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Faculty of Mathematics

 

 

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

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
Helical phase of chiral nematic liquid crystals as the Bianchi VII0 group manifold
GW Gibbons, CM Warnick
– Physical review. E, Statistical, nonlinear, and soft matter physics
(2011)
84,
031709
Some spacetimes with higher rank Killing–Stäckel tensors
GW Gibbons, T Houri, D Kubiznak, CM Warnick
– Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
(2011)
700,
68
The geometry of sound rays in a wind
GW Gibbons, CM Warnick
– Contemporary Physics
(2011)
52,
197
Optical metrics and projective equivalence
S Casey, M Dunajski, G Gibbons, C Warnick
– Physical Review D - Particles, Fields, Gravitation and Cosmology
(2011)
83,
084047
Hidden symmetry in the presence of fluxes
D Kubiznak, CM Warnick, P Krtous
– Nuclear Physics B
(2011)
844,
185
Nonexistence of Skyrmion-Skyrmion and Skyrmion-anti-Skyrmion static equilibria
GW Gibbons, CM Warnick, WW Wong
– Journal of Mathematical Physics
(2011)
52,
012905
Symmetries of the Dirac operator with skew-symmetric torsion
T Houri, D Kubiznak, C Warnick, Y Yasui
– Classical and Quantum Gravity
(2010)
27,
185019
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Research Group

Relativity and Gravitation

Room

E1.14

Telephone

01223 766831