General relativity: a concise introduction
Saved in:
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2019
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| Edition: | First edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xi, 141 Seiten Illustrationen |
| ISBN: | 9780198822165 9780198822158 |
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Record in the Search Index
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| adam_text | Contents 1 Gravity as geometry Further reading 2 Geodesics 2.1 Straight iines and great circles 2.2 Spacetime and causal structure 2.3 The metric 2.4 The geodesic equation 2.5 The Newtonian limit Further reading 4 4 8 9 12 13 14 3 Geodesics in the SolarSystem 3.1 The Schwarzschild metric 3.2 Geodesics in the Schwarzschild metric 3.3 Planetary orbits 3.4 Light deflection 3.5 Shapiro time delay 3.6 Gravitational red shift 3.7 The PPN formalism Further reading 15 15 15 18 19 20 21 23 24 4 Manifolds and tensors 4.1 Manifolds 4.2 Tangent vectors 4.3 Cotangent vectors and gradients 4.4 Tensors 4.5 The metric 4.6 Isometries and Killing vectors 4.7 Orthonormal bases 4.8 Differential forms Further reading 25 25 27 29 31 33 34 35 36 36 Derivatives and curvature 5.1 Integration 5.2 Why derivatives are more complicated 5.3 Derivatives of p-forms: Cartan calculus 5.4 Connections and covariant derivatives 5.5 The Christoffel/Levi-Civita connection 5.6 Parallel transport 5.7 Curvature 37 37 38 38 39 42 44 45 5 1 3
x Contents 5.8 Properties of the curvature tensor 5.9 The Cartan structure equations Further reading 47 50 51 6 The Einstein field equations 6.1 Gravity and geodesic deviation 6.2 The Einstein-Hilbert action 6.3 Conservation laws 6.4 Generalizing the action Further reading 52 52 53 56 57 58 7 The stress-energy tensor 7.1 Energy as a rank two tensor 7.2 Th(i stress-energy tensor for a point particle 7.3 Perfect fluids 7.4 Other fields 7.5 Differential and integral conservation laws 7.6 Conservation and the geodesic equation Further reading 59 59 60 61 61 62 63 65 8 The weak fieldapproximation 8.1 The linearized field equations 8.2 The Newtonian limit 8.3 Gravitoinagnetism 8.4 Higher orders 8.5 Bootstrapping the field equations Further reading 66 66 68 69 69 71 71 9 Gravitational waves 9.1 Solving the weak field equations 9.2 Propagating waves 9.3 Detecting gravitational waves 9.4 Sources and signals Further reading 72 72 74 76 77 79 10 Black holes 10.1 Static spacetimes 10.2 Spherical symmetry 10.3 Schwarzschild again 10.4 The event horizon 10.5 An extended spacetime 10.6 Conformal structure and Penrose diagrams 10.7 Properties of the horizon Further reading 80 80 81 82 84 86 87 88 91 11 Cosmology 11.1 Homogeneity andisotropy 11.2 The FLRW metric 92 92 94
Contents xi 11.3 Observational implications 11.4 Inflation Further reading 96 98 100 12 The Hamiltonian formalism 12.1 The ADM metric 12.2 Extrinsic curvature 12.3 The Hamiltonian action 12.4 Constraints 12.5 Degrees of freedom 12.6 Boundary terms Further reading 101 101 102 104 105 105 107 108 13 Next steps 13.1 Solutions and approximations 13.2 Mathematical relativity 13.3 Alternative models 13.4 Quantum gravity 13.5 Experimental gravity Further reading 109 109 110 112 112 115 116 Appendix A Mathematical details A.l Manifolds A. 2 Maps between manifolds A.3 Topologies A.4 Cohomology A.5 Integrals of d-forms and Stokes’ theorem A.6 Curvature and holonomies A.7 Symmetries and Killing vectors A.8 The York decomposition Further reading 117 117 118 119 121 122 123 126 127 128 References 129 Index 135
Einstein’s general theory of relativity -currently our best theory of gravity is important not only to specialists, but to a much wider group of physicists. This short introductory textbook on general relativity and gravitation offers students glimpses of the vast landscape of science connected to general relativity, it incorporates some of the latest research in gravitational theory and experiment. The book is aimed at readers with a broad range՝ of interests in physics, from cosmology, to gravitational radiation, to high energy physics, to condensed matter theory. The pedagogical approach is “physics first’’: readers move very quickly to the calculation of observational predictions, and only return to the mathematical foundations after the՝ physics is established. In addition to standard topics covered by most introductory textbooks, it contains short introductions to mon՝ advanced topics: for instance, how to treat gravitational energy. A concluding chapter discusses directions for further study. After seven years as a printer, editor, factory worker, and activist, Steven Garlip attended graduate school at the University of Texas at Austin, where he earned his Fh.I). Following a stint as a postdoctoral fellow at the Institute lor Advanced Study in Princeton, he joined the՝ faculty of the University of California at Davis, where he has remained since. His main research focus is quantum gravity, but ht՝ has also worked on classical general relativity, quantum field theory, and the interface between physics and topology. ( iovei՝ in muc: Slini Ιπ’νΙιη Leom ISBN 978-0-1
9-882216-5 OXFORD 9780198822165 UNIVERSITY PRESS www.oup.com KU
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| isbn | 9780198822165 9780198822158 |
| language | English |
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| physical | xi, 141 Seiten Illustrationen |
| publishDate | 2019 |
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| spelling | Carlip, Steven 1953- Verfasser (DE-588)13355712X aut General relativity a concise introduction Steven Carlip, The University of California at Davis First edition Oxford Oxford University Press 2019 xi, 141 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030842122&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030842122&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
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| title | General relativity a concise introduction |
| title_auth | General relativity a concise introduction |
| title_exact_search | General relativity a concise introduction |
| title_full | General relativity a concise introduction Steven Carlip, The University of California at Davis |
| title_fullStr | General relativity a concise introduction Steven Carlip, The University of California at Davis |
| title_full_unstemmed | General relativity a concise introduction Steven Carlip, The University of California at Davis |
| title_short | General relativity |
| title_sort | general relativity a concise introduction |
| title_sub | a concise introduction |
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