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| Heusler M., Goddard P. — Black Hole Uniqueness Theorems |
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| Предметный указатель |
action see Lagrangian
ADM mass 15
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  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 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
Torsion, along mapping 184
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