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Choquet-Bruhat Y. — General Relativity and the Einstein Equations
Choquet-Bruhat Y. — General Relativity and the Einstein Equations



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Название: General Relativity and the Einstein Equations

Автор: Choquet-Bruhat Y.

Аннотация:

General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with a manifold of dimensions possibly greater than four and debatable topology opening a vast field of investigation for mathematicians and physicists alike. Remarkable conjectures have been proposed, many results have been obtained but many fundamental questions remain open. In this monograph, aimed at researchers in mathematics and physics, the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2009

Количество страниц: 812

Добавлена в каталог: 08.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abstract index notation      4
Acausal      376
Achronal      376 393
ADM equations      156
Alfven cone      295
Alfven waves      295
Algebraic identity      13
Anti de Sitter spacetime      120
Apparent horizon      417 419
Aspherical      138
Asymptotically Euclidean manifold      221
Asymptotically Euclidean manifold with boundary      460
Asymptotically Euclidean manifold with non-compact interior      460
Asymptotically strongly predictable      419
Asymptotically Velocity Term Dominated (AVTD)      403
Atlas      1
Axisymmetric      467
Bach tensor      498
Back reaction      358
Barotropic fluids      54
Beginning and age of the universe      122
Behaviour with increasing t      123
Bel tensor      254 255 530
Bel — Robinson energy      256 530
Belinskii, Khalatnikov, and Lifshitz (BKL) conjecture in Iwasawa variables      440
Bianchi classification      127
Bianchi identity      13
Bianchi models      126
Birkhoff theorem      75
Black hole region $\beta$      419
Bondi mass      427
Bounded curvature conjecture      615
Canonical choice      575
Carter — Robinson theorem      475
Cattaneo — Ferrarese frame      285
Cauchy adapted frame      146
Cauchy horizon      394
Cauchy regular      622
Cauchy surface      371 394
Causal future      376
Causal structure      374 377
Causal subset      170 578
Causal vector      9
Characteristic cone      618
Characteristic determinant      622
Characteristic equation      344
Characteristic tangent vectors      618
Chart      1
Christoffel symbols      11
Chronological past      376
Circular spacetimes      468
Codazzi tensors      529
Codifferential operator      11
Comoving/proper frame      34
Compact towards the past      620
Complete Riemannian manifold      372
Cone property      535
conformal      660
Conformal Killing fields      203
Conformal thin sandwich      198
Connection      656
Connection coefficients      10 656
Conservation laws      146
Conservation of energy      581
Continuity equation      260
Contracted Bianchi identity      14
Contracted product      5
Contravariant tensor      5
Cosmic censorship conjecture      103
Cosmic time      107
Cosmological constant      192
Cosmological principle      107
Cotangent space      3
Coton tensor      498 646
Covariant derivative      9 10
Covariant differential      50
Covariant tensor      5
Covariant vectors      3
Cronstroem gauge      615
Curvature      656
Curvature tensor      13
Curve      375 389
Damped wave coordinates      162
de Sitter spacetime      118
Deceleration parameter      117
Degenerate horizon      477
Degree of symmetry      137
Density parameter      125
Derivation      4
Derivation formula      62
Development      156 400
Differentiable manifold      1
Distortion of signals      347
Distribution function      302
Domain of dependence      394
Domain of dependence property      620
Domain of outer communications      477
Dominant energy condition      51 267
Double null foliation      504
Dual frames      3
Dust      54
Eikonal      270 618
Einstein equations      43
Einstein equations in vacuum      43
Einstein static universe      115
Einstein tensor      14 145
Einstein — de Sitter universe      123
Einstein — Yang — Mills solitons      466
Einsteinian development      156
electromagnetic field      45
Ellipticity constant      242
END      537
End point      375
Energy equality      577 626
Energy estimate      626
Energy functional      626
Energy inequality      318 626
Energy momentum vector      31 267
Equation of state      54
Ergosphere      473
Euclidean at infinity      537
Euclidean space      537
Euclidean space form      138
Euler equations      266
Event horizon      92 419 652
Exceptional characteristic manifolds      346
Exceptionality condition      65 357
expansion      409
Exponential mapping      383
Extendible      375
Exterior derivative      6
Exterior global smallness condition      504
Exterior p-form      6
Extrinsic curvature      147
Family of timelike geodesics parametrized      410
Final Bondi mass      433
First moment      305
First variation      17
First-order symmetric hyperbolic (FOSH) systems      244 617 628
Fisher — Marsden criterion      185
Flat space      8
Flat type      138
Fluid source      259
Frame      4
Friedman equation      114
Friedmann — Lemaitre models      122
Friedrich conformal system      490
Fundamental observers      107
Fundamental subsets      378
future      9
Future completeness      404
Galileo group      20
Gauss formula      456
Generalized null condition      359
Genus      139
Geodesic      12
Geodesic congruence      410
Geodesic coordinates      383
Geodesic deviation      15 411
Geodesic motion      260
Gevrey classes      624
Gevrey index      624
Global hyperbolicity      371 620
Gravitational collapse      92
Gravitational lens      39
Gravitational wave      60
Gromwall lemma      580
H-energy      316
Half polarization      450
Hall effect      46
Hamiltonian constraint      179 194
Harmonic map      50
Harmonic/wave coordinates      61 158
Harmonically flat at infinity      420
Hausdorf manifolds      2
High-frequency wave      62 342
Higher moments      306
Higher order covariant derivatives      50
Hodge adjoint      11
Homogeneous      109
Homogeneous cosmology      125
Hopf — Rinow theorem      372
Hubble constant      116
Hubble law      117
Hyperbolic at      618
Hyperbolic polynomial      618
Hyperbolic space form      138
Hyperbolic system      617
Hyperbolic type      138
Hyperboliques non strictes      624
Incompressible fluid      273
Inertial frames      20
Infinite conductivity      294 297
Initial data set      156
Irrotational      408
Isometry      7 653
Israel theorem      475
Iwasawa decomposition      438
Jordan decomposition      635
Kantowski — Sachs      136
Kasner exponents      130
Kasner spacetimes      128
Killing horizon      477
Kirchhoff — Sobolev formula      615
Komar mass      460
Kretschmann scalar      93 472
Lanczos identity      254
Landau — Lifshitz pseudo tensor      464
Lapse      146
Lemaitre      124
Length      7
Leray — Ohya hyperbolic      624
Leray-hyperbolic system      617 622
Lichnerowicz equation      189
Lie derivative      6
Linearization      17
Linearization stable      181
Liouville — Vlasov equation      307 310
Local $H_{S}(V)$ metrics      56
Local coordinates      1
Local energy inequality      579
Locally isometric      8
Locally rotationally symmetric (LRS)      126 135
Lorentz condition      47
Lorentz contraction      26
Lorentz dilatation      26
Lorentz force      23
Lorentz group      24
Lorentzian manifold      374
Lorentzian metric      8 143
Magnetoacoustic wave fronts      295
Magnetohydrodynamics      46
Majumdar — Papapetrou solutions      476
Manifold      55
Mass hyperboloid      303
Maximal      400
Maxwell tensor      263
Maxwell — Juettner distributions      334
Maxwell’s equations      45
Mean curvature      147
Michelson — Morley experiments      29
Milne universe      124
Moessbauer resonant effect      41
Momentum constraint      179 194
Moncrief theorem      184
Multiplication property      536
Naked singularity      421
Natural coframe      3
Natural frame      3
Navier — Stokes equations      298
No naked singularity conjecture      422
Normal geodesic coordinates      384
Normal neighbourhood      384
Null average ansatz      63
Null condition      358
Null cone      432
Null dust      260
Null mean curvatures      415
Null structure      502
Null vector      9
Optical function      502
Orbit      653
Orientable      2
Orthochronous      24
Orthonormal Lorentzian frames      8
Paracompact      371
Parallel transport      12
PAST      9
Path/parametrized curve      375
Penrose confomorphism      647
Penrose process      474
Perfect fluid      35 54
Phase space      302
Piecewise differentiable      375
Poincare group      23
Poincare inequality      541
Polarization condition      60 64 69 344 360
Polarization operator      365
Polarization vector      350
Polarized case      443
Polarized exceptionality condition      361
Polarized null condition      361
Principle of general covariance      39
Progressive wave      62 342
Propagation equation      361
Propagation speed      271
Proper frame      28 259 265
Proper time      26 39
Pseudo norm      7
Pseudo-Riemannian metric      6
Pullback      5
Quasidiagonal by blocks      623
Quasidiagonalisation      622
Rankine — Hugoniot equations      274
Raychauduri equation      411
Red shift      41
Red shift parameter      115
Regular      432
Regular vector field      372
Regularly asymptotically      419
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