Numerical Algorithms for finding Black Hole solutions of Einstein's Equations
Author(s)
Kitchen, Sam Phillip Lindsey
Type
Thesis
Abstract
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.
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.
Date Issued
2011-08
Date Awarded
2011-09
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Wiseman, Toby
Sponsor
Science and Technology Facilities Council (STFC)
Creator
Kitchen, Sam Phillip Lindsey
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)