Introduction to general relativity:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Physical Description: | XV, 441 S. graph. Darst. |
| ISBN: | 9780521845632 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to general relativity |c Lewis Ryder |
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Record in the Search Index
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|---|---|
| adam_text | Preface
page
xiii
Notation, important formulae and physical constants
xiv
1
Introduction
1
1.1
The need for a theory of gravity
1
1.2
Gravitation and inertia: the Equivalence Principle in mechanics
3
1.3
The Equivalence Principle and optics
9
1.4
Curved surfaces
14
Further reading
16
Problems
16
2
Special Relativity, non-inertial effects and
electromagnetism
18
2.1
Special Relativity: Einstein s train
18
2.2
Twin paradox: accelerations
26
2.3
Rotating frames: the Sagnac effect
29
2.4
Inertia: Newton versus
Mach 34
2.5
Thomas precession
36
2.6
Electromagnetism
40
2.7
Principle of General Covariance
43
Further reading
45
Problems
46
3
Differential geometry I: vectors, differential forms and absolute
differentiation
47
3.1
Space-time as a differentiable manifold
47
3.2
Vectors and vector fields
49
3.3
One-forms
55
3.4
Tensors
61
3.5
Differential forms: Hodge duality
65
3.6
Exterior derivative operator: generalised Stokes theorem
72
3.7
Maxwell s equations and differential forms
77
3.8
Metric tensor
79
3.9
Absolute differentiation: connection forms
86
3.10
Parallel transport
93
3.11
Some relations involving connection coefficients
97
Contents
3.12
Examples
102
3.13
General formula for connection coefficients
107
Further reading
110
Problems
110
4
Differential geometry II: geodesies and curvature
112
4.1
Autoparallel
curves and geodesies
112
4.2
Geodesic coordinates
119
4.3
Curvature
121
4.4
Symmetries of the Riemann tensor
125
4.5
Ricci
tensor and curvature scalar
126
4.6
Curvature 2-form
129
4.7
Geodesic deviation
132
4.8
Bianchi
identities
134
Further reading
135
Problems
135
5
Einstein field equations, the
Schwarzschild
solution and experimental
tests of General Relativity
137
5.1
Newtonian limit
137
5.2
Einstein field equations
139
5.3 Schwarzschild
solution
146
5.4
Time dependence and spherical symmetry: Birkhoffs theorem
151
5.5
Gravitational red-shift
154
5.6
Geodesies in
Schwarzschild
space-time
158
5.7
Precession of planetary orbits
160
5.8
Deflection of light
162
5.9
Note on PPN formalism
164
5.10
Gravitational lenses
165
5.11
Radar echoes from planets
169
5.12
Radial motion in
a
Schwarzschild
field: black holes
-
frozen stars
173
5.13
A gravitational clock effect
176
Further reading
178
Problems
178
6
Gravitomagnetic effects: gyroscopes and clocks
180
6.1
Linear approximation
180
6.2
Precession of gyroscopes: the Lense-Thirring effect
191
6.3
Gravitomagnetism
200
6.4
Gravitomagnetic clock effect
204
6.5
Fermi-Walker transport: tetrad formalism
207
6.6
Lie derivatives, Killing vectors and groups of motion
211
6.7
Static and stationary space-times
219
xi Contents
6.8
Killing vectors and conservation laws
223
Further reading
225
Problems
226
7
Gravitational collapse and black holes
227
7.1
The interior
Schwarzschild
solution and the
Tolman-Oppenheimer-Volkoff equation
228
7.2
Energy density and binding energy
237
7.3
Degenerate stars: white dwarfs and neutron stars
243
7.4 Schwarzschild
orbits: Eddington-Finkelstein coordinates
251
7.5
Kraskal-Szekeres coordinates
255
7.6
Einstein-Rosen bridge and
wormholes
259
7.7
Conformai
treatment of infinity:
Penrose
diagrams
261
7.8
Rotating black holes: Kerr solution
265
7.9
The ergosphere and energy extraction from a black hole
271
7.10
Surface gravity
280
7.11
Thermodynamics of black holes and further observations
287
7.12
Global matters: singularities, trapped surfaces and Cosmic Censorship
291
Further reading
293
Problems
294
8
Action principle, conservation laws and the Cauchy problem
295
8.1
Gravitational action and field equations
295
8.2
Energy-momentum pseudotensor
300
8.3
Cauchy problem
304
Further reading
309
Problems
309
9
Gravitational radiation
310
9.1
Weak field approximation
310
9.2
Radiation from a rotating binary source
317
9.3
Parallels between electrodynamics and General Relativity:
Petrov
classification
328
Further reading
340
Problems
340
10
Cosmology
341
10.1
Brief description of the Universe
341
10.2
Robertson-Walker metric
344
10.3
Hubble s law and the cosmological red-shift
355
10.4
Horizons
357
10.5
Luminosity-red-shift relation
360
10.6
Dynamical equations of cosmology
363
10.7 Friedmann
models and the cosmological constant
371
xü Contents
10.8
Cosmic background
radiation
375
10.9 Brief
sketch
of the early Universe
377
10.10
The inflationary universe and the Higgs mechanism
383
Further reading
391
Problems
391
11
Gravitation and field theory
392
11.1
Electrodynamics as an abelian gauge theory
394
11.2
Non-abelian gauge theories
400
11.3
Gauging
Lorentz
symmetry: torsion
409
11.4
Dirac equation in
Schwarzschild
space-time
416
11.5
Five dimensions: gravity plus
electromagnetism
418
Further reading
423
Problems
424
References
425
Index
439
|
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| isbn | 9780521845632 |
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| spelling | Ryder, Lewis H. 1941- Verfasser (DE-588)141504676 aut Introduction to general relativity Lewis Ryder 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2009 XV, 441 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier General relativity (Physics) Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Allgemeine Relativitätstheorie (DE-588)4112491-1 s DE-604 http://www.loc.gov/catdir/enhancements/fy0906/2009005862-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0906/2009005862-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0906/2009005862-t.html Table of contents only Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017371767&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ryder, Lewis H. 1941- Introduction to general relativity General relativity (Physics) Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| subject_GND | (DE-588)4112491-1 (DE-588)4123623-3 |
| title | Introduction to general relativity |
| title_auth | Introduction to general relativity |
| title_exact_search | Introduction to general relativity |
| title_full | Introduction to general relativity Lewis Ryder |
| title_fullStr | Introduction to general relativity Lewis Ryder |
| title_full_unstemmed | Introduction to general relativity Lewis Ryder |
| title_short | Introduction to general relativity |
| title_sort | introduction to general relativity |
| topic | General relativity (Physics) Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| topic_facet | General relativity (Physics) Allgemeine Relativitätstheorie Lehrbuch |
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