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| De Felice F., Clarke C.J.S. — Relativity on curved manifolds |
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| Предметный указатель |
Abelian ring 19
Absolute space 5 6
Absolute time 6
Acceleration 4 6
Acceleration, deceleration parameter in cosmology 382
Acceleration, four-acceleration 138 253 255 257 259
Acceleration, nearby a singularity 370
Acceleration, relative acceleration of nearby geodesics 117 118 257 258
Acceleration, uniform 9
Achronal sets 238
Action of a field 188 189
Action of a gravitational field 191
Action, Hilbert 192
Affine connection 78 108
Affine geodesic 76
Affine parameter 76 107
Affine transformation 78
Age of the universe 380 429
Algebra of bivectors 155
Algebra of tensors 34 57
Algebra, exterior 51
Algebra, Lie 151
Algebraic classification of the Weyl tensor 180ff
Alternating tensors 48
Analytical extension 330 331
angle 281
Angle, definition of 281
Angle, variation induced by curvature 285
Antisymmetrization of tensors 38 39
Apsidal points 347 348
Area theorem 412
Aristotle 1
Asymptotic flatness 207ff
Asymptotic properties of space-time 338ff 361ff
Atlas 17
Axial symmetry 239 389
Basis in cotangent space 29
Basis in tangent space 24
Basis orthonormal 43 110
Basis, coordinate (natural) 25
Bending of light rays 354
Bianchi identities 114 116 254
Bifurcation point 247
Binding energy of marginally stable orbits 347 416
Birkoff theorem 324 342
Bitensors 77
Bivector space 107
Black holes 324 338 357
Black holes, energy extraction from 409 410 411 412
Black holes, evaporation of 428
Black holes, mini black holes 429
Black holes, no hair theorem 424
Boltzman 427
Bouguer 355
Boyer 247 402 416
Carter 400 421 424
Cauchy see "Initial value problem"
Causal curve 236
Causal structure of space-time 236ff
Center of mass 216ff
Chart 13 17
Christoffel symbols 85
Circular orbits in Kerr 414
Circular orbits in Schwarzschild 345
Class of a function 19
Class of a manifold 19
Codazzi 253
Commutator see "Lie brackets"
Commutator of matrices 169
Compact spaces see "Spaces"
Complex, Einstein 203
Complex, Freud 204
Complex, Landau and Lifschitz 205
Conformal compactification 341
Conformal factor 114 174ff
Conformal invariance of the Weyl tensor 114
Conformal spinors 174ff
Conformal transformations 114
Conformal weight 175ff
Congruence 57ff 60 62
Congruence, geometry of 250ff
Congruence, hypersurface orthogonal 141 143 145 260 374 390
Congruence, null 261 271
Conjugate points 118
Conjugate points to a surface 272 273
connecting vector 117
Connection coefficients 77
Connection, compatibility with metric 84
Connection, spinor 166ff
Connection, vanishing of 83 84
Connector 68ff
Conservation laws 186 206ff 387
Constant curvature spaces 116 117 127 128
Contraction 36 47 58
Contravariant components 26 34
Coordinate system 17ff
Coordinate, Boyer — Lindquist 402 416
Coordinate, local 17
Coordinate, normal 83 107 108
Coordinate, right- and left-handed 45 48
Coordinate, standard in cosmology 374
Cosmic radiation 378
Cosmic time 374
Cosmological constant 384
Cosmological principle 373
Cosmology 372ff
Cotangent space 28 29
Covariant components 31 35 36
Covariant derivative see "Derivative"
Covector 29
Current density 229
Curvature tensor 104ff 143
Curvature tensor, number of components 107
Curvature tensor, symmetry properties 106
Curvature, Gaussian 108 116 128 322 375
Curvature, intrinsic 252
Curvature, invariants 332 401
Curvature, scalar 112
Curvature, sectional 108
Curvature, small curvature limit 306ff
Curvature, spatially projected 143
Curvature, spinor see "Spinors"
Curve 21
Curve, integral 62
D'alambertian 228 313
de Rham 228 231
Deceleration parameter 382
Decomposable r-forms 53
Degree of freedom see "Gauge transformations"
Derivative, absolute 78 79
Derivative, convective 63 68
Derivative, covariant of one-forms 79 80
Derivative, covariant of spinors 176
Derivative, covariant of tensors 81
Derivative, covariant of vectors 79
Derivative, covariant, application of 86ff
Derivative, exterior 88ff
Derivative, Lie 62ff
Determinant of a  matrix 49 53
Determinant of a k-rowed minor 49
Diffeomorphism 20 60 330
Differential forms 28ff 57
Dirac delta 199
Discontinuities of an electromagnetic field 232ff
Distance in cosmology (luminosity distance) 388
Distance, spatial 132 275 277
Dragging (gravitational) 243 406 408
Dual (Hodge) 50
Dual (Hodge) map 55
Dual (Hodge), right- left-dual 50
| Dual (Hodge), self-dual and anti-self-dual 157 171 181
Eddington 334 335
Eikonal equation 235 286 385
Einstein 11 116 191 193 260 354 384
Einstein complex 203 204
Einstein equations 191 193
Einstein equations in axial symmetry 390 391
Einstein equations in spherical symmetry 323 378
Einstein equations in tetrad forms 260ff
Einstein equations in the weak field limit 309 310 312 313
Einstein tensor 116
Einstein Universe 385
Einstein — Maxwell equations 358 421
Electrodynamics 230 231
Electromagnetic fields with charges and currents 228ff
Electromagnetic fields, free 227ff
Electromagnetic fields, measure of 298
Electromagnetic fields, null 235
Electromagnetic fields, polarization of 236
Electromagnetic fields, radiation field 231ff
Energy conditions 269
Energy density of a fluid 185 301ff
Energy density of an electromagnetic field 304
Energy extraction form a black-hole 409
Energy momentum tensor for Newtonian fluids 187
Energy momentum tensor in special relativity 187 188
Energy momentum tensor of a perfect fluid 195 197
Energy momentum tensor of a single particle 199 200 222
Energy momentum tensor of an electromagnetic field 200
Energy momentum tensor, pseudotensor 201 204 205
Energy of a particle 297 343 344
entropy 195 305 306
EQUIVALENCE see "Principle of"
Ergoregion-ergosphere 409
Ernst 391 424
Euclidean geometry 1 2
Euler equation 186 306
Eulerian coordinates 195
Evaporation of a black-hole 428
Event horizon 245 338 424
Event horizon, future and past 337 338
expansion 140 225 256
Expansion in the weak field limit 310
Expansion, isotropic (volumetric) 257
Exponential map 108
Exterior derivative 88ff
Exterior product 52 53
Extrinsic curvature 252 260
Fermi (Walker) transport 138 139 221
Fermi rotation coefficients 138 259
Fields (of vectors and tensors) 57ff
Fields, basis 58
Finkelstein 334 335
Fluids 185ff
Fluids, Newtonian 186 187
Fluids, perfect 195ff
Forms 51 52
Forms, integrable 94
Forms, irrotational 96
Forms, one-forms 57
Forms, r-forms 51
Forms, simple r-forms 52
Frames, freely falling 10
Frames, inertial 6
Frames, locally inertial 11
Frames, locally non-rotating 408
Frames, non-inertial 11
Frames, spin-entangled 160
Frames, tetrads see "Tetrads"
Fraser 7
frequency 286 385 427
Frequency, Doppler shift 287 386
Frequency, red-shift in cosmology 385 386
Frequency, shifts 286 287 357
Freud 204
Friedmann 320 378ff 384
Frobenius 90ff 241 245
Galileo 4ff
Galileo transformations 6 7
Gauge transformations in electromagnetic fields 200 227
Gauge transformations in the weak gravitational field limit 308ff
Gauge transformations, Lorentz in gravitational radiation theory 314
Gauge transformations, transverse traceless in gravitational radiation theory 314
Gauss equation 143 252
Gaussian curvature see "Curvature"
General covariance 11
General relativity 7 11
Geodesics 72 75
Geodesics, affine 76
Geodesics, deviation equation 117 258 351
Geodesics, null in the Kerr metric 418
Geodesics, null in the Schwarzschild metric 351
Geodesics, time-like and circular in the Kerr metric 406 414
Geodesics, time-like in the Schwarzschild metric 342ff
Geometrical optics 235
Geroch 271
Globally pseudo-Euclidean coordinates 110 111
Goldberg — Sachs theorem 406
Gravitation, equations of the field 191ff
Gravitation, surface gravity 249 427
Gravitation, weak gravitational field 306ff
Gravitational radiation 314
Gravitational red-shift 357
Green's function 119 231
Group,  146
Group, Lorentz 135ff 146ff
Group, rotation SO(3) 320
Hamilton — Jacobi equation 225 342 407
Harmonic function 315 390
Hausdorff 14 129 331
Hawking 271 426
Hawking radiation 426ff
Hermitian matrices 147
hilbert 192
Homeomorphism 17 21
Homogeneity of the Universe 373ff
Homomorphism 42 150 154
Homotopy 109
Horizon 245
Horizon, bifurcated 247 248
Horizon, event 245 338 339 354 363 403 404 426ff
Horizon, particle 383 385
Hubble 380 386 387
Hypersurface 21
Hypersurface, orthogonal see "Congruence"
Immersion 21
Inertial forces 6 9
Inertial frames 6
Inertial observer 6ff
Inflationary universe 385
Initial value problem 261
Integral curve 62
Irreducible mass see "Mass"
Isometries 99ff
Isomorphism 42 132 154 162
Isotropic coordinates 354
Isotropy of the Universe 373ff
Jacobi field 118
Jacobi identity 65 151 251
Jacobian 48
Kant 1
Kennedy — Thorndyke 7
Kerr 392ff
Kerr horizons 397 410 411 416 421
Kerr solution 397
Kerr — Killing one-forms 398
Kerr — Newman solution 421
Killing equations 99
Killing fields 99 125 126 225
Killing one-forms in conservation laws 209
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