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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

Backreaction of frame dragging
CAR Herdeiro, C Rebelo, CM Warnick
– Physical Review D - Particles, Fields, Gravitation and Cosmology
(2009)
80,
084037
Universal properties of the near-horizon optical geometry
GW Gibbons, CM Warnick
– Physical Review D
(2009)
79,
064031
Stationary metrics and optical Zermelo-Randers-Finsler geometry
GW Gibbons, CAR Herdeiro, CM Warnick, MC Werner
– Physical Review D
(2009)
79,
044022
Light bending in Schwarzschild–de Sitter: projective geometry of the optical metric
GW Gibbons, CM Warnick, MC Werner
– Classical and Quantum Gravity
(2008)
25,
245009
Ricci flows connecting Taub-Bolt and Taub-NUT metrics
G Holzegel, T Schmelzer, C Warnick
– Classical and Quantum Gravity
(2007)
24,
6201
Hidden symmetry of hyperbolic monopole motion
GW Gibbons, CM Warnick
– Journal of Geometry and Physics
(2007)
57,
2286
Semi-classical stability of AdS NUT instantons
C Warnick
– Classical and Quantum Gravity
(2006)
23,
3801
A model problem for quasinormal ringdown on asymptotically flat or extremal black holes
D Gajic, C Warnick
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