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| Sachs R.K., Wu H. — General relativity for mathematicians |
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| Предметный указатель |
Petrov type, of a spacetime 254
Photon 68 129—133 162—163
Photon distribution function 142—147
Photon distribution function, Planck 144—146 152ff
Photon gas 152—158 178 264—265
Photon gas, conserved 156 157 264—265
Photon gas, number density of 157
Photon gas, Planck, with temperature T 153
Photon gas, spatially isotropic 154
Photon gas, stress-energy tensor of 154
Photon occupation number 147
Photon, absorbed 130
Photon, beam 71 210 213 215
Photon, emitted 130
Photon, freely falling 130
Photon, frequency of 131
Photon, received 130
Photon, sent out 130
Photon, spatial direction of, measured by (z,Z) 130
Photon, standard 133 162—163
Photon, wavelength of 131
Photons in Einstein-de Sitter spacetime 133 162—163
Photons, microwave 173
Photons, specific intensity of 143
Photons, total energy density of 143
Photons, total number of (in space-sections) 157 265
Physical equivalence of tensor fields 17
Physical equivalence of tensor fields over a map 37
Physical theories 8—9
Planck function 144 156
Planck photon distribution function 144—146
Planck photon distribution function, temperature of 144
Planck spectrum 145
Planck spectrum, of the microwave radiation 174 203 207
Planck's constant 131 143 199
Planck, M. 131 145
Plane electromagnetic wave 84
Plane electromagnetic wave, amplitude of 84
Plane electromagnetic wave, angular frequency of 84
Poincare group 260
Poincare, H. 9
Poisson equation 112
Positive affine function 1
Positive affine reparametrization of a curve 4
Poynting vector 86 269
Predicted Hubble time 186 189
Predicted Hubble time of a simple cosmological model 208
Predicted Hubble time of Einstein — de Sitter model 186
Pressure gradient 118 119
Pressure of perfect fluid 108
Pressure of quasi-gas 108
Primordial fireball 205—208
Projection tensor, relative to (z,Z) 45
Proper time function: of proper time synchronizable reference frame 53
Proper time function: on general spacetime 259
Proper time ratio 138
Pulsar 7 218
Pure radiation universe 182 196 209
Quantum effects, on cosmological models 210
Quantum theory 8—9
Quasar 147 169 195 207
Quasi-gas 104
Quasi-gas, energy density of 108
Quasi-gas, energy of component in 110
Quasi-gas, pressure of 108
Quasi-gas, random 3-velocity of a component in 110
Radar 134—135 230
Radiation 131
Radiation, blackbody 174
Radiation, microwave 173—174
Radiation, Planck 174
Radiation, thermal equilibrium 174
Radio waves 131 152
Random 3-velocity 94
Rapid decay, function of 150 152
Rapid vertical decay, function of 151 152
Raychaudhuri equation 122 254
Redshift, cosmological 164
Redshift, gravitational 219 220 229
Redshift, observed cosmological 170
Reference frame 52—59
Reference frame, "infinitesimally nearby" observer in 54
Reference frame, absolute 219 224
Reference frame, acceleration of 253
Reference frame, comoving 33 57 103 108 160 179—181
Reference frame, expansion of 253
Reference frame, geodesic 53 59 114—117
Reference frame, inertial 59
Reference frame, irrotational 56
Reference frame, local geodesic 246
Reference frame, locally proper time synchronizable 53
Reference frame, mean relative-acceleration of 114ff 254
Reference frame, observers in 53
Reference frame, proper time synchronizable 53
Reference frame, rigid 56
Reference frame, rotation of 253
Reference frame, shear of 253
Reference frame, static 219 224
Reference frame, stationary 219
Reference frame, synchronizable 53 136—137
Reflections 129
Relativistic model 76
Relativity see "General relativity" "Special
Rest-mass 67 69
Ricci flat: manifold 18
Ricci flat: spacetime see "Spacetime"
Ricci: curvature 18 114ff 254
Ricci: scalar 18
Ricci: tensor 18
Riemannian manifold 4
Robertson — Walker model 208
Robertson — Walker spacetimes 32 183—185 208
Robertson — Walker spacetimes of negative spatial curvature 183 190 191 208
Robertson — Walker spacetimes of positive spatial curvature 183 191 208
Robertson — Walker spacetimes of zero spatial curvature 183
Rotations, generator of, on 2-sphere 216 225—226
Rotations, spatial, in Einstein — de Sitter spacetime 162 188
Schwarzschild black hole 30
Schwarzschild black hole, geometry of 220—228
Schwarzschild black hole, Killing vector fields in 82
Schwarzschild spacetimes 30 see "Particles "Schwarzschild
Schwarzschild spacetimes, characterization of 261
Schwarzschild spacetimes, curvatures of 222
Schwarzschild spacetimes, geometry of 220—228
Second fundamental form 122 256
Second order differential equation 91 265
Self-adjoint linear transformation 20
Simple cosmological model 196—202
Simple cosmological model, microwave photons in 197—198
Simple cosmological spacetime 31 167—168 180 183 200—201
Simple cosmological spacetime, characterization of 260
Simple matter equations 95 102
Simply convex neighborhood 126
Skew-adjoint linear transformation 20
Solar system 228—237
Solar system, bending of light in 233—236
Solar system, idealizations of 228
Solar system, orbit function of particle in 231
Solar system, particle orbits in 231—233
Solar system, perihelion precession of planets in 237
Solar system, total bending angle of light signal in 234 236
Solid angle 141
Space form 184
Space slice 161
Space-section 64 157
Space-section, total number of photons in 157
Spacelike: 1-form 22
Spacelike: submanifold 22
Spacelike: subspace 20
Spacelike: vector 20 24
| Spacelike: vector field 22
Spacetime 27 256 see "Einstein "Gravitational "Kruskal "Minkowski "Normal "Schwarzschild "Schwarzschild "Simple
Spacetime diagram 34
Spacetime, Cauchy surface in 258
Spacetime, causally continuous 258
Spacetime, chronology condition on 257
Spacetime, complete 28 256
Spacetime, conformal 87
Spacetime, containing another 28
Spacetime, globally hyperbolic 258
Spacetime, maximal 29
Spacetime, Ricci flat 31 113—117 262
Spacetime, spherically symmetric 261
Spacetime, stably causal 258
Spacetime, static 219 261
Spacetime, stationary 218—220 219 261
Spacetime, strongly causal 257
Spatial direction (z,Z) measures for photon 130
Spatial distances 171—172
Spatial infinity 95 222
Spatial isotropy 47 175
Spatial rotation around x 162 188
Spatially isotropic photon gas 154 158
Spatially isotropic spacetime 47
Spatially isotropic stress-energy tensor 107—109
Spatially isotropic tensor for (z,Z) 47
Special relativity 8 29
Specific flux 147
Specific intensity of photons 143
Spectrum, energy 143
Spectrum, equilibrium 145
Spectrum, Planck 145
Spectrum, thermal equilibrium 145
Spin 68 247
Spray 264 265
Stably causal see "Spacetime"
Standard cylinder 63
Standard cylinder, boundary manifolds of 63
Standard light signal in Einstein — de Sitter spacetime 133
Standard light signal in normal Schwarzschild spacetimes 226
Standard photon, in Einstein — de Sitter spacetime 133 164
Star, end-states of 218
Star, history of 217
Star, neutron 218
Static, reference frame see "Reference frame"
Static, spacetime see "Spacetime"
Stationary, observer see "Observer"
Stationary, reference frame see "Reference frame"
Stationary, spacetime see "Spacetime"
Steady State cosmology 195
Stokes' theorem 62
Stress-energy tensor 71—73 104—106
Stress-energy tensor in cosmology 174
Stress-energy tensor of matter model 77
Stress-energy tensor of particle flow 72
Stress-energy tensor of photon gas 154
Stress-energy tensor, dominant energy condition on 252
Stress-energy tensor, electromagnetic 85 86 253
Stress-energy tensor, energy density of 72
Stress-energy tensor, normal 105
Stress-energy tensor, spatially isotropic 107—109
Stress-energy tensor, strong energy condition on 252
Stress-energy tensor, timelike convergence condition on 123 158 179 183 252
Strong energy condition see "Stress-energy tensor"
Strongly causal see "Spacetime"
Submanifold 3
Submanifold, extrinsic curvature of 256
Submanifold, imbedded 3
Submanifold, totally geodesic 228
subspace 2
Subspace, invariant 251
Summation convention 78—80
Superposition of matter models 104
Superposition of matter models, collision-free 104
Superposition of matter models, components of 104
Superposition of matter models, finite 104
Symmetric hyperbolic system, of partial differential equations 101
Symmetry condition, of Levi-Civita connection 4
Synchotron frequency 90
Synchronizable reference frame see "Reference frame"
Tangent bundle, of a manifold 3
Tangent vector field, of a curve 37
Temperature of a Planck function 144
Temperature of a system of particles 146
Tensor 2
Tensor field 3
Tensor field, components of 78
Tensor field, covariant constant 59
Tensor field, derivation of 37
Tensor field, divergence of 80
Tensor field, over a map 36—37
Tensor field, parallel 59
Tensor field, physical equivalence of 17 37
Tensor field, restriction of 37
Tensor, algebra 2
Tensor, Einstein 18 111 180 184
Tensor, metric 4
Tensor, Ricci 18
Thermal equilibrium 145—146
Thermal spectrum 145
Thermodynamics, second law of 27
Thomas precession 52
Time development, in Ricci-flat spacetime 262
Time dilation 48
time function 53
Time function proper, of proper time synchronizable reference frame 53
Time function proper, on general spacetime 259
Time orientability 24—27 255
Time orientable Lorentzian manifold 25
Time oriented, by vector field 26
Time-dependent vector field 266
Timelike convergence condition 123 158 179 183 252 see
Timelike, 1-form 22
Timelike, submanifold 22
Timelike, subspace 20
Timelike, vector 20 24
Timelike, vector field 22
Total energy density of photons 143
Total energy, conservation law of 97
Total energy, in Minkowski space 97
Total number of particles 69
Total number of photons 157 265
Trivial gravitational field 29
Twentieth century, model of the history of 241
Twin "paradox" 42—43
Type, of particle flow 71
Ultraviolet radiation 131
Unit sphere 5
Unit vector 2
Units, physical 9—10
Universe, early 203ff
Universe, early, nonconservation of sources in 195
Universe, expansion of 140
Universe, inhomogeneity of 195 208
University of California, regents of 27
VACUUM 113 115 222 237 240 243
Vacuum, complete 104
Variational Principle 263
Vector fields, conservation laws for 64
Vector fields, derivation of 37
Vector fields, divergence of 64
Vector fields, Lie bracket of 3
Vector fields, Lie parallel, over a curve 39
Vector fields, lightlike 22
Vector fields, spacelike 22
Vector fields, timelike 22
Vector, causal 20
Vector, norm of 2
Vector, orthogonal 2
Vector, unit 2
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