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Title: Numerical algorithms for finding Black Hole solutions of Einstein's equations
Author: Kitchen, Sam Phillip Lindsey
ISNI:       0000 0004 2709 932X
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2011
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Einstein's Theory of General Relativity has proven remarkably successful at modelling a wide range of gravitational phenomena. Amongst some of the novel features in this description is the existence of black holes; regions of space-time where gravity is so strong that light cannot escape. The properties of black holes have been extensively studied within General Relativity, culminating in the result that the few known space-times are the only allowed stationary black hole solutions in four dimensions. In the past half century, research has focused on how to unify the distinct theories of gravity and quantum mechanics. A common theme amongst several strong candidates is that space-time, the backdrop for gravity, is fundamentally higher dimensional. In these theories, the structure of black hole solutions is relatively unknown and expected to be much richer; finding such solutions is, however, a very hard task. In this thesis, we introduce new numerical methods to study higher dimensional black holes. The methods, based on refinements of existing work and the novel application of standard techniques, are then used to study a number of black hole space-times. Namely the structure of black holes on a Kaluza-Klein background, and rotating Kerr black holes. We demonstrate that these algorithms can be applied in a wide class of situations and yield good quality results with comparative ease. New results are presented in both cases studied. We examine the predicted merger between non-uniform black strings and localised black holes on a Kaluza-Klein background. We find evidence for a new type of non-uniform black string with one Euclidean negative mode and lower entropy than the uniform strings. We discover a window of localised black holes with one Euclidean negative mode but positive specific heat. We also look at the local structure of the merger point and find consistency with Kol's cone prediction.
Supervisor: Wiseman, Toby Sponsor: Science and Technology Facilities Council (STFC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral