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Department of Pure Mathematics and Mathematical Statistics

 

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 a University Associate Professor 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

Effective field theory and classical equations of motion
HS Reall, CM 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
– Communications in mathematical physics
(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
On Quasinormal Modes of Asymptotically Anti-de Sitter Black Holes
CM Warnick
– Communications in Mathematical Physics
(2014)
333,
959
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Room

E1.14

Telephone

01223 766831