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| Ïîèñê ïî óêàçàòåëÿì |
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| Poisson E. — A relativists toolkit |
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| Ïðåäìåòíûé óêàçàòåëü |
Acceleration 17 18 92 104 105 185
Accretion onto a black hole ix 109 201 223
Action functional for gravitation x 118 121 122 124 126 127 136—139 141 145 157 158
Action functional in general 118—122 125 128 129 132 138
ADM mass see “Mass Arnowitt
Advanced time 152 161 165 173 199 204 207 213 214 218
Affine parameter 1 7 10 16 17 20 21 45 48 50—52 56 58 61 63 66 98 104—106 108 110—113 171 173 186 193 194 199 204 207
Angular momentum of a black hole ix 109 163 187 190 192 200 201 206 209—211 221—223
Angular momentum of a particle 10 27 155 183 188 192
Angular momentum of a rotating shell 94 109
Angular momentum of an axisymmetric body 148 150 151
Angular momentum of an isolated body ix 118 119 146 147 205 210
Angular momentum, definition in terms of gravitational Hamiltonian ix x 147 156 177
Angular momentum, definition in terms of Komar integral 149 151 177 209
Angular momentum, flux vector 155
Angular momentum, transfer across a hypersurface 155 156 160—162
Angular velocity of a rotating black hole 190 191 200 204 209 221
Angular velocity of a rotating shell 96 97 112
Angular velocity of a rotating star 82
Angular velocity of an inertial frame 94 97
Angular velocity of an observer 27 189 190 192
Angular velocity of null generators 110 112 191
Angular velocity of ZAMOs 188
Apparent horizon 171—176 178 180 190 191 203 214—217
Area theorem see “Black-hole mechanics second
Asymptotically-flat spacetime x 54 118 119 126 127 138 146—148 151 157 162 180 183 187 198 217
Auxiliary null vector 46—51 56 57 63 66 99 107 207
Basis vectors 19 22 24 29 57 66 73 75 99 101 103 106—108 110 113 130 150 207 222
Bianchi identities 15 16 127 128
Bifurcation two-sphere 176 199 200 204 208
Birkhoff’s theorem 163 164
Black hole, extreme 178 184 190 199 200 203 213 214 216
Black hole, general viii ix 84 151 163 201—211
Black hole, Kerr 97 109 187—201 205 206 208 209 211 213 215 218 219 221
Black hole, Kerr — Newman 187 221—223
Black hole, Reissner — Nordstroem 176—187 191 194 196—198 206 213 216 217
Black hole, Schwarzschild 55 90 109 110 163—176 180 184 205
Black hole, stationary 204—206
Black-hole entropy 214—216
Black-hole mechanics, first law viii 192 209 211—212 215 216 223
Black-hole mechanics, second law viii 192 201 212—213 215 216
Black-hole mechanics, third law viii 213—214 216
Black-hole mechanics, zeroth law viii 208—209 214—216 220 221
Black-hole tunnel 180 181 183 184 198 217 218
Bondi — Sachs mass see “Mass Bondi
Boundary viii 69 90 92 117—119 126 132 134 136 141 142 148 150 151 156 163 167 169 172 174 196 202 203 209 218
Boundary terms x 118 119 121 124 137—142 144 146 156 212
Boyer — Lindquist coordinates 187 192 196
Brane worlds 114
Canonical momentum 118 128 129 131 133 140
Carter constant 192 219
Casimir effect 32
Cauchy horizon 217 218
Cauchy problem 218
Causal structure 163 168 170 174 194 198 202 203
Caustic 41 51 203 212
Centrifugal force 183
Chandrasekhar on the perfection of black holes 206
Charge 25 176 177 184 187 206 213 216 217 221 223
Christoffel symbols 6 7 22 23 86 87 101 122 219
Cofactor 65 69 131
Collapse, gravitational see “Gravitational collapse”
Completeness relations 29 63 67 68 78 79 99 102 107 123 134 135 207 222
Conformal flatness 84
Congruence of null geodesies viii 28 45—54 56—58 105 116 163 171—175 186 190 192—194 203 205 207 212 220 221
Congruence of timelike curves 54 129 135
Congruence of timelike geodesics viii 28 36—45 54 55 76 85 99 100 104 114
Connection 4—6 8 9 11 12 22 73 74 86
Conservation laws 16 71 91 116 125 153 155 185
Constraint equations 79—84 116 145 146
Coordinates, Boyer — Lindquist see “Boyer — Lindquist coordinates”
Coordinates, Eddington — Finkelstein see “Eddington — Finkelstein coordinates”
Coordinates, Fermi normal see “Fermi normal coordinates”
Coordinates, Kerr — Schild see “Kerr — Schild coordinates”
Coordinates, Kruskal see “Kruskal coordinates”
Coordinates, Painleve — Gullstrand see “Painleve — Gullstrand coordinates”
Coordinates, Riemann normal see “Riemann normal coordinates”
Cosmological constant 117
Cosmology ix 41 54 80 112—113
Covariant differentiation x 1 4—6 8 9 47 73 74 76 123 139 143 159
Cross section 42—45 48 51—53 66 105 174 200 202 207—209 212
Curvature tensors, Einstein x 2 16 78 88 89 101 142 144 152
Curvature tensors, extrinsic see “Extrinsic curvature”
Curvature tensors, Ricci x 2 16 26 31 55 78 79 82 84 88 98 115 121 137 146 207 220
Curvature tensors, Riemann x 2 15—17 19 23 24 26 59 76—78 86—89 98 101 115 116 188 204
Curvature tensors, Weyl x 26 55 58 98
Curve 1—6 8 9 17 18 21 22 36 39 46 52 53 60 62 83 111 129 130 135 160 164 166 170 171 202 217
de Sitter spacetime 117
Delta function see “Dirac distribution”
density see “Mass density” or “Energy density”
Derivative, covariant see “Covariant differentiation”
Derivative, Lie see “Lie differentiation”
Determinant 2 12—14 45 53 64—68 71 121 122 131 135 207
Deviation vector viii 16—18 21 23 36 37 45—47
Deviation, geodesic see “Geodesic deviation equation”
Dirac distribution 85—89 98 101 104 113 158
Divergence formula 13 70 72 133
Dragging of inertial frames 97 110 188 189
Dual vector 1—3 5 9
Dust 90 91 153 155 173 175 213 216—218
Eddington — Finkelstein coordinates 167 168 173
Einstein field equations viii ix 2 16 26 31 40 50 59 78 80 84 86 88 90 91 101 115 117 118 122 124—126 145 146 151—154 157 158 163 164 173 177 187 201 205 207 209 220
Einstein tensor see “Curvature tensors Einstein”
Einstein — Hilbert priority dispute 157
Einstein — Maxwell field equations 176 187 217 221
electromagnetic field 32 152 157 176 177 214 216 222
Embedding 25 59 67 68 76 115 127 134 135 138 147 148 153 160
Energy conditions in general ix 28—33 54 173 174 214
Energy conditions, averaged 32
Energy conditions, dominant 32 209 220
Energy conditions, null 31 50 174 203—205 212 215
Energy conditions, strong 31 40 41 204
Energy conditions, violations 32 54
Energy conditions, weak 30—31 213 214
Energy density 29 30 32 55 113 153 156 173 214 218
Energy of a particle 10 27 42 92 109 155 181 191 192
Energy, binding 93
Energy, electrostatic 184
Energy, flux vector 155
Energy, gravitational potential 159
Energy, internal 214
Energy, kinetic 93 159
Energy, mass-energy see “Mass”
Energy, rotational 192
entropy see “Black-hole entropy”
Equivalence principle see “Principle of equivalence”
Ergosphere 189 191 192
Euler — Lagrange equation 6 7 120 121 128
Event horizon viii ix 28 163 170—176 178 180 185 186 189—192 196 197 199 200 202—205 207—209 211—213 215—217 220—223
Expansion scalar 28 34 35 37 40—43 46 48 51 52 55 56 58 76 105 113 114 116 171—175 190 203 212 220
Extrinsic curvature ix 59 75—77 79—81 83 89 92 95 102 103 114 115 118 121 124 127 134—136 138—140 145 147—150 153 158 160
Fermi normal coordinates 2 18—24 26
Field equations, Einstein see “Einstein field equations”
Field equations, Einstein — Maxwell see “Einstein — Maxwell field equations”
Field equations, Klein — Gordon see “Klein — Gordon equation”
Field equations, Maxwell see “Maxwell field equations”
Flat space 25 60 70 80 82—84 115 138 147 149 154 159 160 168 217
Flat spacetime 17 26 32 51 56 63 65 66 83 93 95 107 115 116 126 127 138 146 153 160 165 194 195 217 219
Flatness, asymptotic see “Asymptotically-flat spacetime”
Flatness, conformal see “Conformal flatness”
Flatness, local see “Local flatness theorem”
Fluid 30 55 90 96 97 111—113 117 153 155 158 173 218
Focusing action of gravity ix 28 109 116 175 205
Focusing theorem for null geodesics 28 50—51 175 212
Focusing theorem for timelike geodesics 28 40—41 43
Friedmann — Robertson — Walker spacetime 54 81 90
Frobenius’ theorem 28 38—40 48—50 186
Gauss — Codazzi equations 76—79 115
Gauss — Weingarten equation 75
Gauss’ law 177
| Gauss’ Theorem 69 71 120 133 209
Generators of a null hypersurface 49 51 61—63 65 66 98 104—113
Generators of an event horizon viii 174—176 185 186 191 199 200 203—205 207 208 212 220 223
Geodesic deviation equation 2 16—18 21 23
Geodesic equation in affine parameter form 7 10 17 18 20 22 25 39 52 56 92 100 155 158 173 186 192 200 204 219
Geodesic equation in general form 7 25 50 61 186 204
Geodesic, defined 6—8
Gravitational collapse in general 167 176 200 205 209
Gravitational collapse of a pressureless star 90—92
Gravitational collapse of a thin shell 93 107—109
Gravitational collapse of null dust 216 217
Gravitational repulsion 184
Gravitational waves 152 156 164 223
GRTensorII x
Hamiltonian in general 118 128 129 131 132
Hamiltonian, density 131 132 140
Hamiltonian, formulation of general relativity x 118 136—146 156
Hamiltonian, gravitational ix 118 119 136—147 157
Hamilton’s equations 128 132 133 145—146
Hawking evaporation 206 214—216
Hawking temperature 214
Hawking — Hartle formula 223
Hilbert action 121 122
Hilbert — Einstein priority dispute see “Einstein — Hilbert priority dispute”
Horizon, apparent see “Apparent horizon”
Horizon, Cauchy see “Cauchy horizon”
Horizon, event see “Event horizon”
Horizon, Killing see “Killing horizon”
Horizon, trapping see “Trapping horizon”
Hypersurface orthogonal 28 38—40 42 43 48—50 52 56 57 76 82 105 129 186 190 205
Hypersurface, defined 60
Ideal gas 159
Induced metric ix 59 62—63 68 71 73 74 76 80 82 84 86 91 94—96 102 103 106 108 110 113—115 117 118 121 122 124 126 131 134—136 139 145 148 153 158 160 168 200
Inertial frame 94 97 110 112
Infinity, null 152 153 161 169 170 202 206
Infinity, spatial ix 71 97 110 119 126 147 151 153 168—170 185 188 191 209
Infinity, timelike 169 170
Initial-value problem ix 79—84 114 145
Integration over a hypersurface ix 59 64—69 118 150 151 155 156 163 209—211
Jacobian 12 14 36
Junction conditions ix 60 84—90 92
Kerr spacetime 94 109 163 187—201 205 206 208 211 215 218 219 221
Kerr — Newman spacetime 187 221—223
Kerr — Schild coordinates 194—196
Kerr — Schild metric 195 219
Killing horizon 175—176 185 191 204
Killing tensor 192 219
Killing vector x 1 10—11 25—27 82 96 149 150 176 185—189 191 192 204 207 208 219 220
Klein — Gordon equation 121 125 133
Komar integral for angular momentum see “Angular momentum definition
Komar integral for mass see “Mass definition
Kruskal coordinates 164—168 171 176 178—180 184 186 196 197 216
Kruskal diagram 166—168 170 172 176 180
Lagrangian in general 6 118—120 124
Lagrangian, density 118 120—122 125 131 133 139 157
Lagrangian, formulation of general relativity x 118 121—128 156
Laplace’s equation 84 217
Lapse function 118 119 130 131 139 145—147
Lense — Thirring effect see “Dragging of inertial frames”
Levi-Civita tensor 2 13—15 26 64 65
Lie differentiation x 1 8—10 17 25 44 53 76 80 103 127 130 131 139 146 158 207
Lie transport 9 45 75 103 160
Light cone 51 63—64 66 170
Local flatness theorem 1 11—12 18 19 22
Local Lorentz frame 2 11 12 15 37 46 123 185
Lorentz transformation 11
Mach’s principle 97
Majumdar — Papapetrou spacetime 216 217
Manifold 1—3 8 12 26 59 60 68 69 76 120 126 127 138 146 166 169 178 202
mass density 84 90—93 96 97 102 104 106 109 111—113 116 117 155 159 164
Mass in spherical symmetry 82 115 152 158 164 173 184 217
Mass of a black hole ix 55 109 110 163 176 177 184 187 200 201 206 209—211 213 221—223
Mass of a collapsing shell 93 94 108 109 111
Mass of a particle 10 27 42 157 181 185
Mass of an isolated body ix 82 91 92 116—119 146 148 150 164 198 210
Mass transfer across a hypersurface 155 156 160 161
Mass, Arnowitt — Deser — Misner 147 151—156 158 159 177 187 217
Mass, Bondi — Sachs 151—156
Mass, definition in terms of gravitational Hamiltonian ix x 147 156 177
Mass, definition in terms of Kotnar integral 149 177 209
Mass-energy see “Energy”
Matrix 11—14 34 35 56—58 65 66
Matter distribution 16 26 30 59 82 88 90 93 109 121 175 205 210 211 213
Maximal extension of a spacetime 167 176 196—198
Maxwell field equations 157 176 177
Membrane paradigm 216
Metric determinant see “Determinant”
Minkowski metric 11 19 22 23 29 56 64 95 195 219
Minkowski spacetime see “Flat spacetime”
Moment of time symmetry 81—84 115
Momentum vector 32 191
Multipole moments 206
Normal coordinates, Fermi see “Fermi normal coordinates”
Normal coordinates, Riemann see “Riemann normal coordinates”
Normal vector 38 48 60—61 63 65—69 71 75 80—82 85 87 92 95 99 100 103 109 114 115 123 126 129 130 134 136 147—149 153 160 174 185 190
Numerical relativity 84 114 146 157
Oppenheimer — Snyder collapse see “Gravitational collapse of a pressureless star”
Painleve — Gullstrand coordinates 168
Parallel transport 1 4 6 7 19 22 24 25 37 47 57 58
Penrose process 191—192
Penrose — Carter diagram 168—170 180 198 216
Penrose’s description of the event horizon 203 212 215
Permutation symbol 13
Perturbation of a black hole 184 201 211 212
Poisson’s equation 84
Pressure 29 55 90 91 93 96 97 102 104—107 109 111—113 116 117 153 159 173
Price’s theorem 206
Principal null congruences of the Kerr spacetime 192—194
Principle of equivalence 6 11
Projection of a tensor 24 47 56 73 74 77 96 100 101 139
Proper distance 7 8 19—21 85 115 160 185
Proper time 7 8 19 20 24 25 36 41 43 85 91 99 100 104 116 147 158 168 181 188 192
Radiation 112 152—155 160—162 173 185 206 213 215 218 223
Raychaudhuri’s equation 28 40—41 50—51 55 57 58 105 116 205 207 212
Redshift 185
Reissner — Nordstroem spacetime 163 176—187 194 196 197 217
Retarded time 152 153 155 160 161 165
Ricci tensor see “Curvature tensors Ricci”
Riemann normal coordinates 26
Riemann tensor see “Curvature tensors Riemann”
Rigid rotation 161
Rotation tensor 28 35—41 48 50 51 55—57 205 220
Rotation, gravitational effects 97
Schwarzschild spacetime 26 42 52 55 90 93 108 114—117 152 158 163—176 205 217
Shear tensor 28 34—37 40 41 48 50 51 55—58 105 205 220 223
Shift vector 118 119 130 139 145—147
Singularity of a congruence see “Caustic”
Singularity of null-dust collapse 217
Singularity of the Boyer — Lindquist coordinates 187 192
Singularity of the Eddington — Finkelstein coordinates 182
Singularity of the Kerr spacetime 187 190 195—196 198
Singularity of the Kruskal coordinates 179 180 197
Singularity of the Reissner — Nordstroem spacetime 178 180
Singularity of the Schwarzschild coordinates 164 165 178
Singularity of the Schwarzschild spacetime 169 170
Singularity theorems 28 204 215
Smarr’s formula 200 209—211 215 222
Stokes’ Theorem 69 71 150
Stress-energy tensor in general ix 16 29 105 113 125 155 205 207 211 213 215
Stress-energy tensor of a perfect fluid 30 96 155 158
Stress-energy tensor of a point particle 158
Stress-energy tensor of a scalar field 125 161
Stress-energy tensor of a surface layer 87—90 93 95 96 98 100—104 107 111 113 116
Stress-energy tensor of an electromagnetic field 157 177
Stress-energy tensor of null dust 153 173 213 214 218
Stress-energy tensor, decomposed in terms of density and principal pressures 29
Surface area of a black hole ix 163 200 201 209 211—213 222 223
Surface element ix 59 64—69 72 106 133 149 207 210 211
Surface gravity of a black hole 184—187 198—200 204 208 209 213—215 220 222 223
Surface integral see “Integration over hypersurfaces”
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