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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 Lecturer 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

Asymptotic properties of linear field equations in anti-de Sitter space
G Holzegel, J Luk, J Smulevici, C Warnick
– Communications in Mathematical Physics
(2020)
374,
1125
Quasinormal modes in extremal Reissner-Nordström spacetimes
D Gajic, C Warnick
Stability of the Toroidal AdS Schwarzschild Solution in the Einstein--Klein-Gordon System
J Dunn, C Warnick
Aspherical photon and anti-photon surfaces
GW Gibbons, CM Warnick
– Physics Letters B
(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
Boundedness and growth for the massive wave equation on asymptotically anti-de Sitter black holes
GH Holzegel, CM Warnick
– Journal of Functional Analysis
(2014)
266,
2436
The Massive Wave Equation in Asymptotically AdS Spacetimes
CM Warnick
– Communications in Mathematical Physics
(2013)
321,
85
Local metrics admitting a principal Killing–Yano tensor with torsion
T Houri, D Kubizák, CM Warnick, Y Yasui
– Classical and Quantum Gravity
(2012)
29,
165001
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