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| Sachs R.K., Wu H. — General relativity for mathematicians |
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| Предметный указатель |
"Aberration" 46 132
"Atomic clock" 53
"Conservation" of energy-momentum 96—98
"Conservation" of energy-momentum, differential law of 97
"Cosmological principle" 181
"Expansion of the universe" 58 140
"Logic vs. history" 46—47 159
"Mathematics vs. physics" 44—45 159
"Observable universe" 168
"Phase space" 143
"Present determines future" 70 90 98 102 157 262
"Receding", one observer from another 139
"Rigid meter stick" 59
"Rotation" 50—52
"Solid angle" subtended by object 147
"Spatial homogeneity" 169 175 192
"Spatial reflection" 129
"Test matter" 77 174 198
"Tidal force" 112 242 271
 -equivalence 6
3-momentum space 147 148
3-space 177
Absolute luminosity 146
Absolute luminosity of galaxy 212 214 215
Acceleration 38 253
Active mass 30 218 237
Actual observer 170 173 179
Adjustable parameters 182
Alexandrov basis 251
Alexandrov topology 257
Amplitude of electromagnetic wave 84
Amplitude of gravitational plane wave 243
Apparent luminosity 146 169 214
Apparent luminosity in the visible 147
Apparent size 147
Approaching the big bang 161
Appropriate matter equations 102—103 112
Area-distance 171 185
Area-radius 224 229
Associated orthogonal decomposition, of instantaneous observer 45
At rest 139 146 170 173 180 214
At rest, observer, in stationary spacetime 219
Average world velocity 94
Baryon number 68
Basis of a vector space 2
Basis, dual 5
Basis, ordered 2
Basis, orthonormal 2
Bending of light see "Solar system"
Bianchi identity 79
big bang 28 163
Black hole 7 218 237—242
Black hole, Cygnus X1, as a candidate for 241
Black hole, Schwarzschild 30
Blackbody constant 145 156
Blackbody radiation 145
Boundary manifolds of standard cylinder 63
Boundary of a set 1
Brouwer's fixed point theorem 105
Cambridge catalogue of radio sources 171
Cauchy surface see "Spacetime"
Causal 1-form 22
Causal box 63 269
Causal character 20—24
Causal curve 22
Causal past 124
Causal past, in Einstein — de Sitter spacetime 165
Causal vector 20 24
Causal vector field 22
Causality relation 124 257
Causality relation in Einstein — de Sitter spacetime 166—167
Causality relation, conformal invariance of 125 202
Causally continuous spacetime see "Spacetime"
Celestial sphere 130
Center of mass frame 94
Charge-current density 74
Charge-current density, electric charge of 86
Charge-current density, of matter model 77
Chronological future 210
Chronological past 124
Chronologically follows 125
Chronologically precedes 124
Chronology condition see "Spacetime"
Chronology relation 124 257
Chronology relation in Einstein — de Sitter spacetime 166—167
Chronology relation, conformal invariance of 125 202
Closure of a set 1
Collision event 92—95
Collision event, particle created in 92
Collision event, particle destroyed in 92
Collision-free superpositions 104
Comoving instantaneous observer 43
Comoving observer 43 57
Comoving reference frame in cosmological models 179—181
Comoving reference frame in dust 103
Comoving reference frame in Einstein — de Sitter spacetime 33 57 160
Comoving reference frame in perfect fluid 108
Complete matter vacuum 104
Complete Riemannian manifold 5 28
Complete semi-Riemannian manifold 5 28
Complete spacetime see "Spacetime"
Complete vacuum 104
Components of matter models 104
Components of superpositions 104
Components of tensors 78
Conformal diffeomorphism 131
Conformal spacetimes 87
Conformally invariant 125
Connection of a metric 4
Connection, compatability of, with a metric 4
Connection, forms 18
Connection, induced 38
Connection, over a map 37
Connection, symmetry of 4
Conservation law for vector fields 64—65
Conservation law for vector fields, differential 64
Conservation law for vector fields, integral 64
Conservation of charge 268
Conservation of electric charge at collision 92
Conservation of energy 269—271
Conservation of energy in special relativity 96—97
Conservation of energy-momentum at collision 92
Conservation of momentum 269 270
Conservation of photons 211
Conservation of total energy 97
Conserved photon gas 156
Conserved world density of particle flow 69
Consistency condition of time measurement 137
Consistent particle set 92
Consistent particle set, average world velocity of, at collision event 94
Consistent particle set, center of mass frame of, at collision event 94
Consistent particle set, conservation laws of 92
Constants of motion 129 225
Constraint equations 98 262
Convexity, of causal regions 26
Coordinate function 5
Cosmic rays 175
Cosmological 164
Cosmological constant 177
Cosmological frequency ratio 163 186 194
Cosmological model 176—184
Cosmological model, automorphism of 185
Cosmological model, comoving reference frame in 179
Cosmological model, electromagnetic field in 179 208
Cosmological model, interpretation rule for 179
Cosmological model, intuitive discussion of 176—178
Cosmological model, matter model in 159 178 197—201 203
Cosmological model, quantum effects on 210
Cosmological nucleosynthesis 206
Cosmological redshift 164
| Cosmological redshift, observed 170
Cosmological time 161
Cosmological time in simple cosmological model 200
Cosmology 110 159—215
Cosmology, data of 168—175
Cosmology, nonquantum general relativistic 179
Cosmology, stress-energy tensor in 174
Coulomb force 88
Crab Nebula 218
Crab nebula, pulsar in 218
Curvature 18
Curvature form 19
Curvature infinitesimal and negligible 44—45
Curvature operator 18
Curvature Ricci 18 114ff 254
Curvature scalar 18
Curvature tensor 18
Curve 4
Curve, Cygnus X1 see "Black hole"
Curve, endpoint of causal 92
Curve, future-pointing causal 27
Curve, inextendible 4
Curve, orientation-preserving reparametrization of 4
Curve, past-pointing causal 27
Curve, positive affine reparametrization of 4
Curve, reparametrization of 4
de Rham decomposition theorem 122
de Sitter, W. 32
Decay 93
Deceleration parameter 184 190
Density, charge-current 74
Density, energy 72 108
Density, energy-momentum 74
Density, world 66
Derivation 37
Deuterium 206
Diffeomorphism 3
Diffeomorphism, conformal 131
Differential form see "Form"
Direction-energy space 141
Displacement current hypothesis of Maxwell 268
Distance, by apparent angular diameter 171
Distance, by apparent size 171
Distance, luminosity 171
Distance, Newtonian 172
Distance, parallax 171
Distance, radar 171
Distance, spatial 171—172 215
Divergence of tensor field 80
Divergence of vector field 64
Dominant energy condition see "Stress-energy tensor"
Doppler effect 139
Dust 103 110 119—121 181 198—200
Dust, matter equations of 103
Early Universe 203ff
Early universe, primordial fireball in 205—208
Eigenvalue see "Linear transformation"
Eigenvector of Einstein tensor 33
Eigenvector of normal stress-energy tensor 105
Einstein addition law 48
Einstein field equation 52 111—123 179—180 198 200 247 259 262—264
Einstein field equation, linearized vacuum 263
Einstein tensor 18 33 35 111 180 184
Einstein tensor, eigenvector of 33
Einstein — de Sitter gravitational field 32 43
Einstein — de Sitter model 182 184—195 200
Einstein — de Sitter model, energy density of 185
Einstein — de Sitter model, luminosity distance in 210—215
Einstein — de Sitter model, modified 197—198 200
Einstein — de Sitter model, predicted Hubble time of 186
Einstein — de Sitter spacetime 31—34 47 49 57 133 135 160 180—182 220 259
Einstein — de Sitter spacetime, characterization of 180—181
Einstein — de Sitter spacetime, comoving observer in 43 57
Einstein — de Sitter spacetime, comoving reference frame in 33 57
Einstein — de Sitter spacetime, curvatures of 32—33
Einstein — de Sitter spacetime, focusing effect in 189—190
Einstein — de Sitter spacetime, isometries of 161—162
Einstein — de Sitter spacetime, Killing vector fields in 82
Einstein — de Sitter spacetime, light signals in 162—163
Einstein — de Sitter spacetime, number counts of galaxies in 192—195
Einstein — de Sitter spacetime, photons in 133 162—164
Einstein, A. 8 9 32 42 44 131 136 179
Electric charge in space-section 86
Electric charge of particle 68
Electric charge of particle flow 86
Electric field, in Minkowski space 75
electromagnetic field 74—76
Electromagnetic field in cosmological models 179 208
Electromagnetic field, electric vector of 75
Electromagnetic field, magnetic vector of 75
Electromagnetic field, source of 83
Electromagnetic field, stress-energy tensor of 85
Electromagnetic radiation 131
Electromagnetic stress-energy tensor see "Stress-energy tensor"
Electromagnetic wave, plane linearly polarized 84
Electromagnetism 66—78 83—106
Electron-lepton number 68
Endless causal curve 92
Endpoint of causal curve, future 92
Endpoint of causal curve, past 92
Energy of a particle 67
Energy, density of a quasi-gas 108
Energy, density of a stress-energy tensor 72
Energy, spectrum of a photon distribution function 143
Energy-momentum of a particle 67
Energy-momentum, density of a particle flow 74
entropy 27
Equation of continuity 65 267
Equilibrium spectrum 145
Equivalence of tensors 6
Equivalence, physical 17
Equivalent models 168
Exhaustive sequence 149
Exponential map 5 126
Faraday's law 268
Fermi — Walker connection 51—52
Fermi — Walker parallelism 131
Feynman, R.P. 7
Flat manifold 18
Focusing effect in Einstein — de Sitter spacetime 189—190
Form, closed 3
Form, connection 18
Form, curvature 19
Form, exact 3
Freely falling particle 67 115—117
Freely falling, observer 42
Freely falling, photon 130
Frenet — Serret theory of curves 41
Frequency of photon 131
Frequency ratio 137—140
Frequency ratio, cosmological 163
Frequency, ratio of emitted to observed 138
Friedmann, A. 32
Function, of rapid decay 150
Function, of rapid vertical decay 151
Function, over a map 37
Function, photon distribution 142
Function, Planck 144
Future endpoint 92
Future lightcone: in tangent bundle 151
Future lightcone: in tangent space 26
Future-pointing 1-form 26
Future-pointing causal curve 27
Future-pointing vector 13 26
Future-pointing vector field 26
Galaxies 168—169
Galaxies, random 3-velocity of 110
Galaxy, absolute luminosity of 212
Galaxy, elliptic 169
Galaxy, emitting 210—214
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