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Sachs R.K., Wu H. — General relativity for mathematicians
Sachs R.K., Wu H. — General relativity for mathematicians

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Название: General relativity for mathematicians

Авторы: Sachs R.K., Wu H.

Язык: en

Рубрика: Физика/Гравитационное взаимодействие/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 291

Добавлена в каталог: 28.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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
$\Phi$-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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