Verfügbarkeit: General relativity and the Einstein equations

General relativity and the Einstein equations:

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Bibliographische Detailangaben
Beteilige Person:	Choquet-Bruhat, Yvonne 1923-2025 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Oxford Oxford Univ. Press 2009
Ausgabe:	1. publ.
Schriftenreihe:	Oxford mathematical monographs
Schlagwörter:	Einstein-Feldgleichungen Allgemeine Relativitätstheorie
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016683902&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XXIV, 785 S. graph. Darst.
ISBN:	9780199230723

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Datensatz im Suchindex

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adam_text	CONTENTS I Lorentz geometry 1 1 Introduction 1 2 Manifolds 1 3 Differentiable mappings 2 4 Vectors and tensors 2 4.1 Tangent and cotangent space 2 4.2 Vector fields 3 4.3 Tensors and tensor fields 5 5 Pseudo-Riemannian metrics 6 5.1 General properties 6 5.2 Riemannian and Lorentzian metrics 8 6 Riemannian connection 9 7 Geodesies 12 8 Curvature 13 9 Geodesic deviation 14 10 Maximum of length and conjugate points 15 11 Linearized Ricci and Einstein tensors 17 12 Second derivative of the Ricci tensor 17 II Special Relativity 19 1 Newton's mechanics 19 1.1 The Galileo-Newton spacetime 19 1.2 Newton's dynamics - the Galileo group 20 2 Maxwell's equations 20 3 Minkowski spacetime 21 3.1 Definition 21 3.2 Maxwell's equations on Mą 22 4 Poincaré group 23 5 Lorentz group 24 5.1 General formulae 24 5.2 Transformation of electric and magnetic vector fields (case η = 3) 25 5.3 Lorentz contraction and dilatation 26 6 Special Relativity 26 6.1 Proper time 26 6.2 Proper frame and relative velocities 28 7 Dynamics of a pointlike mass 30 7.1 Newtonian law 30 Contents 7.2 Relativistic law ЗО 7.3 Equivalence of mass and energy 32 8 Continuous matter 33 8.1 Case of dust (incoherent matter) 34 8.2 Perfect fluids 35 III General relativity and Einstein's equations 37 1 Introduction 37 2 Newton's gravity law 37 3 General relativity 39 3.1 Physical motivations 39 4 Observations and experiments 40 4.1 Deviation of light rays 40 4.2 Proper time, gravitational time delay 40 5 Einstein's equations 42 5.1 Vacuum case 42 5.2 Equations with sources 43 6 Field sources 45 6.1 Electromagnetic sources 45 6.2 Electromagnetic potential 47 6.3 Yang-Mills fields 47 6.4 Scalar fields 49 6.5 Wave maps 49 6.6 Energy conditions 51 7 Lagrangians 51 7.1 Einstein-Hilbert Lagrangian 51 7.2 Lagrangians and stress energy tensors of sources 52 7.3 Coupled Lagrangian 53 8 Fluid sources 54 9 Einsteinian spacetimes 55 9.1 Definition 55 9.2 Regularity hypotheses 55 10 Newtonian approximation 57 10.1 Equations for potentials 57 10.2 Equations of motion 59 11 Gravitational waves 60 11.1 Minkowskian approximation 60 11.2 General linear waves 61 12 High-frequency gravitational waves 62 12.1 Phase and polarizations 64 12.2 Radiative coordinates 66 12.3 Energy conservation 68 13 Coupled electromagnetic and gravitational waves 68 Contents ix 13.1 Phase and polarizations 69 13.2 Propagation equations 69 IV Schwarzschild spacetime and black holes 72 1 Introduction 72 2 Spherically symmetric spacetimes 72 3 Schwarzschild metric 74 4 Other coordinates 75 4.1 Isotropie coordinates 75 4.2 Wave coordinates 76 4.3 Painlevé-Gullstr and-like coordinates 77 4.4 Regge-Wheeler coordinates 77 5 Schwarzschild spacetime 78 6 The motion of the planets and perihelion precession 78 6.1 Equations 78 6.2 Results of observations 81 6.3 Escape velocity 81 7 Stability of circular orbits 83 8 Deflection of light rays 84 8.1 Theoretical prediction 84 8.2 Results of observation 85 8.3 Fermat's principle and light travel parameter time 85 9 Red shift and time delay 86 10 Spherically symmetric interior solutions 87 10.1 Static solutions. Upper limit on mass 88 10.2 Matching with an exterior solution 91 10.3 Non-static solutions 91 11 The Schwarzschild black hole 92 11.1 The event horizon 92 11.2 The Eddington-Finkelstein extension 93 11.3 Eddington-Finkelstein white hole 94 11.4 Kruskal complete spacetime 94 11.5 Observations 96 12 Spherically symmetric gravitational collapse 96 12.1 Tolman metric 98 12.2 Monotonically decreasing density 101 13 The Reissner-Nordström solution 103 14 Schwarzschild spacetime in dimension η + 1 104 14.1 Standard coordinates 104 14.2 Wave coordinates 104 V Cosmology 106 1 Introduction 106 2 Cosmological principle 107 Contents 3 Isotropie and homogeneous Riemannian manifolds 108 3.1 Isotropy 108 3.2 Homogeneity 109 4 Robertson-Walker spacetimes 111 4.1 Space metrics 112 4.2 Robertson-Walker spacetime metrics 113 4.3 Robertson-Walker dynamics 113 4.4 Einstein static universe 115 4.5 Cosmological red shift and the Hubble constant 115 4.6 De Sitter spacetime 118 4.7 Anti de Sitter (AdS) spacetime 120 5 Friedmann-Lemaitre models. 121 5.1 Equation of state 121 5.2 General properties 122 5.3 Friedmann models 123 5.4 Some other models 124 5.5 Confrontation with observations 125 6 Homogeneous non-isotropic cosmologies 125 7 Bianchi class I universes 128 7.1 Kasner solutions 128 7.2 Models with matter 131 8 Bianchi type IX 132 9 The Kantowski-Sachs models 134 10 Taub and Taub NUT spacetimes 135 10.1 Taub spacetime 135 10.2 Taub NUT spacetime 136 11 Locally homogeneous models 136 11.1 n-dimensional compact manifolds 137 11.2 Compact 3-manifolds 139 12 Recent observations and conjectures 140 VI Local Cauchy problem 142 1 Introduction 142 2 Moving frame formulae 142 2.1 Frame and coframe 142 2.2 Metric 143 2.3 Connection 144 2.4 Curvature 145 3 η + 1 splitting adapted to space slices 146 3.1 Adapted frame and coframe 146 3.2 Structure coefficients 147 3.3 Splitting of the connection. 147 3.4 Extrinsic curvature 148 3.5 Splitting of the Riemann tensor 148 Contents 4 Constraints and evolution 149 4.1 Equations. Conservation of constraints 149 5 Hamiltonian and symplectic formulation 151 5.1 Hamilton equations 151 5.2 Symplectic formulation 154 6 Cauchy problem 155 6.1 Definitions 155 6.2 The analytic case 156 7 Wave gauges 157 7.1 Wave coordinates 158 7.2 Generalized wave coordinates 161 7.3 Damped wave coordinates 162 7.4 Globalization in space, ê wave gauges 162 7.5 Local in time existence in a wave gauge 164 8 Local existence for the full Einstein equations 166 8.1 Preservation of the wave gauges 166 8.2 Geometric local existence 168 8.3 Geometric uniqueness 168 8.4 Causality 170 9 Constraints in a wave gauge 172 10 Einstein equations with field sources 173 10.1 Maxwell constraints 174 10.2 Lorentz gauge 175 10.3 Existence and uniqueness theorems 176 10.4 Wave equation for F 177 VII Constraints 179 1 Introduction 179 2 Linearization and stability 180 2.1 Linearization of the constraints map, adjoint map 181 2.2 Linearization stability 183 3 CF (Conformally Formulated) constraints 186 3.1 Hamiltonian constraint 187 3.2 Momentum constraint 188 3.3 Scaling of the sources 189 3.4 Summary of results 194 3.5 Conformai transformation of the CF constraints 195 3.6 The momentum constraint as an elliptic system 197 4 Case η = 2 200 5 Solutions on compact manifolds 200 6 Solution of the momentum constraint 201 7 Lichnerowicz equation 204 7.1 The Yamabe classification 204 Contents 7.2 Non-existence and uniqueness 210 7.3 Existence theorems 211 8 System of constraints 217 8.1 Constant mean curvature τ, sources with York-scaled momentum 217 8.2 Solutions with τ φ. constant or Jq φ 0 218 9 Solutions on asymptotically Euclidean Manifolds 221 10 Momentum constraint 222 11 Solution of the Lichnerowicz equation 223 11.1 Uniqueness theorem 223 11.2 Generalized Brill-Cantor theorem 223 11.3 Existence theorems 226 12 Solutions of the system of constraints 229 12.1 Decoupled system 229 12.2 Coupled system 230 13 Gluing solutions of the constraint equations 232 13.1 Connected sum gluing 233 13.2 Exterior (Corvino-Schoen) gluing 235 VIII Other hyperbolic-elliptic well-posed systems 238 1 Introduction 238 2 Leray-Ohya non-hyperbolicity of ^Лц = 0 238 3 Wave equation for К 240 3.1 Hyperbolic system 240 3.2 Hyperbolic-elliptic system 242 4 Fourth-order non-strict and strict hyperbolic systems for g 243 5 First-order hyperbolic systems 243 5.1 FOSH systems 243 6 Bianchi-Einstein equations 244 6.1 Wave equation for the Riemann tensor 245 6.2 Case η = 3, FOS system 246 6.3 Cauchy-adapted frame 247 6.4 FOSH system for и = {E, H, D, B, g, ÜT, f) 250 6.5 Elliptic-hyperbolic system 250 7 Bel-Robinson tensor and energy 254 7.1 The Bel tensor 254 7.2 The Bel-Robinson tensor and energy 255 8 Bel-Robinson energy in a strip 256 IX Relativistic fluids 259 1 Introduction 259 2 Case of dust 260 2.1 Equations 260 Contents 2.2 Motion of isolated bodies (Choquet-Bruhat and Friedrichs 2006) 262 3 Charged dust 263 3.1 Equations 263 3.2 Existence and uniqueness theorem in wave and Lorentz gauges 264 3.3 Motion of isolated bodies 265 4 Perfect fluid, Euler equations 265 5 Energy properties 266 6 Particle number conservation 267 7 Thermodynamics 268 7.1 Definitions. Conservation of entropy 268 7.2 Equations of state 268 8 Wave fronts, propagation speeds, shocks 270 8.1 General definitions 270 8.2 Case of perfect fluids 272 8.3 Shocks 273 9 Stationary motion 274 10 Dynamic velocity for barotropic fluids 274 10.1 Fluid index and equations 274 10.2 Vorticity tensor and Helmholtz equations 276 10.3 Irrotational flows 277 11 General perfect fluids 278 12 Hyperbolic Leray system 279 12.1 Hyperbolicity of the Euler equations. 279 12.2 Reduced Einstein-Euler entropy system 280 12.3 Cauchy problem for the Einstein-Euler entropy system 281 12.4 Motion of isolated bodies 282 13 First-order symmetric hyperbolic system 282 14 Equations in a flow adapted frame 284 14.1 η + 1 splitting in a time adapted frame 285 14.2 Bianchi equations (case η = 3) 287 14.3 Vacuum case 287 14.4 Perfect fluid 288 14.5 Conclusion 290 15 Charged fluids 290 15.1 Equations 290 15.2 Fluids with zero conductivity 291 16 Fluids with finite conductivity 293 17 Magnetohydrodynamics 294 17.1 Equations 294 17.2 Wave fronts 295 18 Yang-Mills fluids 296 Contents 19 Dissipative fluids 297 19.1 Viscous fluids 297 19.2 The heat equation 300 X Relativistic kinetic theory 301 1 Introduction 301 2 Distribution function 302 2.1 Definition 302 2.2 Interpretation 303 2.3 Moments of the distribution function 304 3 Vlasov equations 307 3.1 Liouville- Vlasov equation. 307 3.2 Maxwell- Vlasov equation 310 3.3 Yang-Mills-Vlasov equation 311 3.4 Particles of a given rest mass 311 3.5 Conservation of moments 312 4 Cauchy problem for the Liouville- Vlasov equation 313 4.1 General solution 313 4.2 Distribution function on a Robertson-Walker space time 313 4.3 Energy estimates 314 4.4 Existence theorem 322 4.5 Stress energy tensor of a distribution function 323 5 The Einstein-Vlasov system 324 5.1 Constraints 324 5.2 Cauchy problem for the Einstein equations 325 5.3 Cauchy problem for the coupled system 325 6 The Einstein-Maxwell-Vlasov system 326 7 Boltzmann equation. Definitions 328 8 Moments and conservation laws 329 9 Einstein-Boltzmann system 331 10 Thermodynamics 331 10.1 Entropy and Я theorem 331 10.2 Maxwell-Jüttner equilibrium distribution 333 10.3 Dissipative fluids 334 11 Extended thermodynamics 334 11.1 The phenomenological 14 moments theory 335 11.2 Extended thermodynamics of moments 338 11.3 Maximum characteristic velocity 339 XI Progressive waves 341 1 Introduction 341 2 Quasilinear systems 342 3 Quasilinear first-order systems 343 3.1 Phase and polarization 343 3.2 Propagation equations 344 Contents 4 Progressive waves in relativistic fluids 348 4.1 Equations 348 4.2 Progressive waves 348 4.3 Phases and polarizations 349 4.4 Polarization and propagation of acoustic waves 351 4.5 Polarization and propagation of matter waves 354 4.6 "Gauge" gravitational waves 354 5 Quasilinear quasidiagonal second-order systems 354 5.1 Definitions 354 5.2 Hyperquasilinear systems with ƒ quadratic in Du 356 5.3 The null condition 358 6 Non quasidiagonal second-order systems 359 6.1 Phase and polarization 360 6.2 Propagation equations 360 7 Yang-Mills-scalar equations 361 7.1 Fields and equations 361 7.2 Phase and polarization 362 7.3 Propagation 363 8 Strong gravitational waves 364 8.1 Einstein equations 364 8.2 Phase and polarization 365 8.3 Propagation and back reaction 366 8.4 Example 368 XII Global hyperbolicity and causality 371 1 Introduction 371 2 Global existence of Lorentzian metrics 371 3 Time orientation 374 4 Futures and pasts 375 4.1 Paths and curves 375 4.2 Chronology and causality 375 5 Causal structure of Minkowski spacetime 377 6 Causal structures on general spacetimes 378 7 Geodesic coordinates, normal neighbourhoods 382 8 Topology on a space of paths 387 8.1 Rectifiable paths 387 8.2 Topology on sets of rectifiable paths 388 9 Global hyperbolicity 389 9.1 Definition and first criterion 389 9.2 Maximum of proper length 390 9.3 Images in V of subsets of V{x, y) 391 10 Strong and stable causalities 391 10.1 Strong causality 392 10.2 Stable causality 392 Contents 11 Cauchy surface 393 11.1 Domain of dependence. Cauchy horizon 393 11.2 Cauchy surface 394 11.3 Global existence of solutions of linear wave equations 397 11.4 Sufficient condition from analysis for global hyperbolicity 397 12 Globally hyperbolic Einsteinian spacetimes 399 12.1 Existence 399 12.2 Global uniqueness 399 12.3 Examples 400 13 Strong cosmic censorship 400 XIII Singularities 402 1 Introduction 402 2 Criteria for completeness or incompleteness 404 2.1 A completeness criterion 404 2.2 An incompleteness criterion 406 3 Congruence of timelike curves 408 3.1 Definitions 408 3.2 Geodesic deviation 410 3.3 Raychauduri equation 411 3.4 Null geodesic congruence 412 4 First singularity theorem 412 4.1 Conjugate points 412 4.2 Incompleteness theorem 414 5 Trapped surfaces and singularities 414 5.1 Trapped surfaces 414 5.2 Singularities linked to trapped surfaces 418 6 Black holes 418 6.1 Definitions 418 6.2 The Hawking area theorem 420 6.3 The Riemannian Penrose inequality. Case η = 3 420 7 Weak cosmic censorship conjectures 421 7.1 Naked singularity 421 7.2 Weak cosmic censorship 422 8 Spherically symmetric Einstein scalar equations 423 8.1 Spherically symmetric spacetimes 423 8.2 Einstein equations in adapted frame 424 8.3 Reduction to one integro-differential equation 425 8.4 Bondi mass 427 8.5 Global existence for small data 427 8.6 Existence of a global generalized solution for large data 429 Contents xvii 8.7 Structure of generalized solutions 432 8.8 Formation of a black hole. Cosmic censorship 433 8.9 Numerical results 434 8.10 Instability of naked singularities 434 9 Cosmological singularities. BKL conjecture 435 10 AVTD behaviour 441 10.1 Definitions 441 10.2 Fuchs theorem 441 11 Case of 1-parameter spatial isometry 443 11.1 Equations 443 11.2 VTD solutions of the 2 + 1 Einstein evolution equations 445 11.3 The polarized case 446 11.4 The unpolarized case 449 XIV Stationary spacetimes and black holes 451 1 Introduction 451 2 Spacetimes with 1-parameter isometry group 452 2.1 Connection and Riemann tensor 454 2.2 Curvature tensor 454 2.3 Ricci tensor 455 3 Stationary spacetimes 455 3.1 General case 455 3.2 Static spacetimes 457 4 Gravitational solitons 458 4.1 Elementary proofs 458 4.2 Case η = 3, Komar mass 460 5 Electrovac solitons 465 6 The Einstein-Yang-Mills case 466 7 Stationary black holes 466 7.1 Definitions 466 7.2 Axisymmetry 467 8 The rigidity theorem for black holes 469 9 The Kerr metric and black hole 471 9.1 Kerr metric in Boyer-Linquist coordinates 471 9.2 The Kerr-Schild spacetime 472 10 Uniqueness of stationary black holes (dimension 3+1) 474 10.1 Static black holes 475 10.2 Axisymmetric black holes 475 10.3 Uniqueness of the Kerr black hole 475 11 Further results 476 11.1 Multi black hole solutions 476 11.2 The Emparan-Reali "black rings" 478 Contents XV Global existence theorems asymptotically Euclidean data 482 1 Introduction 482 2 Global existence for small data via the Penrose map 483 2.1 Yang-Mills and associated equations 484 2.2 Quasi-linear wave equations 484 2.3 Cases η = 3, the null condition 487 2.4 Wave maps 488 3 H. Friedrich conformai system, η + 1 = 4 488 3.1 Equations 488 3.2 Friedrich hyperbolic system 490 4 Einstein's equations in higher dimensions 491 4.1 Conformai mapping 491 4.2 Transformed equations 492 4.3 Local Cauchy problem in iž™"1"1, n > 5 and odd 494 4.4 Global Cauchy problem 496 4.5 Conclusion 497 5 Christodoulou-Klainerman theorem 497 5.1 CK main theorem 497 5.2 Local existence 499 5.3 Global existence 500 6 The Klainerman-Nicolo theorem 504 7 The Linblad-Rodnianski theorem 505 7.1 The Einstein equations in wave coordinates 506 7.2 Initial data 507 7.3 Unknowns and norms 507 7.4 LR theorem 508 XVI Global existence theorems the cosmological case 510 1 Introduction 510 2 Gowdy cosmological models 511 3 S1 invariant Einsteinian universes, equations 514 3.1 Introduction 514 3.2 Definition 514 3.3 Equations 515 3.4 Twist potential 515 3.5 Wave map system 516 3.6 Three-dimensional Einstein equations 517 3.7 Teichmüller parameters. 520 4 S1 invariant Einstein universes, Cauchy problem 521 4.1 Cauchy data 521 4.2 Construction of A when F is known 522 Contenis xix 4.3 Local in time existence theorem 522 4.4 Global existence theorem 522 4.5 Future complete existence 526 4.6 Einstein-Maxwell-Higgs system 526 4.7 Conclusion 527 5 Andersson-Moncrief theorem 528 5.1 CMC gauge, elliptic system for N and К 529 5.2 SH gauge, elliptic system for g and β 529 5.3 The Bianchi equations 530 5.4 Existence theorems 531 5.5 Global existence theorem 532 6 Einstein non-linear scalar field system 533 APPENDICES I Sobolev spaces on Riemannian manifolds 534 1 Definitions 534 2 Embedding and multiplication properties 535 2.1 Open subsets of Rn 535 2.2 Riemannian manifolds 536 3 Weighted Sobolev spaces 537 3.1 Definitions 537 3.2 Embedding and multiplication properties 538 II Second-order elliptic systems on Riemannian manifolds 542 1 Linear elliptic systems 542 2 Linear elliptic systems on compact M 544 2.1 General second-order systems 544 2.2 Poisson operator 551 2.3 Conformai Laplace operator 552 3 Asymptotically Euclidean manifolds 553 3.1 Definitions 553 3.2 Second-order linear elliptic systems 554 4 Special systems 560 4.1 Poisson operator 560 4.2 Conformai Laplace operator 561 5 Equation ΔΊφ = f (x, φ), compact M 562 6 ΑΊφ = ƒ (χ, φ) on (M, 7) asymptotically Euclidean 567 ΠΙ Quasi-diagonal, quasi-linear, second-order hyperbolic systems 571 1 Introduction 571 2 Wave equation on (V,g) 571 2.1 Definitions 572 Contents IV V 2.2 Stress energy tensor. Energy momentum vector 572 2.3 Energy density 574 2.4 Energy equality on a compact domain 575 2.5 Energy inequality in a compact causal domain 578 2.6 Uniqueness theorem and causality 580 2.7 Case of a strip 581 2.8 Estimate of и 582 2.9 Cauchy problem 583 2.10 Generalizations 589 ! Quasidiagonal linear systems 590 3.1 Definitions 590 3.2 Stress energy tensor 590 3.3 Energy inequality in a compact causal domain 591 3.4 Case of a strip Vt 592 3.5 Existence, uniqueness, causality and continuity 594 3.6 Higher order estimates 594 3.7 Other hypotheses on g 600 3.8 Cauchy data in local spaces 601 і Quasilinear systems 604 4.1 Semilinear systems 604 4.2 Further results for semilinear equations 607 4.3 Quasilinear systems 608 5 Global I existence 613 5.1 Semilinear systems 613 5.2 Quasilinear equations 616 General hyperbolic systems 617 1 Introduction 617 2 Leray hyperbolic systems 617 2.1 Case of one equation 617 2.2 Leray hyperbolic systems 622 3 Leray-Ohya hyperbolic systems 624 4 First-order symmetric hyperbolic systems 625 4.1 FOSH systems on Rn+1 625 4.2 FOSH systems on a sliced manifold 627 Cauchy-Kovalevski and Fuchs theorems 631 1 Introduction 631 2 Cauchy-Kovalevski theorem 631 2.1 Linear system 631 2.2 Non-linear system 634 3 Fuchs theorem 634 3.1 Definitions 634 3.2 Theorem 636 Contents 3.3 Equivalence with an integral equation 637 3.4 Equivalence with another mapping 638 3.5 Convergence of iterations 641 3.6 Global in space theorem 642 VI Conformai methods 643 1 Introduction 643 2 Conformai metrics. Confomorphisms 643 2.1 Connections of conformai metrics 643 2.2 Riemann tensors of conformai metrics 644 2.3 Ricci tensors of conformai metrics 644 3 The Weyl tensor 645 4 Conformai transformations of field equations 646 4.1 Maxwell and Yang-Mills equations 646 5 Invariance of wave equations 647 6 Penrose transform 647 7 Einstein spaces with cosmological constant 650 7.1 Conformai transformation of De Sitter spacetime 650 7.2 Conformai transformation of anti-De Sitter spacetime 650 8 Asymptotically simple spacetimes 650 8.1 Conformai compactifications 650 8.2 Black holes 652 VII Kaluza-Klein theories 653 1 Introduction 653 2 Isometries 653 3 Kaluza-Klein metrics 654 3.1 Metric in adapted frame 654 3.2 Structure coefficients 655 3.3 Kaluza-Klein connection 656 4 Curvature tensor 657 5 Ricci tensor and K-K equations 659 6 Equations in conformai spacetime metric 660 RELATED PAPERS Causality of classical supergravity 665 Lecture Notes in Physics 1986, E. Flaherty ed. Springer. 61-84 Gravitation with gauss bonnet terms 689 Australian National University Publications, 1988 R. Bartnik ed. 53-72 xxii Contents Interaction of gravitational and fluid waves 709 In collaboration with A. Greco, Cericolo nat. di Paleruno 1994 Serie II n° 45, III. 123. Positive-energy theorems 723 Relativity, Group and Topology II, B. Dewitt and R. Stora ed. 742-786. REFERENCES 771 INDEX 781
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language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016683902
oclc_num	255254900
open_access_boolean
owner	DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-898 DE-BY-UBR DE-83 DE-91G DE-BY-TUM
owner_facet	DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-898 DE-BY-UBR DE-83 DE-91G DE-BY-TUM
physical	XXIV, 785 S. graph. Darst.
publishDate	2009
publishDateSearch	2009
publishDateSort	2009
publisher	Oxford Univ. Press
record_format	marc
series2	Oxford mathematical monographs
spellingShingle	Choquet-Bruhat, Yvonne 1923-2025 General relativity and the Einstein equations Einstein-Feldgleichungen (DE-588)4013941-4 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd
subject_GND	(DE-588)4013941-4 (DE-588)4112491-1
title	General relativity and the Einstein equations
title_auth	General relativity and the Einstein equations
title_exact_search	General relativity and the Einstein equations
title_full	General relativity and the Einstein equations Yvonne Choquet-Bruhat
title_fullStr	General relativity and the Einstein equations Yvonne Choquet-Bruhat
title_full_unstemmed	General relativity and the Einstein equations Yvonne Choquet-Bruhat
title_short	General relativity and the Einstein equations
title_sort	general relativity and the einstein equations
topic	Einstein-Feldgleichungen (DE-588)4013941-4 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd
topic_facet	Einstein-Feldgleichungen Allgemeine Relativitätstheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016683902&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT choquetbruhatyvonne generalrelativityandtheeinsteinequations

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