General relativity:
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| Sprache: | English |
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Dordrecht [u.a.]
Springer
2013
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| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate texts in physics
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| Beschreibung: | XIX, 735 S. graph. Darst. |
| ISBN: | 9789400754096 |
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| 100 | 1 | |a Straumann, Norbert |d 1936- |e Verfasser |0 (DE-588)134199545 |4 aut | |
| 245 | 1 | 0 | |a General relativity |c Norbert Straumann |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Dordrecht [u.a.] |b Springer |c 2013 | |
| 300 | |a XIX, 735 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
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| 650 | 0 | 7 | |a Allgemeine Relativitätstheorie |0 (DE-588)4112491-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Relativistische Astrophysik |0 (DE-588)4121581-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804149684247199744 |
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| adam_text | Titel: General relativity
Autor: Straumann, Norbert
Jahr: 2013
Contents
Part I The General Theory of Relativity
1 Introduction...............
Physics in External Gravitational Fields................ 7
2.1 Characteristic Properties of Gravitation............... 7
2.1.1 Strength of the Gravitational Interaction .......... 7
2.1.2 Universality of Free Fall................... 8
2.1.3 Equivalence Principle.................... 9
2.1.4 Gravitational Red-and Blueshifts.............. 10
2.2 Special Relativity and Gravitation.................. 12
2.2.1 Gravitational Redshift and Special Relativity........ 12
2.2.2 Global Inertial Systems Cannot Be Realized in the
Presence of Gravitational Fields............... 13
2.2.3 Gravitational Deflection of Light Rays........... 14
2.2.4 Theories of Gravity in Flat Spacetime............ 14
2.2.5 Exercises........................... 18
2.3 Spacetime as a Lorentzian Manifold................. 19
2.4 Non-gravitational Laws in External Gravitational Fields...... 21
2.4.1 Motion of a Test Body in a Gravitational Field....... 22
2.4.2 World Lines of Light Rays.................. 23
2.4.3 Exercises........................... 23
2.4.4 Energy and Momentum Conservation in the Presence of
an External Gravitational Field............... 25
2.4.5 Exercises........................... 27
2.4.6 Electrodynamics....................... 28
2.4.7 Exercises........................... 31
2.5 The Newtonian Limit........................ 32
2.5.1 Exercises........................... 33
2.6 The Redshift in a Stationary Gravitational Field.......... 34
2.7 Fermat s Principle for Static Gravitational Fields.......... 35
2.8 Geometric Optics in Gravitational Fields.............. 38
2.8.1 Exercises........................... 42
2.9 Stationary and Static Spacetimes.................. 42
2.9.1 Killing Equation....................... 44
2.9.2 The Redshift Revisited.................... 45
2.10 Spin Precession and Fermi Transport................ 48
2.10.1 Spin Precession in a Gravitational Field........... 49
2.10.2 Thomas Precession ..................... 50
2.10.3 Fermi Transport....................... 51
2.10.4 The Physical Difference Between Static and Stationary
Fields............................. 53
2.10.5 Spin Rotation in a Stationary Field............. 55
2.10.6 Adapted Coordinate Systems for Accelerated Observers . . 56
2.10.7 Motion of a Test Body.................... 58
2.10.8 Exercises........................... 60
2.11 General Relativistic Ideal Magnetohydrodynamics......... 62
2.11.1 Exercises........................... 63
Einstein s Field Equations........................ 65
3.1 Physical Meaning of the Curvature Tensor............. 65
3.1.1 Comparison with Newtonian Theory............ 69
3.1.2 Exercises........................... 69
3.2 The Gravitational Field Equations.................. 72
3.2.1 Heuristic Derivation of the Field Equations........ 73
3.2.2 The Question of Uniqueness................. 74
3.2.3 Newtonian Limit, Interpretation of the Constants A and k . 78
3.2.4 On the Cosmological Constant A.............. 79
3.2.5 The Einstein-Fokker Theory ................ 82
3.2.6 Exercises........................... 82
3.3 Lagrangian Formalism........................ 84
3.3.1 Canonical Measure on a Pseudo-Riemannian Manifold . . 84
3.3.2 The Einstein-Hilbert Action................. 85
3.3.3 Reduced Bianchi Identity and General Invariance ..... 87
3.3.4 Energy-Momentum Tensor in a Lagrangian Field Theory . 89
3.3.5 Analogy with Electrodynamics............... 92
3.3.6 Meaning of the Equation V • T = 0............. 94
3.3.7 The Equations of Motion and V • T = 0........... 94
3.3.8 Variational Principle for the Coupled System........ 95
3.3.9 Exercises........................... 95
3.4 Non-localizability of the Gravitational Energy........... 97
3.5 On Covariance and Invariance.................... 98
3.5.1 Note on Unimodular Gravity ................ 101
3.6 The Tetrad Formalism........................ 102
3.6.1 Variation of Tetrad Fields.................. 103
3.6.2 The Einstein-Hilbert Action................. 104
3.6.3 Consequences of the Invariance Properties of the
Lagrangian C ........................ 107
3.6.4 Lovelock s Theorem in Higher Dimensions......... 110
3.6.5 Exercises........................... Ill
3.7 Energy, Momentum, and Angular Momentum for Isolated Systems 112
3.7.1 Interpretation......................... 116
3.7.2 ADM Expressions for Energy and Momentum....... 119
3.7.3 Positive Energy Theorem.................. 121
3.7.4 Exercises........................... 122
3.8 The Initial Value Problem of General Relativity .......... 124
3.8.1 Nature of the Problem.................... 124
3.8.2 Constraint Equations..................... 125
3.8.3 Analogy with Electrodynamics............... 126
3.8.4 Propagation of Constraints ................. 127
3.8.5 Local Existence and Uniqueness Theorems......... 128
3.8.6 Analogy with Electrodynamics............... 128
3.8.7 Harmonic Gauge Condition................. 130
3.8.8 Field Equations in Harmonic Gauge............. 130
3.8.9 Characteristics of Einstein s Field Equations........ 135
3.8.10 Exercises........................... 136
3.9 General Relativity in 3 + 1 Formulation............... 137
3.9.1 Generalities......................... 138
3.9.2 Connection Forms...................... 139
3.9.3 Curvature Forms, Einstein and Ricci Tensors........ 142
3.9.4 Gaussian Normal Coordinates................ 145
3.9.5 Maximal Slicing....................... 146
3.9.6 Exercises........................... 147
3.10 Domain of Dependence and Propagation of Matter Disturbances . . 147
3.11 Boltzmann Equation in GR..................... 149
3.11.1 One-Particle Phase Space, Liouville Operator for Geodesic
Spray............................. 149
3.11.2 The General Relativistic Boltzmann Equation ....... 153
Part II Applications of General Relativity
4 The Schwarzschild Solution and Classical Tests of General Relativity 157
4.1 Derivation of the Schwarzschild Solution.............. 157
4.1.1 The Birkhoff Theorem.................... 161
4.1.2 Geometric Meaning of the Spatial Part of the
Schwarzschild Metric.................... 164
4.1.3 Exercises........................... 164
4.2 Equation of Motion in a Schwarzschild Field............ 166
4.2.1 Exercises........................... 169
4.3 Perihelion Advance......................... 170
4.4 Deflection of Light.......................... 174
4.4.1 Exercises........................... 178
4.5 Time Delay of Radar Echoes .................... 180
4.6 Geodetic Precession......................... 184
4.7 Schwarzschild Black Holes..................... 187
4.7.1 The Kruskal Continuation of the Schwarzschild Solution . 188
4.7.2 Discussion.......................... 194
4.7.3 Eddington-Finkelstein Coordinates............. 197
4.7.4 Spherically Symmetric Collapse to a Black Hole...... 199
4.7.5 Redshift for a Distant Observer............... 201
4.7.6 Fate of an Observer on the Surface of the Star....... 204
4.7.7 Stability of the Schwarzschild Black Hole......... 207
4.8 Penrose Diagram for Kruskal Spacetime.............. 207
4.8.1 Conformal Compactification of Minkowski Spacetime . . . 208
4.8.2 Penrose Diagram for Schwarzschild-Kruskal Spacetime . . 210
4.9 Charged Spherically Symmetric Black Holes............ 211
4.9.1 Resolution of the Apparent Singularity........... 211
4.9.2 Timelike Radial Geodesies ................. 214
4.9.3 Maximal Extension of the Reissner-Nordstr0m Solution . . 216
Appendix: Spherically Symmetric Gravitational Fields....... 220
4.10.1 General Form of the Metric................. 220
4.10.2 The Generalized Birkhoff Theorem............. 224
4.10.3 Spherically Symmetric Metrics for Fluids.......... 225
4.10.4 Exercises........................... 226
5 Weak Gravitational Fields........................227
5.1 The Linearized Theory of Gravity..................227
5.1.1 Generalization........................230
5.1.2 Exercises...........................233
5.2 Nearly Newtonian Gravitational Fields...............234
5.2.1 Gravitomagnetic Field and Lense-Thirring Precession . . . 235
5.2.2 Exercises...........................236
5.3 Gravitational Waves in the Linearized Theory ...........237
5.3.1 Plane Waves......................... 238
5.3.2 Transverse and Traceless Gauge............... 239
5.3.3 Geodesic Deviation in the Metric Field of a Gravitational
Wave............................. 240
5.3.4 A Simple Mechanical Detector............... 242
5.4 Energy Carried by a Gravitational Wave .............. 245
5.4.1 The Short Wave Approximation...............246
5.4.2 Discussion of the Linearized Equation R$ [h] - 0.....248
5.4.3 Averaged Energy-Momentum Tensor for Gravitational
Waves............................ 250
5.4.4 Effective Energy-Momentum Tensor for a Plane Wave ... 252
5.4.5 Exercises........................... 253
5.5 Emission of Gravitational Radiation................. 256
5.5.1 Slow Motion Approximation................ 256
5.5.2 Rapidly Varying Sources ..................259
5.5.3 Radiation Reaction (Preliminary Remarks).........261
5.5.4 Simple Examples and Rough Estimates...........261
5.5.5 Rigidly Rotating Body....................261
5.5.6 Radiation from Binary Star Systems in Elliptic Orbits . . . 266
5.5.7 Exercises...........................269
5.6 Laser Interferometers........................270
5.7 Gravitational Field at Large Distances from a Stationary Source . . 272
5.7.1 The Komar Formula.....................278
5.7.2 Exercises...........................280
5.8 Gravitational Lensing........................280
5.8.1 Three Derivations of the Effective Refraction Index .... 281
5.8.2 Deflection by an Arbitrary Mass Concentration.......283
5.8.3 The General Lens Map ...................286
5.8.4 Alternative Derivation of the Lens Equation........288
5.8.5 Magnification, Critical Curves and Caustics ........290
5.8.6 Simple Lens Models.....................292
5.8.7 Axially Symmetric Lenses: Generalities ..........292
5.8.8 The Schwarzschild Lens: Microlensing...........295
5.8.9 Singular Isothermal Sphere.................298
5.8.10 Isothermal Sphere with Finite Core Radius.........300
5.8.11 Relation Between Shear and Observable Distortions .... 300
5.8.12 Mass Reconstruction from Weak Lensing..........301
The Post-Newtonian Approximation..................307
6.1 Motion and Gravitational Radiation (Generalities).........307
6.1.1 Asymptotic Flatness..................... 308
6.1.2 Bondi-Sachs Energy and Momentum............ 309
6.1.3 The Effacement Property.................. 311
6.2 Field Equations in Post-Newtonian Approximation......... 312
6.2.1 Equations of Motion for a Test Particle........... 319
6.3 Stationary Asymptotic Fields in Post-Newtonian Approximation . 320
6.4 Point-Particle Limit......................... 322
6.5 The Einstein-Infeld-Hoffmann Equations ............. 326
6.5.1 The Two-Body Problem in the Post-Newtonian
Approximation........................329
6.6 Precession of a Gyroscope in the Post-Newtonian Approximation . 335
6.6.1 Gyroscope in Orbit Around the Earth............ 338
6.6.2 Precession of Binary Pulsars ................ 339
6.7 General Strategies of Approximation Methods........... 340
6.7.1 Radiation Damping..................... 345
6.8 Binary Pulsars............................ 346
6.8.1 Discovery and Gross Features................346
6.8.2 Timing Measurements and Data Reduction.........351
6.8.3 Arrival Time.........................351
6.8.4 Solar System Corrections.................. 352
6.8.5 Theoretical Analysis of the Arrival Times.......... 354
6.8.6 Einstein Time Delay..................... 355
6.8.7 Roemer and Shapiro Time Delays.............. 356
6.8.8 Explicit Expression for the Roemer Delay ......... 359
6.8.9 Aberration Correction.................... 361
6.8.10 The Timing Formula..................... 363
6.8.11 Results for Keplerian and Post-Keplerian Parameters . . . . 366
6.8.12 Masses of the Two Neutron Stars.............. 366
6.8.13 Confirmation of the Gravitational Radiation Damping . . . 367
6.8.14 Results for the Binary PSRB 1534+12........... 369
6.8.15 Double-Pulsar........................ 372
White Dwarfs and Neutron Stars.................... 375
7.1 Introduction............................. 375
7.2 White Dwarfs ............................ 377
7.2.1 The Free Relativistic Electron Gas............. 378
7.2.2 Thomas-Fermi Approximation for White Dwarfs ..... 379
7.2.3 Historical Remarks ..................... 383
7.2.4 Exercises........................... 384
7.3 Formation of Neutron Stars..................... 385
7.4 General Relativistic Stellar Structure Equations........... 387
7.4.1 Interpretation of M ..................... 390
7.4.2 General Relativistic Virial Theorem............. 391
7.4.3 Exercises........................... 392
7.5 Linear Stability ........................... 392
7.6 The Interior of Neutron Stars.................... 395
7.6.1 Qualitative Overview.................... 395
7.6.2 Ideal Mixture of Neutrons, Protons and Electrons ..... 397
7.6.3 Oppenheimer-Volkoff Model................ 399
7.6.4 Pion Condensation...................... 400
7.7 Equation of State at High Densities................. 401
7.7.1 Effective Nuclear Field Theories.............. 401
7.7.2 Many-Body Theory of Nucleon Matter........... 401
7.8 Gross Structure of Neutron Stars.................. 402
7.8.1 Measurements of Neutron Star Masses Using Shapiro
Time Delay ......................... 404
7.9 Bounds for the Mass of Non-rotating Neutron Stars ........ 405
7.9.1 Basic Assumptions...................... 405
7.9.2 Simple Bounds for Allowed Cores............. 408
7.9.3 Allowed Core Region.................... 408
7.9.4 Upper Limit for the Total Gravitational Mass........ 410
7.10 Rotating Neutron Stars........................ 412
7.11 Cooling of Neutron Stars ...................... 415
7.12 Neutron Stars in Binaries ...................... 416
7.12.1 Some Mechanics in Binary Systems............. 416
7.12.2 Some History of X-Ray Astronomy............. 419
7.12.3 X-Ray Pulsars........................ 420
7.12.4 The Eddington Limit..................... 422
7.12.5 X-Ray Bursters ....................... 423
7.12.6 Formation and Evolution of Binary Systems........ 425
7.12.7 Millisecond Pulsars..................... 427
8 Black Holes................................ 429
8.1 Introduction............................. 429
8.2 Proof of Israel s Theorem...................... 430
8.2.1 Foliation of 17, Ricci Tensor, etc............... 431
8.2.2 The Invariant(4)RapY8{4)Ra/iyS............... 434
8.2.3 The Proof (W Israel, 1967)................. 435
8.3 Derivation of the Kerr Solution................... 442
8.3.1 Axisymmetric Stationary Spacetimes............ 443
8.3.2 Ricci Circularity....................... 444
8.3.3 Footnote: Derivation of Two Identities........... 446
8.3.4 The Ernst Equation ..................... 447
8.3.5 Footnote: Derivation of Eq. (8.90).............. 449
8.3.6 Ricci Curvature....................... 450
8.3.7 Intermediate Summary.................... 455
8.3.8 Weyl Coordinates...................... 455
8.3.9 Conjugate Solutions..................... 458
8.3.10 Basic Equations in Elliptic Coordinates........... 459
8.3.11 The Kerr Solution...................... 462
8.3.12 Kerr Solution in Boyer-Lindquist Coordinates....... 464
8.3.13 Interpretation of the Parameters a and m.......... 465
8.3.14 Exercises........................... 467
8.4 Discussion of the Kerr-Newman Family .............. 467
8.4.1 Gyromagnetic Factor of a Charged Black Hole....... 468
8.4.2 Symmetries of the Metric.................. 470
8.4.3 Static Limit and Stationary Observers............ 470
8.4.4 Killing Horizon and Ergosphere............... 471
8.4.5 Coordinate Singularity at the Horizon and Kerr Coordinates 475
8.4.6 Singularities of the Kerr-Newman Metric.......... 476
8.4.7 Structure of the Light Cones and Event Horizon...... 476
8.4.8 Penrose Mechanism..................... 477
8.4.9 Geodesies of a Kerr Black Hole............... 478
8.4.10 The Hamilton-Jacobi Method................ 478
8.4.11 The Fourth Integral of Motion................ 480
8.4.12 Equatorial Circular Geodesies................ 482
8.5 Accretion Tori Around Kerr Black Holes.............. 485
8.5.1 Newtonian Approximation ................. 486
8.5.2 General Relativistic Treatment............... 488
8.5.3 Footnote: Derivation of Eq. (8.276)............. 490
8.6 The Four Laws of Black Hole Dynamics.............. 491
8.6.1 General Definition of Black Holes ............. 491
8.6.2 The Zeroth Law of Black Hole Dynamics.......... 492
8.6.3 Surface Gravity....................... 492
8.6.4 The First Law........................ 495
8.6.5 Surface Area of Kerr-Newman Horizon .......... 495
8.6.6 The First Law for the Kerr-Newman Family........ 496
8.6.7 The First Law for Circular Spacetimes........... 497
8.6.8 The Second Law of Black Hole Dynamics......... 502
8.6.9 Applications......................... 503
8.7 Evidence for Black Holes...................... 505
8.7.1 Black Hole Formation.................... 505
8.7.2 Black Hole Candidates in X-Ray Binaries ......... 507
8.7.3 The X-Ray Nova XTEJ118+480.............. 508
8.7.4 Super-Massive Black Holes................. 509
Appendix: Mathematical Appendix on Black Holes ........ 511
8.8.1 Proof of the Weak Rigidity Theorem............ 511
8.8.2 The Zeroth Law for Circular Spacetimes.......... 512
8.8.3 Geodesic Null Congruences................. 514
8.8.4 Optical Scalars........................ 515
8.8.5 Transport Equation ..................... 516
8.8.6 The Sachs Equations..................... 519
8.8.7 Applications......................... 520
8.8.8 Change of Area....................... 522
8.8.9 Area Law for Black Holes.................. 525
9 The Positive Mass Theorem.......................527
9.1 Total Energy and Momentum for Isolated Systems.........528
9.2 Witten s Proof of the Positive Energy Theorem...........531
9.2.1 Remarks on the Witten Equation.............. 534
9.2.2 Application ......................... 534
9.3 Generalization to Black Holes.................... 535
9.4 Penrose Inequality.......................... 537
9.4.1 Exercises........................... 538
Appendix: Spin Structures and Spinor Analysis in General
Relativity............................... 538
9.5.1 Spinor Algebra........................538
9.5.2 Spinor Analysis in GR....................542
9.5.3 Exercises...........................545
10 Essentials of Friedmann-Lemaitre Models...............547
10.1 Introduction.............................547
10.2 Friedmann-Lemaitre Spacetimes..................549
10.2.1 Spaces of Constant Curvature................550
10.2.2 Curvature of Friedmann Spacetimes.............551
10.2.3 Einstein Equations for Friedmann Spacetimes.......551
10.2.4 Redshift...........................553
10.2.5 Cosmic Distance Measures.................555
10.3 Thermal History Below 100 MeV..................557
10.3.1 Overview...........................557
10.3.2 Chemical Potentials of the Leptons.............558
10.3.3 Constancy of Entropy....................559
10.3.4 Neutrino Temperature....................561
10.3.5 Epoch of Matter-Radiation Equality.............562
10.3.6 Recombination and Decoupling...............563
10.4 Luminosity-Redshift Relation for Type la Supernovae.......565
10.4.1 Theoretical Redshift-Luminosity Relation .........566
10.4.2 Type la Supernovae as Standard Candles..........570
10.4.3 Results............................572
10.4.4 Exercises...........................573
Part III Differential Geometry
11 Differentiable Manifolds.........................579
12 Tangent Vectors, Vector and Tensor Fields...............585
12.1 The Tangent Space..........................585
12.2 Vector Fields.............................592
12.3 Tensor Fields.............................594
13 The Lie Derivative............................599
13.1 Integral Curves and Flow of a Vector Field.............599
13.2 Mappings and Tensor Fields.....................601
13.3 The Lie Derivative..........................603
13.3.1 Local Coordinate Expressions for Lie Derivatives.....604
14 Differential Forms............................607
14.1 Exterior Algebra........................... 607
14.2 Exterior Differential Forms..................... 609
14.2.1 Differential Forms and Mappings.............. 610
14.3 Derivations and Antiderivations................... 611
14.4 The Exterior Derivative....................... 613
14.4.1 Morphisms and Exterior Derivatives ............ 615
14.5 Relations Among the Operators d, ix and Lx ........... 615
14.5.1 Formula for the Exterior Derivative............. 616
14.6 The *-Operation and the Codifferential............... 617
14.6.1 Oriented Manifolds..................... 617
14.6.2 The *-Operation....................... 618
14.6.3 Exercises........................... 619
14.6.4 The Codifferential...................... 622
14.6.5 Coordinate Expression for the Codifferential........ 623
14.6.6 Exercises........................... 624
14.7 The Integral Theorems of Stokes and Gauss............624
14.7.1 Integration of Differential Forms..............624
14.7.2 Stokes Theorem......................626
14.7.3 Application.........................627
14.7.4 Expression for div qX in Local Coordinates........628
14.7.5 Exercises..........................629
15 Affine Connections............................631
15.1 Covariant Derivative of a Vector Field...............631
15.2 Parallel Transport Along a Curve .................633
15.3 Geodesies, Exponential Mapping and Normal Coordinates .... 635
15.4 Covariant Derivative of Tensor Fields...............636
15.4.1 Application......................... 638
15.4.2 Local Coordinate Expression for the Covariant Derivative 639
15.4.3 Covariant Derivative and Exterior Derivative....... 640
15.5 Curvature and Torsion of an Affine Connection, Bianchi Identities 640
15.6 Riemannian Connections...................... 643
15.6.1 Local Expressions..................... 645
15.6.2 Contracted Bianchi Identity................ 647
15.7 The Cartan Structure Equations.................. 649
15.7.1 Solution of the Structure Equations............ 652
15.8 Bianchi Identities for the Curvature and Torsion Forms...... 653
15.8.1 Special Cases........................ 655
15.9 Locally Flat Manifolds....................... 658
15.9.1 Exercises.......................... 660
15.10 Weyl Tensor and Conformally Flat Manifolds........... 662
15.11 Covariant Derivatives of Tensor Densities............. 663
16 Some Details and Supplements.....................665
16.1 Proofs of Some Theorems.....................665
16.2 Tangent Bundles..........................670
16.3 Vector Fields Along Maps.....................671
16.3.1 Induced Covariant Derivative...............672
16.3.2 Exercises..........................675
16.4 Variations of a Smooth Curve...................675
16.4.1 First Variation Formula...................676
16.4.2 Jacobi Equation ......................677
Appendix A Fundamental Equations for Hypersurfaces.........679
A. 1 Formulas of Gauss and Weingarten................679
A.2 Equations of Gauss and Codazzi-Mainardi............681
A.3 Null Hypersurfaces.........................684
A.4 Exercises..............................684
Appendix B Ricci Curvature of Warped Products ............687
B.l Application: Friedmann Equations.................689
Appendix C Frobenius Integrability Theorem............... 691
C.l Applications............................ 695
C.2 Proof of Frobenius Theorem (in the First Version)........ 698
Appendix D Collection of Important Formulas.............. 701
D.l Vector Fields, Lie Brackets..................... 701
D.2 Differential Forms......................... 701
D.3 Exterior Differential........................ 702
D.4 Poincare Lemma.......................... 702
D.5 Interior Product........................... 702
D.6 Lie Derivative ........................... 703
D.7 Relations Between Lx, ix andn d.................. 703
D.8 Volume Form............................ 703
D.9 Hodge-Star Operation....................... 704
D.10 Codifferential............................ 704
D.ll Covariant Derivative........................ 704
D.12 Connection Forms......................... 705
D.13 Curvature Forms.......................... 705
D.14 Cartan s Structure Equations.................... 705
D.15 Riemannian Connection...................... 705
D.16 Coordinate Expressions ...................... 705
D.l7 Absolute Exterior Differential................... 706
D.18 Bianchi Identities.......................... 706
References................................... 709
Textbooks on General Relativity: Classical Texts......... 709
Textbooks on General Relativity: Selection of (Graduate)
Textbooks.......................... 709
Textbooks on General Relativity: Numerical Relativity...... 710
Textbooks on General Physics and Astrophysics ......... 710
Mathematical Tools: Modern Treatments of Differential
Geometry for Physicists.................. 710
Mathematical Tools: Selection of Mathematical Books...... 711
Historical Sources......................... 711
Recent Books on Cosmology.................... 712
Research Articles, Reviews and Specialized Texts: Chapter 2 . . . 712
Research Articles, Reviews and Specialized Texts: Chapter 3 . . . 713
Research Articles, Reviews and Specialized Texts: Chapter 4 . . . 713
Research Articles, Reviews and Specialized Texts: Chapter 5 . . . 714
Research Articles, Reviews and Specialized Texts: Chapter 6 . . . 715
Research Articles, Reviews and Specialized Texts: Chapter 7 . . . 716
Research Articles, Reviews and Specialized Texts: Chapter 8 . . . 717
Research Articles, Reviews and Specialized Texts: Chapter 9 . . . 718
Research Articles, Reviews and Specialized Texts: Chapter 10 . . 718
Index...................................... 721
|
| any_adam_object | 1 |
| author | Straumann, Norbert 1936- |
| author_GND | (DE-588)134199545 |
| author_facet | Straumann, Norbert 1936- |
| author_role | aut |
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| building | Verbundindex |
| bvnumber | BV040596375 |
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| ctrlnum | (OCoLC)844023187 (DE-599)OBVAC09582517 |
| discipline | Physik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV040596375 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:26:56Z |
| institution | BVB |
| isbn | 9789400754096 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025424216 |
| oclc_num | 844023187 |
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| owner | DE-11 DE-384 DE-91G DE-BY-TUM DE-20 DE-19 DE-BY-UBM DE-83 DE-188 |
| owner_facet | DE-11 DE-384 DE-91G DE-BY-TUM DE-20 DE-19 DE-BY-UBM DE-83 DE-188 |
| physical | XIX, 735 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series2 | Graduate texts in physics |
| spelling | Straumann, Norbert 1936- Verfasser (DE-588)134199545 aut General relativity Norbert Straumann 2. ed. Dordrecht [u.a.] Springer 2013 XIX, 735 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in physics Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Relativistische Astrophysik (DE-588)4121581-3 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 s Relativistische Astrophysik (DE-588)4121581-3 s DE-604 Erscheint auch als Online-Ausgabe 978-94-007-5410-2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025424216&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Straumann, Norbert 1936- General relativity Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Relativistische Astrophysik (DE-588)4121581-3 gnd |
| subject_GND | (DE-588)4112491-1 (DE-588)4121581-3 |
| title | General relativity |
| title_auth | General relativity |
| title_exact_search | General relativity |
| title_full | General relativity Norbert Straumann |
| title_fullStr | General relativity Norbert Straumann |
| title_full_unstemmed | General relativity Norbert Straumann |
| title_short | General relativity |
| title_sort | general relativity |
| topic | Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Relativistische Astrophysik (DE-588)4121581-3 gnd |
| topic_facet | Allgemeine Relativitätstheorie Relativistische Astrophysik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025424216&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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