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Heusler M., Goddard P. — Black Hole Uniqueness Theorems
Heusler M., Goddard P. — Black Hole Uniqueness Theorems

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Название: Black Hole Uniqueness Theorems

Авторы: Heusler M., Goddard P.

Аннотация:

A self-contained introduction to the mathematical theory of black holes.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 263

Добавлена в каталог: 05.01.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
action      see Lagrangian
ADM mass      15
angular momentum      25
Angular momentum, horizon      110
Angular momentum, Kerr metric      53
Angular momentum, Kerr — Newman metric      80
Angular velocity, Killing horizon      91
Angular velocity, uniformity      91
Angular velocity, weak rigidity      94
Anti-derivative      3
Apparent horizon      88
Area theorem      119
Asymptotic expansion      16
Asymptotic expansion, electric potential      151
Asymptotic expansion, Kerr — Newman metric      83
Asymptotic expansion, stationary metric      11 16
Asymptotic flatness      14
Asymptotic flatness, Kerr metric      54
Asymptotic flatness, static spacetime      146
Asymptotic predictability      87
Axial Killing field      90
Axisymmetry      25
Axisymmetry, electromagnetic field      62 69
Axisymmetry, scalar mapping      207
Bach tensor      20
Bach tensor, electrovac spacetime      155
Bach tensor, vacuum spacetime      149
Bekenstein black hole solution      203
Bianchi identity      11
Bifurcate Killing horizon      89 97 106
Bifurcation surface      89
Black hole      87
Black hole at time $\Sigma$      88
Black hole, rotating, nonrotating      91
Bochner identity      188
Boyer — Lindquist coordinates      52
Boyer — Lindquist coordinates, Kerr — Newman metric      52 79
Cart an, structure equations      19
Cauchy horizon      55
Cauchy surface      87
Causal past      87
Christoffel symbols, circular spacetime      36
Christoffel symbols, static spacetime      21
Circularity      26
Circularity theorem      28
Circularity theorem, electrovac      70 124
Circularity theorem, general      124
Circularity theorem, scalar mappings      208
Circularity, Ricci-circularity      27
Circularity, zeroth law      107
Closed form      3
Co-derivative      4
Co-derivative, product      5
Co-derivative, stationary 1-form      33
Codazzi — Mainardi equations      22
Conformal flatness      20 149 154
Conformal scalar field      200
Conformal scalar field, field equations      200
Conformal scalar field, stress-energy tensor      201
Conformal transformation      147
Conjugate electromagnetic potential      80
Conjugate Ernst 1-form      46
Conjugate solution      46 51
Connection      1
Connection along a mapping      182 183 184
Connection, coordinate representation      183
Connection-forms      19
Cosmic censor conjecture      87
Covariant derivative, commutation rule      2
Curvature      2
Curvature along a mapping      184
Curvature, singularity in Kerr spacetime      54
Curvature-forms      19
Degree, of Skyrme mapping      188
Differential form      2
Differential form, closed, exact      3
Differential form, harmonic      4
Differential, of mapping between manifolds      185
Dominant energy condition, cosmic censor conjecture      87
Dominant energy condition, topology      98
Dominant energy condition, zeroth law      105
Einstein equations      2
Einstein tensor      2
Einstein tensor, static metric      21
Einstein tensor, submanifold      22
Einstein — Hilbert principle      114
Einstein — Maxwell equations, circular spacetime      73
Einstein — Maxwell equations, static      152 158
Einstein — Maxwell equations, stationary      136
Electric charge      80 130
Electromagnetic action      57
electromagnetic field      57 58 60
Electromagnetic field, algebraic relations      60
Electromagnetic field, invariance conditions      62
Electromagnetic field, Kerr — Newman spacetime      80
Electromagnetic field, Ricci-circularity      70
Electromagnetic field, stationarity and axisymmetry      69
Electromagnetic field, stationary      62
Electromagnetic potential and gravitational potential      137
Electromagnetic potential, asymptotic expansion      151
Electromagnetic potential, complex circular      73
Electromagnetic potential, Kerr — Newman solution      80
Electromagnetic potential, Reissner — Nordstrom solution      157
Electromagnetic potential, uniformity on Killing horizon      129
Energy density, harmonic      185
Energy density, Skyrme      188
entropy      120
Ergoregion      15
Ergoregion, Kerr spacetime      55
Ergoregion, staticity      127
Ernst equations, electrovac      65 74 76
Ernst equations, vacuum      44 49
Ernst equations, variational principle      13 45 50 76
Ernst potential, conjugate      46
Ernst potential, electrovac      66 73 74
Ernst potential, vacuum      12 43
Euler characteristic      98
Euler — Lagrange equations, electrovac Ernst potential      66 73
Euler — Lagrange equations, harmonic mappings      186
Euler — Lagrange equations, sigma models      172
Event horizon      87
Event horizon at time $\Sigma$      88
Event horizon, future and past      90
Event horizon, Kerr spacetime      55
Event horizon, Killing horizon      89
Exact differential form      3
Expansion, of null congruence      99 118
Exterior algebra      2
Exterior derivative      3
Exterior product      5
Extrinsic curvature      21 142 145 150
First law      see mass variation
Flux integrals      130
Gauge potential, symmetry condition      62
Gauss curvature of horizon      98
Gauss equation      22
Gauss — Bonnet theorem      98 144
Generalized entropy      120
Generating technique      202
Geodesic congruence      97
Geodesic equation      187
Global hyperbolicity      87
Gravitational collapse      87
Harmonic energy density      185
Harmonic form      4
Harmonic function      187
Harmonic mapping      185
Harmonic mapping, solitons      211
Harmonic mapping, symmetric space      172 178
Harmonic mapping, uniqueness theorem      218 222 227
Harmonic mapping, variational equation      186
Hawking radiation      104 120
Hawking temperature      214
Higgs field      210 217
Hodge dual      3
Horizon, bifurcate      89 97
Horizon, event horizon      87
Horizon, Kerr — Newman      83
Horizon, Killing horizon      88 90 92
Horizon, Papapetrou — Majumdar      163
Induced connection, along a mapping      182 183
Integrability conditions, circularity      26
Integrability conditions, Killing 2-form      28
Integrability conditions, staticity      18
Interior multiplication      3 5
Invariance conditions      8
Invariance conditions, electromagnetic field      62 63
Invariance conditions, gauge potential      62
Isometry      7
Kerr metric      52
Kerr metric in Boyer — Lindquist coordinates      53
Kerr-Newman metric      79 175
Killing 2-form      28
Killing equation      8
Killing field      7
Killing field, axial      90
Killing field, horizon      90
Killing horizon      88 89 90
Killing horizon, bifurcate      89 97
Killing horizon, twist      92 95
Killing parameter      97
Kinnersley vector      68 170
Komar integral      130
Komar integral, Kerr spacetime      54
Komar integral, positivity      213
Komar mass      16 23 54 110 130 210 212
Lagrangian, conformal scalar field      200
Lagrangian, electromagnetic      57
Lagrangian, electrovac Ernst equations      75 169
Lagrangian, Ernst equations      13 45 50
Lagrangian, harmonic      179 185
Lagrangian, sigma model      170 179
Lagrangian, Skyrme      188 190 193 198
Lagrangian, spherically symmetric gravity      198
Lagrangian, vacuum equations with Killing field      13
Laplacian      4
Laplacian along mapping      185
Laplacian, stationary and axisymmetric      33
Lie derivative      7
Mass, ADM      15
Mass, electrovac spacetime      116 134
Mass, Kerr spacetime      53
Mass, Kerr — Newman spacetime      80
Mass, Komar      16 23 54 110 130 210 212
Mass, variation formula      109 114 116
Maurer — Cartan form      193 195
Maxwell equations      63 129 136
Mazur identity      168 171 172
Metric in prolate spheroidal coordinates      48
Metric, circular      33 38 43
Metric, circular electrovac      73
Metric, induced on null surface      98
Metric, orbit manifold      33
Metric, Papapetrou      39
Multi black hole solutions      163
Naked singularity      87
Null congruence      99 118
Null congruence, energy condition      118
Null congruence, generator      91 95
Null congruence, infinity      87
Null congruence, surface      see Killing horizon
Null congruence, tetrad      118
Papapetrou metric      40
Papapetrou — Majumdar solution      163
Penrose conjecture      211 214
Poincare lemma      3
Positive mass theorem      148
Potential space      68
Poynting vector      58 71 127
Prolate spheroidal coordinates      48
Raychaudhuri equation      118
Reissner — Nordstroem solution      157
Reissner — Nordstroem solution, extreme      161
Reissner — Nordstroem solution, uniqueness      157 160
Ricci 1-form      8 10 208
Ricci identity      8 188
Ricci scalar      2
Ricci scalar, conformal transformation      147
Ricci tensor      2
Ricci tensor, circular spacetime      27
Ricci tensor, static spacetime      20 146
Ricci-circularity      27
Ricci-circularity, circularity theorem      28 124
Ricci-circularity, electrovac      70
Ricci-staticity      18 125
Riemann tensor      2
Riemann tensor, 3-dimensional      20
Rigidity theorem      89 90 94
Robinson identity      176
Rotating black hole      91
Rotation-form      see twist
Scalar field, uniqueness theorem      213
Schwaxzschild metric      150
Second fundamental form      147
Second law      119
Second law, generalized version      120
Sigma model      178 187
Singularity, Kerr metric      54
Singularity, naked      87
Singularity, Papapetrou — Majumdar metric      164
Skyrme, energy bound      190 194
Skyrme, energy density      188
Skyrme, Lagrangian, SU(2)      193
Smarr formula      133
Spherically symmetric action      190
Staticity      18 107
Staticity proof      126
Staticity theorem      125
Staticity theorem, electrovac      127 138
Staticity theorem, scalar mappings      208
Stationarity and staticity      125
Stationarity, strict      15
Stationary and axisymmetric spacetime      25
Stationary electromagnetic field      62 69
Stationary mapping      207
Stationary spacetime      15
Stokes' theorem in presence of Killing field      8
Stress-energy tensor      2
Stress-energy tensor, circularity condition      124
Stress-energy tensor, conformal scalar field      201
Stress-energy tensor, electromagnetic      58
Stress-energy tensor, staticity condition      125
Strong energy condition      210
Strong rigidity theorem      89 90
Structure equations, Cartan      19
Surface gravity      95 96
Surface gravity, geodesic congruence      97
Surface gravity, Kerr solution      117
Surface gravity, Reissner — Nordstrom metric      117
Surface gravity, spherical symmetry      214
Surface gravity, uniformity      see zeroth law
Surface gravity, variation      112
Symmetric space      178
Symmetry conditions      see invariance conditions
Tangent space      1
Tangential field, along mapping      182
Third law      119
Topological bound      190 194
Topological censorship      100
Topology of horizon      98
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