Spacetime and geometry: an introduction to general relativity
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2019
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| Edition: | Reissued |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xiv, 513 Seiten Illustrationen, Diagramme 26 cm |
| ISBN: | 9781108488396 1108488390 |
Staff View
MARC
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Record in the Search Index
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Contents 1 ■ Special Relativity and Flat Spacetime 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 Prelude 1 Space and Time, Separately and Together Lorentz Transformations 12 Vectors 15 Dual Vectors (One-Forms) 18 Tensors 21 Manipulating Tensors 25 Maxwell’s Equations 29 Energy and Momentum 30 Classical Field Theory 37 Exercises 45 2 ■ Manifolds 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 3 48 Gravity as Geometry 48 What Is a Manifold? 54 Vectors Again 63 Tensors Again 68 The Metric 71 An Expanding Universe 76 Causality 78 Tensor Densities 82 Differential Forms 84 Integration 88 Exercises 90 3 ■ Curvature 3.1 3.2 3.3 1 Overview 93 Covariant Derivatives 94 Parallel Transport and Geodesics 93 102 xi
xii Contents 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 Properties of Geodesics 108 The Expanding Universe Revisited 113 The Riemann Curvature Tensor 121 Properties of the Riemann Tensor 126 Symmetries and Killing Vectors 133 Maximally Symmetric Spaces 139 Geodesic Deviation 144 Exercises 146 151 4 ■ Gravitation 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Physics in Curved Spacetime 151 Einstein’s Equation 155 Lagrangian Formulation 159 Properties of Einstein’s Equation 165 The Cosmological Constant 171 Energy Conditions 174 The Equivalence Principle Revisited 177 Alternative Theories 181 Exercises 190 193 5 ■ The Schwarzschild Solution 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 The Schwarzschild Metric 193 Birkhoff’s Theorem 197 Singularities 204 Geodesics of Schwarzschild 205 Experimental Tests 212 Schwarzschild Black Holes 218 The Maximally Extended Schwarzschild Solution Stars and Black Holes 229 Exercises 236 222 6 ■ More General Black Holes 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 The Black Hole Zoo 238 Event Horizons 239 Killing Horizons 244 Mass, Charge, and Spin 248 Charged (Reissner-Nordström) Black Holes 254 Rotating (Kerr) Black Holes 261 The Penrose Process and Black-Hole Thermodynamics Exercises 272 238 267
Contents 7 ■ Perturbation Theory and Gravitational Radiation 7.1 7.2 7.3 7.4 7.5 7.6 Ί.Ί 7.8 323 Maximally Symmetric Universes 323 Robertson-Walker Metrics 329 The Friedmann Equation 333 Evolution of the Scale Factor 338 Redshifts and Distances 344 Gravitational Lensing 349 Our Universe 355 Inflation 365 Exercises 374 9 ■ Quantum Field Theory in Curved Spacetime 9.1 9.2 9.3 9.4 9.5 9.6 274 Linearized Gravity and Gauge Transformations 274 Degrees of Freedom 279 Newtonian Fields and Photon Trajectories 286 Gravitational Wave Solutions 293 Production of Gravitational Waves 300 Energy Loss Due to Gravitational Radiation 307 Detection of Gravitational Waves 315 Exercises 320 8 ■ Cosmology 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 xiii 376 Introduction 376 Quantum Mechanics 378 Quantum Field Theory in Flat Spacetime 385 Quantum Field Theory in Curved Spacetime 394 The Unruh Effect 402 The Hawking Effect and Black Hole Evaporation 412 APPENDIXES 423 A ■ Maps between Manifolds 423 В ■ Diffeomorphisms andLie Derivatives 429 C ■ Submanifolds 439 D ■ Hypersurfaces 443
xiv Contents E ■ Stokes's Theorem 453 F ■ Geodesic Congruences 459 G ■ Conformal Transformations 467 H ■ Conformal Diagrams 471 I ■ The Parallel Propagator 479 J ■ Noncoordinate Bases 483 Bibliography 495 Index 501 |
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| dewey-full | 530.11 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.11 |
| dewey-search | 530.11 |
| dewey-sort | 3530.11 |
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| discipline | Physik |
| edition | Reissued |
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| isbn | 9781108488396 1108488390 |
| language | English |
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| publisher | Cambridge University Press |
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| spelling | Carroll, Sean M. 1966- Verfasser (DE-588)143150189 aut Spacetime and geometry an introduction to general relativity Sean M. Carroll Reissued Cambridge Cambridge University Press 2019 xiv, 513 Seiten Illustrationen, Diagramme 26 cm txt rdacontent sti rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Relativitätstheorie (DE-588)4049363-5 gnd rswk-swf General relativity (Physics) Relativitätstheorie (DE-588)4049363-5 s DE-604 Allgemeine Relativitätstheorie (DE-588)4112491-1 s 1\p DE-604 Erscheint auch als Online-Ausgabe 978-1-108-77555-7 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031534027&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Carroll, Sean M. 1966- Spacetime and geometry an introduction to general relativity Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Relativitätstheorie (DE-588)4049363-5 gnd |
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| title | Spacetime and geometry an introduction to general relativity |
| title_auth | Spacetime and geometry an introduction to general relativity |
| title_exact_search | Spacetime and geometry an introduction to general relativity |
| title_full | Spacetime and geometry an introduction to general relativity Sean M. Carroll |
| title_fullStr | Spacetime and geometry an introduction to general relativity Sean M. Carroll |
| title_full_unstemmed | Spacetime and geometry an introduction to general relativity Sean M. Carroll |
| title_short | Spacetime and geometry |
| title_sort | spacetime and geometry an introduction to general relativity |
| title_sub | an introduction to general relativity |
| topic | Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Relativitätstheorie (DE-588)4049363-5 gnd |
| topic_facet | Allgemeine Relativitätstheorie Relativitätstheorie |
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