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De Felice F., Clarke C.J.S. — Relativity on curved manifolds
De Felice F., Clarke C.J.S. — Relativity on curved manifolds

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Название: Relativity on curved manifolds

Авторы: De Felice F., Clarke C.J.S.

Аннотация:

General relativity is now essential to the understanding of modern physics, but the power of the theory cannot be exploited fully without a detailed knowledge of its mathematical structure. This book aims to implement this structure, and then to develop those applications that have been central to the growth of the theory.


Язык: en

Рубрика: Физика/Гравитационное взаимодействие/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 448

Добавлена в каталог: 15.08.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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
angular momentum      see "Momentum"
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 $n \times n$ 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, $SL(2, \mathbb{C})$      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
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