A college course on relativity and cosmology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2015
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| Edition: | First edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 292 Seiten Illustrationen, Diagramme |
| ISBN: | 9780199693412 9780199693405 |
Staff View
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Record in the Search Index
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| adam_text | Titel: A college course on relativity and cosmology
Autor: Cheng, Ta-Pei
Jahr: 2015
Contents
1 Introduction 1
1.1 Relativity as a coordinate symmetry 2
1.1.1 Coordinate transformations 3
1.1.2 The principle of relativity 6
1.2 Einstein and relativity 8
1.2.1 The new kinematics 8
1.2.2 GR as a field theory of gravitation 10
Review questions 10
2 Special Relativity: The New Kinematics 11
2.1 Einstein s two postulates and Lorentz transformation 12
2.1.1 Relativity of simultaneity and the new conception
oftime 13
2.1.2 Coordinate-dependent time leads to Lorentz
transformation 15
2.2 Physics implications of Lorentz transformation 19
2.2.1 Time dilation and length contraction 19
2.2.2 The invariant interval and proper time 22
2.3 Two counterinmitive scenarios as paradoxes 25
Review questions 29
3 Special Relativity: Fiat Spacetime 31
3.1 Geometrie formulation of relativity 32
3.2 Tensors in special relativity 34
3.2.1 Generalized coordinates: bases and the metric 34
3.2.2 Velocity and momentum 4-vectors 38
3.2.3 Electromagnetic field 4-tensor 45
3.2.4 The energy-momentum-stress 4-tensor for a field
system 49
3.3 The spacetime diagram 51
3.3.1 Invariant regions and causal strueture 52
3.3.2 Lorentz transformation in the spacetime diagram 53
Review questions 56
4 Equivalence of Gravitation and Inertia 57
4.1 Seeking a relativistic theory of gravitation 58
4.1.1 Newtonian potential: a summary 58
4.1.2 Einstein s motivation for general relativity 59
4.2 The equivalence principle: from Galileo to Einstein 60
4.2.1 Inertial mass vs. gravitational mass 60
4.2.2 Einstein: my happiest thought 61
4.3 EP leads to gravitational time dilation and light deflection 63
4.3.1 Gravitational redshift and time dilation 63
4.3.2 Relativity and the Operation of GPS 70
4.3.3 The EP calculation of light deflection 73
4.3.4 Energetics of light transmission in a gravitational
field 75
Review questions 78
5 General Relativity as a Geometrie Theory of Gravity 79
5.1 Metrie description of a curved manifold 80
5.1.1 Gaussian coordinates and the metric tensor 80
5.1.2 The geodesic equation 85
5.1.3 Local Euclidean frames and the flatness theorem 90
5.2 From the equivalence principle to a metric theory of gravity 91
5.2.1 Curved spacetime as gravitational field 92
5.2.2 GR as a field theory of gravitation 94
5.3 Geodesic equation as the GR equation of motion 95
5.3.1 The Newtonian limit 96
Review questions 98
6 Einstein Equation and its Spherical Solution 99
6.1 Curvature: a short introduetion 101
6.2 Tidal gravity and spacetime curvature 106
6.2.1 Tidal forces—a qualitative discussion 106
6.2.2 Deviation equations and tidal gravity 107
6.3 The GR field equation 109
6.3.1 Einstein curvature tensor 109
6.3.2 Einstein field equation 111
6.3.3 Gravitational waves 112
6.4 Geodesics in Schwarzschild spacetime 114
6.4.1 The geometry of a spherically Symmetrie spacetime 117
6.4.2 Curved spacetime and deflection of light 121
6.4.3 Precession of Mercury s orbit 124
Review questions 131
7 Black Holes 133
7.1 Schwarzschild black holes 134
7.1.1 Time measurements around a black hole 135
7.1.2 Causal strueture of the Schwarzschild surface 137
7.1.3 Binding energy to a black hole can be extremely
large 142
7.2 Astrophysical black holes 144
7.2.1 More realistic black holes 144
7.2.2 Black holes in our universe 147
7.3 Black hole thermodynamics and Hawking radiation 148
7.3.1 Laws of black hole mechanics and thermodynamics 149
7.3.2 Hawking radiation: quantum fluctuation around
thehorizon 150
Review questions 155
8 The General Relativistic Framework for Cosmology 156
8.1 The cosmos observed 157
8.1.1 The expanding universe and its age 158
8.1.2 Mass/energy content of the universe 163
8.2 The homogeneous and isotropic universe 167
8.2.1 Robertson-Walker metric in comoving
coordinates 168
8.2.2 Hubble s law follows from the cosmological
principle 170
8.3 Time evolution in FLRW cosmology 172
8.3.1 Friedmann equations and their simple
interpretation 172
8.3.2 Time evolution of model universes 178
8.4 The cosmological constant A 181
8.4.1 A as vacuum energy and pressure . 182
8.4.2 A-dominated universe expands exponentially 185
Review questions 186
9 Big Bang Thermal Relics 187
9.1 The thermal history of the universe 188
9.1.1 Scale dependence of radiation temperature 188
9.1.2 Different thermal equilibrium stages 190
9.2 Primordial nucleosynthesis 193
9.3 Photon decoupling and cosmic microwave background 197
9.3.1 Universe became transparent to photons 197
9.3.2 CMB anisotropy as a baby picture
of the universe 204
Review questions 209
10 Inflation and the Accelerating Universe 210
10.1 The cosmic inflation epoch 211
10.1.1 Initial condition problems of FLRW cosmology 211
10.1.2 The inflationary scenario 213
10.1.3 Eternal inflation and the multiverse 222
10.2 The accelerating universe in the present era 223
10.2.1 Dark energy and its effect 223
10.2.2 Distant Supernovae and the 1998 discovery 224
10.2.3 The mysterious physical origin of dark energy 231
10.3 ACDM cosmology as the Standard model 234
Review questions 235
11 Tensor Formalism for General Relativity 236
11.1 Covariant derivatives and parallel transport 238
11.1.1 Derivatives in a curved space and Christoffel
Symbols 239
11.1.2 Parallel transport and geodesics as straight lines 243
11.2 Riemann curvature tensor 245
11.2.1 Parallel transport of a vector around
a closed path 246
11.2.2 Equation of geodesic deviation 249
11.2.3 Bianchi identity and the Einstein tensor 252
11.3 GR tensor equations 253
11.3.1 The principle of general covariance 254
11.3.2 Einstein field equation 255
Review questions 257
Appendix A: Keys to Review Questions 259
Appendix B: Hints for Selected Exercises 270
Appendix C: Glossary of Symbols and Acronyms 276
References and Bibliography 281
Index 285
|
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| discipline | Physik |
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| isbn | 9780199693412 9780199693405 |
| language | English |
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| spelling | Cheng, Ta-Pei Verfasser (DE-588)139945954 aut A college course on relativity and cosmology Ta-Pei Cheng First edition Oxford Oxford University Press 2015 xii, 292 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Relativitätstheorie (DE-588)4049363-5 gnd rswk-swf Kosmologie (DE-588)4114294-9 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Relativitätstheorie (DE-588)4049363-5 s DE-604 Kosmologie (DE-588)4114294-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028102514&sequence=000002&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 | Cheng, Ta-Pei A college course on relativity and cosmology Relativitätstheorie (DE-588)4049363-5 gnd Kosmologie (DE-588)4114294-9 gnd |
| subject_GND | (DE-588)4049363-5 (DE-588)4114294-9 (DE-588)4123623-3 |
| title | A college course on relativity and cosmology |
| title_auth | A college course on relativity and cosmology |
| title_exact_search | A college course on relativity and cosmology |
| title_full | A college course on relativity and cosmology Ta-Pei Cheng |
| title_fullStr | A college course on relativity and cosmology Ta-Pei Cheng |
| title_full_unstemmed | A college course on relativity and cosmology Ta-Pei Cheng |
| title_short | A college course on relativity and cosmology |
| title_sort | a college course on relativity and cosmology |
| topic | Relativitätstheorie (DE-588)4049363-5 gnd Kosmologie (DE-588)4114294-9 gnd |
| topic_facet | Relativitätstheorie Kosmologie Lehrbuch |
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