velocity up to
v_{max} ∼ 4,000 km/s with respect to the
center of mass of the initial binary. This challenges the
paradigm that most galaxies form through hierarchical mergers,
yet retain supermassive black holes at their centers despite
having escape velocities much less than v_{max}.
Interaction with a circumbinary disk can align the binary
black hole spins with their orbital angular momentum, reducing
the recoil velocity of the final black hole produced in the
subsequent merger. However, the effectiveness of this alignment
depends on highly uncertain accretion flows near the binary
black holes. In this Letter, we show that if the spin
S_{1} of the more massive binary black
hole is even partially aligned with the orbital angular
momentum L, relativistic spin precession on sub-parsec scales
can align the binary black hole spins with each other. This
alignment significantly reduces the recoil velocity even in
the absence of gas. For example, if the angle between
S_{1} and L at large
separations is 10 degrees while the second spin
S_{2} is isotropically distributed, the
spin alignment discussed in this paper reduces the median
recoil from 864 km/s to 273 km/s for maximally spinning black
holes with a mass ratio of 9/11. This reduction will greatly
increase the fraction of galaxies retaining their supermassive
black holes.
6 pages, 4 figures, 1 table.
Semianalytical estimates of scattering thresholds and gravitational
radiation in ultrarelativistic black hole encounters
Ultrarelativistic collisions of black holes are ideal gedanken
experiments to study the nonlinearities of general relativity.
In this paper we use semianalytical tools to better understand
the nature of these collisions and the emitted gravitational
radiation. We explain many features of the energy spectra
extracted from numerical relativity simulations using two
complementary semianalytical calculations. In the first
calculation we estimate the radiation by a "zero-frequency
limit" analysis of the collision of two point particles with
finite impact parameter. In the second calculation we replace
one of the black holes by a point particle plunging with
arbitrary energy and impact parameter into a Schwarzschild
black hole, and we explore the multipolar structure of the
radiation paying particular attention to the near-critical
regime. We also use a geodesic analogy to provide qualitative
estimates of the dependence of the scattering threshold on
the black hole spin and on the dimensionality of the spacetime.
28 pages, 19 figures, 6 tables.
Final spins from the merger of precessing binary black holes
The inspiral of binary black holes is governed by gravitational
radiation reaction at binary separations r < 1000
M, yet it is too computationally expensive to begin
numerical-relativity simulations with initial separations
r > 10 M. Fortunately, binary evolution
between these separations is well described by post-Newtonian
equations of motion. We examine how this post-Newtonian
evolution affects the distribution of spin orientations at
separations r ∼ 10 M where numerical-relativity
simulations typically begin. Although isotropic spin distributions
at r ∼ 1000 M remain isotropic at r
∼ 10 M, distributions that are initially partially
aligned with the orbital angular momentum can be significantly
distorted during the post-Newtonian inspiral. Spin precession
tends to align (anti-align) the binary black hole spins with
each other if the spin of the more massive black hole is
initially partially aligned (anti-aligned) with the orbital
angular momentum, thus increasing (decreasing) the average
final spin. Spin precession is stronger for comparable-mass
binaries, and could produce significant spin alignment before
merger for both supermassive and stellar-mass black hole
binaries. We also point out that precession induces an intrinsic
accuracy limitation (< 0.03 in the dimensionless spin
magnitude, < 20 degrees in the direction) in predicting
the final spin resulting from the merger of widely separated
binaries.
18 pages, 15 figures, 2 tables.
Numerical relativity for D dimensional axially symmetric
space-times: formalism and code tests
The numerical evolution of Einstein's field equations in a
generic background has the potential to answer a variety of
important questions in physics: from applications to the
gauge-gravity duality, to modelling black hole production in
TeV gravity scenarios, analysis of the stability of exact
solutions and tests of Cosmic Censorship. In order to investigate
these questions, we extend numerical relativity to more general
space-times than those investigated hitherto, by developing
a framework to study the numerical evolution of D
dimensional vacuum space-times with an SO(D-2)
isometry group for D ≥ 5, or SO(D-3)
for D ≥ 6. Performing a dimensional reduction on
a (D-4)-sphere, the D dimensional vacuum Einstein
equations are rewritten as a 3+1 dimensional system with
source terms, and presented in the Baumgarte, Shapiro, Shibata
and Nakamura (BSSN) formulation. This allows the use of
existing 3+1 dimensional numerical codes with small adaptations.
Brill-Lindquist initial data are constructed in D
dimensions and a procedure to match them to our 3+1 dimensional
evolution equations is given. We have implemented our framework
by adapting the LEAN code and perform a variety of simulations
of non-spinning black hole space-times. Specifically, we
present a modified moving puncture gauge which facilitates
long term stable simulations in D = 5. We further
demonstrate the internal consistency of the code by studying
convergence and comparing numerical versus analytic results
in the case of geodesic slicing for D = 5,6.
20 pages, 6 figures.
Comment on `Kerr Black Holes as Particle Accelerators to Arbitrarily
High Energy'
It has been suggested that rotating black holes could serve
as particle colliders with arbitrarily high center-of-mass
energy. Astrophysical limitations on the maximal spin,
back-reaction effects and sensitivity to the initial conditions
impose severe limits on the likelihood of such collisions.
1 page, 1 figure.
Cross section, final spin and zoom-whirl behavior in high-energy
black hole collisions
We study the collision of two highly boosted equal mass,
nonrotating black holes with generic impact parameter. We
find such systems to exhibit zoom-whirl behavior when fine
tuning the impact parameter. Near the threshold of immediate
merger the remnant black hole Kerr parameter can be near
maximal (a / M about 0.95) and the radiated
energy can be as large as 35% of the center-of-mass energy.
4 pages, 3 figures, 1 table.
Momentum flow in black-hole binaries. II. Numerical simulations of
equal-mass, head-on mergers with antiparallel spins
Research on extracting science from binary-black-hole (BBH)
simulations has often adopted a "scattering matrix" perspective:
given the binary's initial parameters, what are the final
hole's parameters and the emitted gravitational waveform? In
contrast, we are using BBH simulations to explore the nonlinear
dynamics of curved spacetime. Focusing on the head-on plunge,
merger, and ringdown of a BBH with transverse, antiparallel
spins, we explore numerically the momentum flow between the
holes and the surrounding spacetime. We use the Landau-Lifshitz
field-theory-in-flat-spacetime formulation of general relativity
to define and compute the density of field energy and field
momentum outside horizons and the energy and momentum contained
within horizons, and we define the effective velocity of each
apparent and event horizon as the ratio of its enclosed
momentum to its enclosed mass-energy. We find surprisingly
good agreement between the horizons' effective and coordinate
velocities. To investigate the gauge dependence of our results,
we compare pseudospectral and moving-puncture evolutions of
physically similar initial data; although spectral and puncture
simulations use different gauge conditions, we find remarkably
good agreement for our results in these two cases. We also
compare our simulations with the post-Newtonian trajectories
and near-field energy-momentum.
25 pages, 20 figures, 1 table.
Non-linear radial oscillations of neutron stars
The effects of nonlinear oscillations in compact stars are
attracting considerable current interest. In order to study
such phenomena in the framework of fully nonlinear general
relativity, highly accurate numerical studies are required.
We present a numerical scheme specifically tailored for
studies, based on formulating the time evolution in terms of
deviations from a stationary equilibrium configuration. Using
this technique, we investigate nonlinear effects associated
with radial oscillations of neutron stars for a wide range
of amplitudes. In particular, we discuss mode coupling due
to nonlinear interactions, the occurrence of resonance
phenomena, shock formation near the stellar surface as well
as the capacity of nonlinearities to stabilize perturbatively
unstable neutron star models.
16 pages, 10 figures, 9 tables.
Status of NINJA: The Numerical INJection Analysis project
The 2008 NRDA conference introduced the Numerical INJection
Analysis project (NINJA), a new collaborative effort between
the numerical relativity community and the data analysis
community. NINJA focuses on modeling and searching for
gravitational wave signatures from the coalescence of binary
system of compact objects. We review the scope of this
collaboration and the components of the first NINJA project,
where numerical relativity groups shared waveforms and data
analysis teams applied various techniques to detect them when
embedded in colored Gaussian noise.
13 pages, 1 figure.
Testing gravitational-wave searches with numerical relativity
waveforms: Results from the first Numerical INJection Analysis
(NINJA) project
The Numerical INJection Analysis (NINJA) project is a
collaborative effort between members of the numerical relativity
and gravitational-wave data analysis communities. The purpose
of NINJA is to study the sensitivity of existing gravitational-wave
search algorithms using numerically generated waveforms and
to foster closer collaboration between the numerical relativity
and data analysis communities. We describe the results of the
first NINJA analysis which focused on gravitational waveforms
from binary black hole coalescence. Ten numerical relativity
groups contributed numerical data which were used to generate
a set of gravitational-wave signals. These signals were
injected into a simulated data set, designed to mimic the
response of the Initial LIGO and Virgo gravitational-wave
detectors. Nine groups analysed this data using search and
parameter-estimation pipelines. Matched filter algorithms,
un-modelled-burst searches and Bayesian parameter-estimation
and model-selection algorithms were applied to the data. We
report the efficiency of these search methods in detecting
the numerical waveforms and measuring their parameters. We
describe preliminary comparisons between the different search
methods and suggest improvements for future NINJA analyses.
51 pages, 25 figures, 9 tables.
Black-hole binary simulations: The Mass ratio 10:1
We present the first numerical simulations of an initially
non-spinning black-hole binary with mass ratio as large as
10:1 in full general relativity. The binary completes
approximately 3 orbits prior to merger and radiates about
0.415% of the total energy and 12.48% of the initial angular
momentum in the form of gravitational waves. The single black
hole resulting from the merger acquires a kick of about 66.7
km/s relative to the original center of mass frame. The
resulting gravitational waveforms are used to validate existing
formulas for the recoil, final spin and radiated energy over
a wider range of the symmetric mass ratio parameter η =
M_{1} M_{2} / (M_{1}
+ M_{2})^{2} than previously possible.
The contributions of l > 2 multipoles are found to
visibly influence the gravitational wave signal obtained at
fixed inclination angles.
10 pages, 8 figures, 1 table.
The High-energy collision of two black holes
We study the head-on collision of two highly boosted equal
mass, nonrotating black holes. We determine the waveforms,
radiated energies, and mode excitation in the center of mass
frame for a variety of boosts. For the first time we are able
to compare analytic calculations, black hole perturbation
theory, and strong field, nonlinear numerical calculations
for this problem. Extrapolation of our results, which include
velocities of up to 0.94 c, indicate that in the
ultra-relativistic regime about (14 ± 3)% of the energy
is converted into gravitational waves. This gives rise to a
luminosity of order 10^{-2} c^{5} /
G, the largest known so far in a black hole merger.
4 pages, 3 figures, 1 table.
PRL Editors' Suggestion
Transformation of the multipolar components of gravitational
radiation under rotations and boosts
We study the transformation of multipolar decompositions of
gravitational radiation under rotations and boosts. Rotations
to the remnant black hole's frame simplify the waveforms from
the merger of generic spinning black hole binaries. Boosts
may be important to get an accurate gravitational-wave phasing,
especially for configurations leading to large recoil velocities
of the remnant. As a test of our formalism we revisit the
classic problem of point particles falling into a Schwarzschild
black hole. Then we highlight by specific examples the
importance of choosing the right frame in numerical simulations
of unequal-mass, spinning binary black-hole mergers.
20 pages, 5 figures.
Multipolar analysis of spinning binaries
We present a preliminary study of the multipolar structure
of gravitational radiation from spinning black hole binary
mergers. We consider three different spinning binary
configurations: (1) one 'hang-up' run, where the black holes
have equal masses and large spins initially aligned with the
orbital angular momentum/ (2) seven 'spin-flip' runs, where
the holes have a mass ratio q = 4, the spins are
anti-aligned with the orbital angular momentum, and the initial
Kerr parameters of the holes j_{1} =
j_{2} = j_{i} are
fine-tuned to produce a Schwarzschild remnant after merger/
(3) three 'super-kick' runs where the mass ratio q =
M_{1} / M_{2} = 1, 2, 4 and the
spins of the two holes are initially located on the orbital
plane, pointing in opposite directions. For all of these
simulations we compute the multipolar energy distribution and
the Kerr parameter of the final hole. For the hang-up run,
we show that including leading-order spin-orbit and spin-spin
terms in a multipolar decomposition of the post-Newtonian
waveforms improves the agreement with the numerical simulation.
9 pages, 3 figures, 1 table.
CQG Highlight 2008/09
Eccentric binary black-hole mergers: The Transition from inspiral to
plunge in general relativity
We study the transition from inspiral to plunge in general
relativity by computing gravitational waveforms of nonspinning,
equal-mass black-hole binaries. We consider three sequences
of simulations, starting with a quasicircular inspiral
completing 1.5, 2.3 and 9.6 orbits, respectively, prior to
coalescence of the holes. For each sequence, the binding
energy of the system is kept constant and the orbital angular
momentum is progressively reduced, producing orbits of
increasing eccentricity and eventually a head-on collision.
We analyze in detail the radiation of energy and angular
momentum in gravitational waves, the contribution of different
multipolar components and the final spin of the remnant,
comparing numerical predictions with the post-Newtonian
approximation and with extrapolations of point-particle
results. We find that the motion transitions from inspiral
to plunge when the orbital angular momentum L =
L_{crit} ≳ 0.8 M_{2}.
For L > L_{crit} the radiated energy
drops very rapidly. Orbits with L ≳
L_{crit} produce our largest dimensionless
Kerr parameter for the remnant, j = J /
M_{2} ≳ 0.724 ± 0.13 (to be compared
with the Kerr parameter j ≳ 0.69 resulting from
quasicircular inspirals). This value is in good agreement
with the value of 0.72 reported in [I. Hinder, B. Vaishnav,
F. Herrmann, D. Shoemaker, and P. Laguna, Phys. Rev. D 77,
081502 (2008).]. These conclusions are quite insensitive to
the initial separation of the holes, and they can be understood
by extrapolating point-particle results. Generalizing a model
recently proposed by Buonanno, Kidder and Lehner [A. Buonanno,
L. E. Kidder, and L. Lehner, Phys. Rev. D 77, 026004 (2008).]
to eccentric binaries, we conjecture that (1) j ≳
0.724 is close to the maximal Kerr parameter that can be
obtained by any merger of nonspinning holes, and (2) no binary
merger (even if the binary members are extremal Kerr black
holes with spins aligned to the orbital angular momentum, and
the inspiral is highly eccentric) can violate the cosmic
censorship conjecture.
22 pages, 11 figures, 4 tables.
A Template bank for gravitational waveforms from coalescing binary
black holes. I. Non-spinning binaries
Gravitational waveforms from the inspiral and ring-down stages
of the binary black hole coalescences can be modelled accurately
by approximation/perturbation techniques in general relativity.
Recent progress in numerical relativity has enabled us to
model also the non-perturbative merger phase of the binary
black-hole coalescence problem. This enables us to coherently
search for all three stages of the coalescence of non-spinning
binary black holes using a single template bank. Taking our
motivation from these results, we propose a family of template
waveforms which can model the inspiral, merger, and ring-down
stages of the coalescence of non-spinning binary black holes
that follow quasi-circular inspiral. This two-dimensional
template family is explicitly parametrized by the physical
parameters of the binary. We show that the template family
is not only effectual in detecting the signals from
black hole coalescences, but also faithful in estimating
the parameters of the binary. We compare the sensitivity of
a search (in the context of different ground-based interferometers)
using all three stages of the black hole coalescence with
other template-based searches which look for individual stages
separately. We find that the proposed search is significantly
more sensitive than other template-based searches for a
substantial mass-range, potentially bringing about remarkable
improvement in the event-rate of ground-based interferometers.
As part of this work, we also prescribe a general procedure
to construct interpolated template banks using non-spinning
black hole waveforms produced by numerical relativity.
22 pages, 14 figures, 2 tables.
High-spin binary black hole mergers
We study identical mass black hole binaries with spins
perpendicular to the binary's orbital plane. These binaries
have individual spins ranging from s / m^{2}
= −0.90 to 0.90, (s_{1} = s_{2}
in all cases) which is near the limit possible with standard
Bowen-York puncture initial data. The extreme cases correspond
to the largest initial spin simulations to date. Our results
expand the parameter space covered by Rezzolla et al.
and, when combining both data sets, we obtain estimations for
the minimum and maximum values for the intrinsic angular
momenta of the remnant of binary black hole mergers of J
/ M^{ 2} = 0.341 ± 0.004 and 0.951 ±
0.004 respectively.
8 pages, 7 figures, 4 tables.
Exploring black hole superkicks
Recent calculations of the recoil velocity in black-hole
binary mergers have found kick velocities of ≈ 2500
km/s for equal-mass binaries with anti-aligned initial spins
in the orbital plane. In general the dynamics of spinning
black holes can be extremely complicated and are difficult
to analyze and understand. In contrast, the "superkick"
configuration is an example with a high degree of symmetry
that also exhibits exciting physics. We exploit the simplicity
of this "test case" to study more closely the role of spin
in black-hole recoil and find that: the recoil is with good
accuracy proportional to the difference between the (l
= 2, m = ±2) modes of Ψ_{4}, the major
contribution to the recoil occurs within 30 M before
and after the merger, and that this is after the time at which
a standard post-Newtonian treatment breaks down. We also
discuss consequences of the (l = 2, m = ±2)
asymmetry in the gravitational wave signal for the angular
dependence of the SNR and the mismatch of the gravitational
wave signals corresponding to the north and south poles.
16 pages, 16 figures, 1 table.
Where post-Newtonian and numerical-relativity waveforms meet
We analyze numerical-relativity (NR) waveforms that cover
nine orbits (18 gravitational-wave cycles) before merger of
an equal-mass system with low eccentricity, with numerical
uncertainties of 0.25 radians in the phase and less than 2%
in the amplitude; such accuracy allows a direct comparison
with post-Newtonian (PN) waveforms. We focus on one of the
PN approximants that has been proposed for use in gravitational-wave
data analysis, the restricted 3.5PN "TaylorT1" waveforms,
and compare these with a section of the numerical waveform
from the second to the eighth orbit, which is about one and
a half orbits before merger. This corresponds to a
gravitational-wave frequency range of Mω = 0.0455 to 0.1.
Depending on the method of matching PN and NR waveforms, the
accumulated phase disagreement over this frequency range can
be within numerical uncertainty. Similar results are found
in comparisons with an alternative PN approximant, 3PN
``TaylorT3''. The amplitude disagreement, on the other hand,
is around 6%, but roughly constant for all 13 cycles that are
compared, suggesting that only 4.5 orbits need be simulated
to match PN and NR waves with the same accuracy as is possible
with nine orbits. If, however, we model the amplitude up to
2.5PN order, the amplitude disagreement is roughly within
numerical uncertainty up to about 11 cycles before merger.
15 pages, 18 figures, 2 tables.
Reducing eccentricity in black-hole binary evolutions with initial
parameters from post-Newtonian inspiral
Standard choices of quasi-circular orbit parameters for
black-hole binary evolutions result in eccentric inspiral.
We introduce a conceptually simple method, which is to integrate
the post-Newtonian equations of motion through hundreds of
orbits, and read off the values of the momenta at the separation
at which we wish to start a fully general relativistic numerical
evolution. For the particular case of non-spinning equal-mass
inspiral with an initial coordinate separation of D =
11M we show that this approach reduces the eccentricity
by at least a factor of five to e < 0.002 as compared
to using standard quasi-circular initial parameters.
6 pages, 3 figures, 2 tables.
Reducing phase error in long numerical binary black hole evolutions
with sixth order finite differencing
We describe a modification of a fourth-order accurate "moving
puncture" evolution code, where by replacing spatial
fourth-order accurate differencing operators in the bulk of
the grid by a specific choice of sixth-order accurate stencils
we gain significant improvements in accuracy. We illustrate
the performance of the modified algorithm with an equal-mass
simulation covering nine orbits.
12 pages, 6 figures, 1 table.
Phenomenological template family for black-hole coalescence
waveforms
Recent progress in numerical relativity has enabled us to
model the non-perturbative merger phase of the binary black-hole
coalescence problem. Based on these results, we propose a
phenomenological family of waveforms which can model the
inspiral, merger, and ring-down stages of black hole coalescence.
We also construct a template bank using this family of waveforms
and discuss its implementation in the search for signatures
of gravitational waves produced by black-hole coalescences
in the data of ground-based interferometers. This template
bank might enable us to extend the present inspiral searches
to higher-mass binary black-hole systems, i.e., systems with
total mass greater than about 80 solar masses, thereby
increasing the reach of the current generation of ground-based
detectors.
11 pages, 7 figures.
Inspiral, merger and ringdown of unequal mass black hole binaries: A
Multipolar analysis
We study the inspiral, merger and ringdown of unequal mass
black hole binaries by analyzing a catalogue of numerical
simulations for seven different values of the mass ratio (from
q = M_{2} / M_{1} = 1
to q = 4). We compare numerical and Post-Newtonian
results by projecting the waveforms onto spin-weighted spherical
harmonics, characterized by angular indices (l,m).
We find that the Post-Newtonian equations predict remarkably
well the relation between the wave amplitude and the orbital
frequency for each (l,m), and that the convergence
of the Post-Newtonian series to the numerical results is
non-monotonic. To leading order the total energy emitted in
the merger phase scales like η^{2} and the spin
of the final black hole scales like eta, where η = q
/ (1 + q)^{2} is the symmetric mass ratio. We
study the multipolar distribution of the radiation, finding
that odd-l multipoles are suppressed in the equal mass
limit. Higher multipoles carry a larger fraction of the total
energy as q increases. We introduce and compare three
different definitions for the ringdown starting time. Applying
linear estimation methods (the so-called Prony methods) to
the ringdown phase, we find resolution-dependent time variations
in the fitted parameters of the final black hole. By
cross-correlating information from different multipoles we
show that ringdown fits can be used to obtain precise estimates
of the mass and spin of the final black hole, which are in
remarkable agreement with energy and angular momentum balance
calculations.
51 pages, 28 figures, 16 tables.
Supermassive Recoil Velocities for Binary Black-Hole Mergers with
Antialigned Spins
Recent calculations of the recoil velocity in binary black
hole mergers have found the kick velocity to be of the order
of a few hundred km/s in the case of non-spinning binaries
and about 500km/s in the case of spinning configurations, and
have lead to predictions of a maximum kick of up to 1300km/s.
We test these predictions and demonstrate that kick velocities
of at least 2500km/s are possible for equal-mass binaries
with anti-aligned spins in the orbital plane. Kicks of that
magnitude are likely to have significant repercussions for
models of black-hole formation, the population of intergalactic
black holes and the structure of host galaxies.
4 pages, 3 figures, 1 table.
See also Phys.Rev. Focus Story
Binary black holes on a budget: Simulations using
workstations
Binary black hole simulations have traditionally been
computationally very expensive: current simulations are
performed in supercomputers involving dozens if not hundreds
of processors, thus systematic studies of the parameter space
of binary black hole encounters still seem prohibitive with
current technology. Here we show how the multi-layered
refinement level code BAM can be used on dual processor
workstations to simulate certain binary black hole systems.
BAM, based on the moving punctures method, provides grid
structures composed of boxes of increasing resolution near
the center of the grid. In the case of binaries, the highest
resolution boxes are placed around each black hole and they
track them in their orbits until the final merger when a
single set of levels surrounds the black hole remnant. This
is particularly useful when simulating spinning black holes
since the gravitational fields gradients are larger. We present
simulations of binaries with equal mass black holes with spins
parallel to the binary axis and intrinsic magnitude of S
/ m^{2} = 0.75. Our results compare favorably
to those of previous simulations of this particular system.
We show that the moving punctures method produces stable
simulations at maximum spatial resolutions up to M /
160 and for durations of up to the equivalent of 20 orbital
periods.
16 pages, 8 figures, 4 tables.
Mining information from binary black hole mergers: A Comparison of
estimation methods for complex exponentials in noise
The ringdown phase following a binary black hole merger is
usually assumed to be well described by a linear superposition
of complex exponentials (quasinormal modes). In the strong-field
conditions typical of a binary black hole merger, non-linear
effects may produce mode coupling. Artificial mode coupling
can also be induced by the black hole's rotation, if the
radiation field is expanded in terms of spin-weighted spherical
(rather than spheroidal) harmonics. Observing deviations from
linear black hole perturbation theory requires optimal fitting
techniques to extract ringdown parameters from numerical
waveforms, which are inevitably affected by errors. So far,
non-linear least-squares fitting methods have been used as
the standard workhorse to extract frequencies from ringdown
waveforms. These methods are known not to be optimal for
estimating parameters of complex exponentials. Furthermore,
different fitting methods have different performance in the
presence of noise. The main purpose of this paper is to
introduce the gravitational wave community to modern variations
of a linear parameter estimation technique first devised in
1795 by Prony: the Kumaresan-Tufts and matrix pencil methods.
Using "test" damped sinusoidal signals in Gaussian white noise
we illustrate the advantages of these methods, showing that
they have variance and bias at least comparable to standard
non-linear least-squares techniques. Then we compare the
performance of different methods on unequal-mass binary black
hole merger waveforms. The methods we discuss should be useful
both theoretically (to monitor errors and search for
non-linearities in numerical relativity simulations) and
experimentally (for parameter estimation from ringdown signals
after a gravitational wave detection).
17 pages, 7 figures, 2 tables.
Beyond the Bowen-York extrinsic curvature for spinning black
holes
It is well-known that Bowen-York initial data contain spurious
radiation. Although this "junk" radiation has been seen to
be small for non-spinning black-hole binaries in circular
orbit, its magnitude increases when the black holes are given
spin. It is possible to reduce the spurious radiation by
applying the puncture approach to multiple Kerr black holes,
as we demonstrate for examples of head-on collisions of
equal-mass black-hole binaries.
11 pages, 2 figures.
Total recoil: The Maximum kick from nonspinning black-hole binary
inspiral
When unequal-mass black holes merge, the final black hole
receives a "kick" due to the asymmetric loss of linear momentum
in the gravitational radiation emitted during the merger. The
magnitude of this kick has important astrophysical consequences.
Recent breakthroughs in numerical relativity allow us to
perform the largest parameter study undertaken to date in
numerical simulations of binary black hole inspirals. We study
non-spinning black-hole binaries with mass ratios from q
= M_{1} / M_{2} = 1 to q
= 0.25 (η = q / (1 + q)^{2} from
0.25 to 0.16). We accurately calculate the velocity of the
kick to within 6%, and the final spin of the black holes to
within 2%. A maximum kick of 175.2 ± 11 km s^{−1}
is achieved for η = 0.195 ± 0.005.
4 pages, 4 figures.
Calibration of Moving Puncture Simulations
16 pages, 16 figures, 1 table.
Binary black-hole evolutions of excision and puncture data
20 pages, 13 figures, 4 tables.
Hydro-without-hydro framework for simulations of black hole-neutron
star binaries
20 pages, 3 figures, 3 tables.
Black hole head-on collisions and gravitational waves with fixed
mesh-refinement and dynamic singularity excision
16 pages, 10 figures, 3 tables.
Deflection of light and particles by moving gravitational lenses
13 pages, 4 figures.
Impact of densitized lapse slicings on evolutions of a wobbling black
hole
10 pages, 10 figures.
Moving black holes via singularity excision
15 pages, 11 figures.
Dynamic cosmic strings 2: Numerical evolution of excited cosmic
strings
15 pages, 11 figures.
Dynamic cosmic strings. 1
14 pages, 9 figures, 4 tables.
Quasi-molecular satellites of Lyman β in ORFEUS observations
of DA white dwarfs
5 pages, 2 figures, 1 table.
Conference Proceedings
Dynamics of Charged Black Holes,
Stockholm, Sweden, 1-7 Jul 2012
In Proceedings of the MG13 Meeting, p.983-985,
Eds: K Rosquist, R T Jantzen, R Ruffini
Gravitational Recoil and Astrophysical Impact,
Sant Cugat, Catalonia, Spain, 22-25 Apr 2014
In Astrophys.Space Sci.Proc. 40 (2015) 185-202,
Ed: C F Sopuerta
Head-On Collisions of Charged Black Holes from Rest,
Guimarães, Portugal, 3-7 Sep 2012
In Springer Proc.Math.Stat. 60 (2014) 451-455
Black Hole Collisions in Asymptotically de Sitter Spacetimes,
Prague, Czech Republic, 25-29 Jun 2012
In Springer Proc.Phys. 157 (2014) 247-254
Black Holes on Supercomputers: Numerical Relativity Applications to
Astrophysics and High-energy Physics,
Zakopane, Poland, 28 Jun - 7 Jul 2013
In Acta Phys.Polon.B 44 (2013) 2463-2536
Numerical Relativity in D dimensional space-times:
Collisions of unequal mass black holes,
Granada, Spain, 6-10 Sep 2010
In J.Phys.Conf.Ser. 314 (2011) 012104
Simulations of black holes in compactified spacetimes,
Granada, Spain, 6-10 Sep 2010
In J.Phys.Conf.Ser. 314 (2011) 012103
Numerical relativity in higher dimensions,
Bilbao, Spain, 7-11 Sep 2009
In J.Phys.Conf.Ser. 229 (2010) 012074
Black holes in a box,
Bilbao, Spain, 7-11 Sep 2009
In J.Phys.Conf.Ser. 229 (2010) 012072
Ultra-relativistic grazing collisions of black holes,
Paris, France, 12-18 Jul 2009
In Proceedings of the MG12 Meeting, p.820-822,
Eds: T Damour, R T Jantzen, R Ruffini
Using openGR for Numerical Relativity,
Paris, France, 12-18 Jul 2009
In Proceedings of the MG12 Meeting, p.826-828,
Eds: T Damour, R T Jantzen, R Ruffini
Using openGR for Numerical Relativity,
Paris, France, 12-18 Jul 2009
In Proceedings of the MG12 Meeting, p.829-831,
Eds: T Damour, R T Jantzen, R Ruffini
Colliding black holes and gravitational waves ,
Mytilene, Island of Lesvos, Greece, 17-22 Sep 2007,
In Lect.Notes Phys. 769 (2009) 125-175
Head-On collisions of different initial data,
Berlin, Germany, 23-29 Jul 2006
In Proceedings of the MG11 Meeting, p.1612-1614,
Eds: H Kleinert, R T Jantzen, R Ruffini
Where do moving punctures go?,
Palma de Mallorca, Spain, 4-8 Sep 2006
In J.Phys.Conf.Ser. 66 (2007) 012047
Non-linear Neutron Star Oscillations viewed as Deviations form an
Equilibrium State,
Kalithea, Chalkidiki, Greece, 30 May - 2 Jun 2002
In Proceedings of the 10th Hellenic Relativity Conference, p.205-209,
Eds: K D Kokkotas, N Stergioulas
Non-linear neutron star oscillations viewed as deviations form an
equilibrium State,
Kiten, Bulgaria, 10-16 Jun 2002
In Gravity, Astrophysics, and Strings '02, p.211-221,
Eds: P P Fiziev, M D Todorov
Quasi-molecular satellites of Lyman β observed with ORFEUS,
Berlin, Germany, 23-29 Jul 2006
In ASP Conference Series 169 (1999) 461,
Eds: J-E Solheim, E G Meistas
Theses
Numerical simulations of astrophysical black-hole binaries,
77 pages, 5 figures.
Non-linear numerical schemes in General Relativity,
217 pages, 65 figures, 10 tables.
Metal abundances of the Absorber-Systems toward HS1700+6416,
91 pages, 11 figures, 26 tables.