Quasinormal Modes and Gravitational Radiation in Black Hole Spacetimes

Brief general introduction......Page 13
I Quasinormal modes in four and higher dimensions......Page 21
Motivation......Page 23
Definition of quasinormal modes......Page 25
What is the importance of QNMs in fundamental physics......Page 28
QNMs and thermalization in the AdS/CFT......Page 29
QNMs and black hole area quantization......Page 30
Outline of Part I......Page 32
Introduction......Page 35
The wave equation......Page 37
QNMs for scalar and electromagnetic perturbations......Page 38
The wave equation......Page 40
Discussion......Page 42
Introduction......Page 45
Maxwell perturbations......Page 46
 Gravitational perturbations......Page 47
Analytical properties......Page 49
Equations and numerical Method......Page 51
Scalar QN frequencies......Page 53
Electromagnetic QN frequencies......Page 56
Gravitational QN frequencies......Page 59
On the isospectrality breaking between odd and even perturbations......Page 63
Why are the scalar and gravitational perturbations isospectral in the large black hole regime?......Page 64
Future directions......Page 65
The limit m  0......Page 67
APPENDIX: Pure AdS normal modes for electromagnetic and gravitational perturbations......Page 68
Introduction......Page 71
Scalar, electromagnetic and gravitational perturbations in a toroidal, cylindrical or planar black hole in an AdS background......Page 72
Scalar field perturbations......Page 73
 Gravitational perturbations......Page 74
Numerical calculation of the QN frequencies......Page 77
Conclusions......Page 80
Introduction......Page 81
Equations......Page 82
Conclusions......Page 85
Introduction......Page 87
QN frequencies of the four-dimensional Schwarzschild black hole......Page 90
Equations and conventions......Page 95
Perturbative calculation of QNMs of D-dimensional Schwarzschild BHs......Page 97
Numerical procedure and results......Page 99
Discussion of results and future directions......Page 105
Introduction......Page 107
Numerical method......Page 109
Modes having l=m=2: a more extensive discussion......Page 110
Modes having l=2, l=m......Page 113
Modes having l=3......Page 114
Scalar modes......Page 115
The asymptotic behaviour of the modes' imaginary part......Page 116
An introduction to the problem......Page 117
Numerical search and QNM multiplets......Page 119
Conclusions......Page 120
II Encounters of black holes with particles in four and higher dimensions: quasinormal modes, gravitational and scalar radiation......Page 129
Introduction......Page 131
Astronomical sources of gravitational waves......Page 132
Microscopic sources of gravitational waves......Page 134
Outline of Part II......Page 137
Introduction......Page 139
Basic Formalism......Page 140
Numerical Results......Page 142
Introduction......Page 147
The Teukolsky and Sasaki-Nakamura formalism......Page 149
The Sasaki-Nakamura equations for an highly relativistic point particle falling along the symmetry axis of the Kerr black hole......Page 151
Implementing a numerical solution......Page 152
Numerical Results and Conclusions......Page 153
 Introduction......Page 159
Formulation of the problem and basic equations......Page 161
 The initial data and boundary conditions......Page 162
 Green's function solution......Page 163
 Numerical results for the waveforms and spectra......Page 165
The Problem, the Equations and the Laplace transform, and the initial and boundary conditions for D-dimensions......Page 167
Results......Page 171
 Conclusions......Page 177
III Gravitational waves in higher dimensions......Page 179
Introduction......Page 181
Outline of Part III......Page 183
Introduction......Page 185
The inhomogeneous wave equation......Page 186
The plane wave solutions......Page 187
The D-dimensional retarded Green's function......Page 188
The even D-dimensional retarded solution in the wave zone......Page 190
Derivation of the even D-dimensional quadrupole formula......Page 191
Applications of the quadrupole formula: test particles in a background geometry......Page 192
Derivation of the radiation formula in terms of a cutoff for a head-on collision......Page 195
Applications: the cutoff frequency when one of the particles is a black hole and radiation from black hole pair creation......Page 196
Summary and discussion......Page 201
Introduction......Page 203
A brief summary of previous analytical results for a specific class of potentials......Page 205
The evolution equations and the reduction of the potential to the standard form......Page 206
Late-time tails......Page 208
Bibliography......Page 210