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Research Interests: PDE analysis, in particular hyperbolic PDE. Classical general relativity.

I am interested in partial differential equations (PDE), with particular application to problems arising in general relativity. PDE are equations that describe how a certain quantity varies from place to place. For example, the wave equation describes how the pressure of the air in a room changes as a function of space and time as a sound wave passes through it. The study of such equations is central to many areas of modern mathematics and physics. The class of PDE that I mostly study arise from the study of general relativity. General relativity is Einstein's theory of the gravitational field in which it is postulated that space and time together form a dynamical geometry, which evolves in time according to a PDE whose character is similar to that of the wave equation. In particular, solutions exists describing propagating gravitational waves, a fact that was recently given spectacular experimental corroboration by the results of LIGO in September 2015.

I'm Professor of Mathematical Physics, with a joint appointment between the two departments of the Faculty of Mathematics: the Department for Pure Mathematics and Mathematical Statistics (DPMMS) and the Department of Applied Mathematics and Theoretical Physics (DAMTP).

 

Publications

Quasinormal modes of Reissner–Nordström–AdS: the approach to extremality
F Ficek, C Warnick
– Classical and Quantum Gravity
(2024)
41,
085011
Effective field theory and classical equations of motion
H Reall, C Warnick
– Journal of Mathematical Physics
(2022)
63,
042901
(In)Completeness of Quasinormal Modes
C Warnick
– Acta Physica Polonica B, Proceedings Supplement
(2022)
15,
1
A model problem for quasinormal ringdown of asymptotically flat or extremal black holes
D Gajic, C Warnick
– Journal of Mathematical Physics
(2020)
61,
102501
Asymptotic Properties of Linear Field Equations in Anti-de Sitter Space.
G Holzegel, J Luk, J Smulevici, C Warnick
– Commun Math Phys
(2019)
374,
1125
Quasinormal Modes in Extremal Reissner–Nordström Spacetimes
D Gajic, C Warnick
– Communications in Mathematical Physics
(2019)
385,
1395
Stability of the Toroidal AdS Schwarzschild Solution in the Einstein--Klein-Gordon System
J Dunn, C Warnick
(2018)
Aspherical photon and anti-photon surfaces
GW Gibbons, CM Warnick
– Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
(2016)
763,
169
The Klein-Gordon equation on the toric AdS-Schwarzschild black hole
J Dunn, C Warnick
– Classical and Quantum Gravity
(2016)
33,
125010
The Einstein-Klein-Gordon-AdS system for general boundary conditions
G Holzegel, CM Warnick
– Journal of Hyperbolic Differential Equations
(2015)
12,
293
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Research Group

Relativity and Gravitation

Room

E1.14

Telephone

01223 766831