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| Sachs R.K., Wu H. — General relativity for mathematicians |
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| Предметный указатель |
Galaxy, idealizations of 188
Galaxy, intrinsic cross-sectional area of 187 189
Galaxy, model for the history of 179
Galaxy, radio 169 195
Galaxy, spiral 169
Galilean, invariance 267
Galilean, velocity transformation 267
Gamma rays 131
Gauge transformation 263
Gauss lemma 40 125
Gauss' law of electric flux 86 268
General relativity 7—8
General relativity, history and current status of 9
General relativity, preview of 12—16
Generator of rotations on 2-sphere see "Rotations"
Geodesic 4 5 125 129 254 259
Geodesic, inextendible 5
Geodesic, maximal 5
Geodesic, reference frame 53 59 114—117
Geodesic, spray 264
Geodesic, vector field 5
Geometric energy function 126—127
Global hyperbolicity see "Spacetime"
Global time function 258
Gravitational collapse 117—123 237 259
Gravitational field 27
Gravitational field, gradient 18
Gravitational field, representative of 27
Gravitational field, trivial 29
Gravitational plane wave 242—249 261 269
Gravitational plane wave, amplitudes of 243
Gravitational plane wave, curvatures of 243
Gravitational plane wave, linearly polarized 243
Gravitational plane wave, linearly polarized, spacetime polarization plane of 249
Gravitational plane wave, monochromatic 243
Gravitational plane wave, monochromatic, frequency of 243
Gravitational plane wave, spacetime propagation direction of 244
Gravitational plane wave, spacetime wavefront of 244
Gravitational wave 242 245 248
Gravitational wave, detector 247
Graviton 68 246 247
Gyroscope 50
Gyroscope, axes 50—52
Hamiltonian mechanics 153
Helium creation epoch 206
Here-now 179
Horizontal vector field 264
Hubble constant 173
Hubble law 168 172—173 185
Hubble time, empirical 172
Hubble time, predicted 186 208
Idealizations in cosmology 169—170
Imbedding 3
Immersion 3
Improper integral, existence of 150
Incoming particle 92
Inextendible, curve 4
Inextendible, geodesic 5
Infrared radiation 131
Initial value theorem 98 102 109 110 262 269
Inner product 2
Inner product, index of 2
Inner product, Lorentzian 2
Instantaneous observer 43 45—46
Instantaneous observer, associated orthogonal decomposition of 45
Instantaneous observer, comoving 43
Instantaneous observer, local rest space of 45
Instantaneous observer, local time axis of 45
Instantaneous observer, projection tensor of 45
Instantaneous observer, stationary 43
Integration on light cones 148ff
Integration region 141 268
Integration region, exhaustive sequence of 149
Interior (of a set) 141 149
Interior product operator 62 80
Interpretation rule, for cosmological models 179
Invariant subspace see "Linear transformation"
Isometry 4
Isometry group, of spacetime 259
Isometry group, orbit of 260
Isometry, local 4
Kelvins (degrees Kelvin) 144
Killing vector field 81—83 95 125 216 223
Kruskal spacetime 237 242 259
Kruskal spacetime, characterization of 261
Kruskal spacetime, relation to Schwarzschild spacetimes 239
Laplace, P.S. 11 12
Levi-Civita connection 4
Lie parallel, tensor field 41
Lie parallel, vector field 39
Light 131
Light signal 133—136 162—163
Light signal, standard, in Einstein — de Sitter spacetime 133
Light signal, standard, in normal Schwarzschild spacetime 226
Lightcone 22 148—151
Lightcone future, in tangent bundle 151
Lightcone future, in tangent space 26
Lightcone in tangent bundle 151
Lightcone integration on 148—152
Lightcone past, in tangent bundle 151
Lightcone past, in tangent space 26
Lightcone volume element on 149
Lightlike 1-form 22
Lightlike submanifold 22
Lightlike subspace 20
Lightlike vector 20 24
Lightlike vector field 22
Linear transformation, eigenvalue of 251
Linear transformation, invariant subspace of 106 251
Linear transformation, self-adjoint 20
Linear transformation, skew-adjoint 20
Linearized Einstein equation see "Einstein field equation"
Liouville operator 264
Liouville theorem 265
Local isometry 4
Local rest space of (z,Z) 45
Local time axis of (z,Z) 45
Longest time like distance to the big bang 166 183
Lorentz contraction 48
Lorentz force law 88 270
Lorentz group 260
Lorentz World Force Law 88—95 265 270
Lorentz, H.A. 9 88
Lorentzian inner product 2
Lorentzian manifold 4
Lorentzian metric 4
Lorentzian metric, wider 257 285
Lorentzian vector space 2
Luminosity distance 171 185 189 193 210—215
Luminosity, absolute 146
Luminosity, apparent 146
Mach's principle 177
Magnetic field in Minkowski space 75
Magnetic field, constant 83
Magnetic induction, law of see "Faraday's law"
Magnetic monopole, hypothesis of nonexistence of 86
Manifold 3
Manifold, complete 5
Manifold, Lorentzian 4
Manifold, Lorentzian, time orientability of 25 255
Manifold, Lorentzian, time oriented 26
Manifold, orientable 3
Manifold, paracompactness of 255
Manifold, piecewise  62
Manifold, Riemannian 4
Manifold, semi-Riemannian 4
Manifold, tangent bundle of 3
Mass, active 30 218 237
Matter 66—73 76—78 88—98 103—110
Matter equations 95—96 102—103
| Matter equations, appropriate 102—103 112
Matter equations, dust 103
Matter equations, perfect fluid 108
Matter equations, simple 95 102
Matter model 76 103—110
Matter model in cosmological model 159 178 197—201 203
Matter model, charge-current density of 77
Matter model, stress-energy tensor of 77
Matter model, superposition of 104 178
Maximal, geodesic 5
Maximal, spacetime 29
Maxwell stress tensor 86 269
Maxwell's displacement current hypothesis 268
Maxwell's equations 83—87 98—102 110 112 179 267—269
Maxwell's equations, classical 267
Mean relative-acceleration 114—117
Mean relative-acceleration, Newtonian 115—117
Meson, pi-nought 93
Metric tensor 4
Metric tensor, index of 4
Metric, induced 24
Metric, isomorphism 6
Metric, Lorentzian 4
Metric, Riemannian 4
Microwave photons 173
Microwave photons in simple cosmological model 197—198 201
Microwave radiation 152 173—174
Microwave radiation, isotropy of 168
Microwave radiation, Planck spectrum of 174 203 207
Microwaves 131
Millimeter radiation 131
Minkowski space 29 47 49 75 96—97 133 259
Minkowski space, 2-dimensional 13 16 134 139
Minkowski space, characterization of 260
Minkowski, H. 9
Morse theory 122
Mu-lepton number 68
Myers' Theorem 122
Neighbor of observer in reference frame 54
Neighbor, 3-acceleration of 54
Neighbor, 3-velocity of 54
Neutrino 68 93
Newtonian, active mass 11
Newtonian, angle, relative to, (z,Z) 45—46
Newtonian, black hole theory 11—12
Newtonian, electromagnetic energy density 86 269
Newtonian, gravitational force 11
Newtonian, gravitational potential 11
Newtonian, length, relative to (z,Z) 45
Newtonian, mean relative-acceleration 117
Newtonian, physics 10
Newtonian, point particles 10—11
Newtonian, speed, relative to (z,Z) 45
Newtonian, velocity, relative to (z,Z) 45
No escape 127—128
Nonconservation of parity 27
Normal Schwarzschild spacetime 30 113
Normal Schwarzschild spacetime, directly incoming standard light signals in 226
Normal Schwarzschild spacetime, directly outgoing standard light signals in 226
Normal Schwarzschild spacetime, escape to infinity in 223
Normal Schwarzschild spacetime, geometry of 220—228
Normal Schwarzschild spacetime, Killing vector fields in 82 223
Normal Schwarzschild spacetime, spatial infinity of 222
Normal Schwarzschild spacetime, static absolute reference frames in 224
Normal stress-energy tensor 104—106
Normal stress-energy tensor, eigenfunction of 105
Normal stress-energy tensor, eigenvector field of 105
Normal stress-energy tensor, eigenvector of 105
Normal, at a point, for a basis of vector fields 79
Normal, neighborhood 126
Number density of photon gas 157
Number of photons measured by (z,Z) 142
Observed cosmological redshift 170
Observed recession velocity 170
Observer 41—50 52—59 see
Observer in a reference frame 53
Observer in Schwarzchild spacetimes see "Particle in Schwarzschild spacetime"
Observer, "infinitesimally nearby" 38 54
Observer, 4-velocity of 42
Observer, actual 170 173 179
Observer, comoving 43
Observer, comoving instantaneous 43 160
Observer, freely falling 42
Observer, instantaneous 43
Observer, instantaneous comoving 43 160
Observer, proper time of 41
Observer, stationary 43 219
Observer, world acceleration of 42
Observer, world line of 41
Observer, world velocity of 42
Optical radiation 131
Orientation, induced 4
Orientation, of a manifold 3
Orientation, time 24—27
Orthogonal vectors 2
Orthogonality, relativistic interpretation of 49—50
Orthonormal basis 2 5
Outgoing particle 92
Parallel tensor field 59
Particle 66—69 269—271
Particle flow 69—71 178
Particle flow, charge-current density of 74
Particle flow, electric charge of 71
Particle flow, energy momentum density of 74
Particle flow, energy momentum of 69
Particle flow, particles potentially in 69
Particle flow, rest-mass of 69
Particle flow, stress-energy tensor of 72
Particle flow, type of 71
Particle flow, world density of 69
Particle in Schwarzschild spacetimes, angular momentum in x direction 225—226
Particle in Schwarzschild spacetimes, circling 226
Particle in Schwarzschild spacetimes, going directly in 226
Particle in Schwarzschild spacetimes, going directly out 226
Particle in Schwarzschild spacetimes, going in 226
Particle in Schwarzschild spacetimes, going out 226
Particle in Schwarzschild spacetimes, hovering 226
Particle in Schwarzschild spacetimes, maintains direction 226
Particle in Schwarzschild spacetimes, maintains height 226
Particle in Schwarzschild spacetimes, total angular momentum of 225
Particle in Schwarzschild spacetimes, total energy of 226
Particle set 92
Particle set, consistent 92 270—271
Particle, created at collision event 92
Particle, destroyed at collision event 92
Particle, electric charge of 68
Particle, energy momentum of 67
Particle, energy of, relative to (z,Z) 67
Particle, freely falling 67
Particle, incoming 92
Particle, outgoing 92
Particle, potentially in particle flow 69
Particle, proper time of 67
Particle, random 3-velocity of 94
Particle, rest-mass of 67
Particle, total Newtonian energy of 272
Past endpoint 92
Past lightcone in tangent bundle 151
Past lightcone in tangent space 26
Past pointing 26
Past pointing, causal curve 27
Pauli exclusion principle 218
Pauli, W. 93
Perfect fluid 107—110 118ff 158 178 199 200
Perfect fluid, comoving reference frame of 108
Perfect fluid, energy density of 108
Perfect fluid, matter equations 108
Perfect fluid, pressure of 108
Perfect fluid, rest-mass zero 108
Perihelion precession 237
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