A first course in general relativity:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Edition: | 20. print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 376 S. Ill., graph. Darst. |
| ISBN: | 9780521277037 |
Staff View
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| 100 | 1 | |a Schutz, Bernard F. |d 1946- |e Verfasser |0 (DE-588)1012853179 |4 aut | |
| 245 | 1 | 0 | |a A first course in general relativity |c Bernard F. Schutz |
| 250 | |a 20. print. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a XIV, 376 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804138133822898176 |
|---|---|
| adam_text | Contents
Preface
xi
1 Special relativity
,
■ 1
1.1
Fundamental principles of special relativity theory
(SR)
1
1.2
Definition of an
inerţial
observer in SR
4
1.3
New units
5
1.4
Spacetime diagrams
6
1.5
Construction of the coordinates used by another observer
7
1.6
Invariance
of the interval
10
1.7
Invariant hyperbolae
15
1.8
Particularly important results
18
1.9
The
Lorentz
transformation
24
1.10
The velocity-composition law
25
1.11
Paradoxes and physical intuition
26
1.12
Bibliography
27
1.13
Appendix
28
1.14
Exercises
30
2
Vector analysis
¡в
special relativity
36
2.1
Definition of a vector
36
2.2
Vector algebra
39
23
The four-velocity
44
2.4
The four-momentum
45
2.5
Scalar product
47
viii Contents
2.6
Applications
50
2.7 Photons 52
2.8
Bibliography
53
2.9
Exercises
54
3
Tensor analysis in special relativity
60
3.1
The metric tensor
60
3.2
Definition of tensors
61
3.3
The
(?)
tensors: one-forms
62
3.4
The
(2)
tensors
71
3.5
Metric as a mapping of vectors into one-forms
73
3.6
Finally:
(£ƒ)
tensors
77
3.7
Index raising and lowering
78
3.8
Differentiation of tensors
80
3.9
Bibliography
81
3.10
Exercises
81
4
Perfect fluids in special relativity
89
ß.1
Fluids
89
4.2
Dust: The number-flux vector
Ñ
90
4.3
One-forms and surfaces
94
4.4
Dust again: The stress-energy tensor
97
4.5
General fluids
99
4.6
Perfect fluids
106
4.7
Importance for general relativity
. 110
4.8
Gauss law
111
4.9
Bibliography
112
4.10
Exercises
113
5
Preface to curvature
1
IS
5.1
On the relation of gravitation to curvature
118
5.2
Tensor algebra in polar coordinates
126
5.3
Tensor calculus in polar coordinates
133
5.4 Christoffel
symbols and the metric
140
5.5
The
tensorial
nature of
Γαβΐί
143
5.6
Noncoordinate bases
144
5.7
Looking ahead
147
5.8
Bibliography
148
5.9
Exercises
148
6
Curved manifolds
151
6.1
Difierentiable manifolds and tensors
151
6.2
Riemannian manifolds
154
Contents ix
6.3 Covariant
differentiation
160
6.4
Parallel-transport, geodesies and curvature
163
6.5
The curvature tensor
167
6.6
Bianchi
identities;
Ricci
and Einstein tensors
173
6.7
Curvature in perspective
175
6.8
Bibliography
176
6.9
Exercises
176
7
Physics in a curved spacetime
182
7.1
The transition from difierential geometry to gravity
182
7.2
Physics in slightly curved spacetimes
185
7.3
Curved intuition
188
7.4
Conserved quantities
189
7.5
Bibliography
191
7.6
Exercises
191
8
The Einstein field equations
195
8.1
Purpose and justification of the field equations
195
8.2
Einstein s equations
199
8.3
Einstein s equations for weak gravitational fields
200
8.4
Newtonian gravitational fields
205
8.5
Bibliography
208
8.6
Exercises
209
9
Gravitational radiation
214
9.1
The propagation of gravitational waves
214
9.2
The detection of gravitational waves
221
9.3
The generation of gravitational waves
226
9.4
The energy carried away by gravitational waves
234
9.5
Bibliography
242
9.6
Exercises
243
10
Spherical solutions for stars
251
10.1
Coordmates for spherically symmetric spacetimes
251
10.2
Static spherically symmetric spacetimes
253
10.3
Static perfect fluid Einstein equations
255
10.4
The exterior geometry
257
10.5
The interior structure of the star
258
10.6
Exact interior solutions
261
10.7
Realistic stars and gravitational collapse
264
10.8
Bibliography
270
10.9
Exercises
271
Contents
11 Schwarzschild
geometry
and black holes
275
11.1
Trajectories in the
Schwarzschild
spacetime
275
11.2
Nature of the surface
г=2М
288
11.3
More-general black holes
294
11.4
Quantum mechanical emission of radiation by black holes: The
Hawking process
305
11.5
Bibliography
310
11.6
Exercises
311
12
Cosmology
318
12.1
What is cosmology?
318
12.2
General-relativistic cosmological models
322
12.3
Cosmological observations
329
12.4
Physical cosmology
334
12.5
Bibliography
338
12.6
Exercises
338
Appendix A:
Summary of linear algebra
342
Appendix B:
Hints and solutions to selected exercises
346
References
359
Index
367
|
| adam_txt |
Contents
Preface
xi
1 Special relativity
,
■ 1
1.1
Fundamental principles of special relativity theory
(SR)
1
1.2
Definition of an
inerţial
observer in SR
4
1.3
New units
5
1.4
Spacetime diagrams
6
1.5
Construction of the coordinates used by another observer
7
1.6
Invariance
of the interval
10
1.7
Invariant hyperbolae
15
1.8
Particularly important results
18
1.9
The
Lorentz
transformation
24
1.10
The velocity-composition law
25
1.11
Paradoxes and physical intuition
26
1.12
Bibliography
27
1.13
Appendix
28
1.14
Exercises
30
2
Vector analysis
¡в
special relativity
36
2.1
Definition of a vector
36
2.2
Vector algebra
39
23
The four-velocity
44
2.4
The four-momentum
45
2.5
Scalar product
47
viii Contents
2.6
Applications
50
2.7 Photons 52
2.8
Bibliography
53
2.9
Exercises
54
3
Tensor analysis in special relativity
60
3.1
The metric tensor
60
3.2
Definition of tensors
61
3.3
The
(?)
tensors: one-forms
62
3.4
The
(2)
tensors
71
3.5
Metric as a mapping of vectors into one-forms
73
3.6
Finally:
(£ƒ)
tensors
77
3.7
Index 'raising' and 'lowering'
78
3.8
Differentiation of tensors
80
3.9
Bibliography
81
3.10
Exercises
81
4
Perfect fluids in special relativity
89
ß.1
Fluids
89
4.2
Dust: The number-flux vector
Ñ
90
4.3
One-forms and surfaces
94
4.4
Dust again: The stress-energy tensor
97
4.5
General fluids
99
4.6
Perfect fluids
106
4.7
Importance for general relativity
. 110
4.8
Gauss' law
111
4.9
Bibliography
112
4.10
Exercises
113
5
Preface to curvature
1
IS
5.1
On the relation of gravitation to curvature
118
5.2
Tensor algebra in polar coordinates
126
5.3
Tensor calculus in polar coordinates
133
5.4 Christoffel
symbols and the metric
140
5.5
The
tensorial
nature of
Γαβΐί
143
5.6
Noncoordinate bases
144
5.7
Looking ahead
147
5.8
Bibliography
148
5.9
Exercises
148
6
Curved manifolds
151
6.1
Difierentiable manifolds and tensors
151
6.2
Riemannian manifolds
154
Contents ix
6.3 Covariant
differentiation
160
6.4
Parallel-transport, geodesies and curvature
163
6.5
The curvature tensor
167
6.6
Bianchi
identities;
Ricci
and Einstein tensors
173
6.7
Curvature in perspective
175
6.8
Bibliography
176
6.9
Exercises
176
7
Physics in a curved spacetime
182
7.1
The transition from difierential geometry to gravity
182
7.2
Physics in slightly curved spacetimes
185
7.3
Curved intuition
188
7.4
Conserved quantities
189
7.5
Bibliography
191
7.6
Exercises
191
8
The Einstein field equations
195
8.1
Purpose and justification of the field equations
195
8.2
Einstein's equations
199
8.3
Einstein's equations for weak gravitational fields
200
8.4
Newtonian gravitational fields
205
8.5
Bibliography
208
8.6
Exercises
209
9
Gravitational radiation
214
9.1
The propagation of gravitational waves
214
9.2
The detection of gravitational waves
221
9.3
The generation of gravitational waves
226
9.4
The energy carried away by gravitational waves
234
9.5
Bibliography
242
9.6
Exercises
243
10
Spherical solutions for stars
251
10.1
Coordmates for spherically symmetric spacetimes
251
10.2
Static spherically symmetric spacetimes
253
10.3
Static perfect fluid Einstein equations
255
10.4
The exterior geometry
257
10.5
The interior structure of the star
258
10.6
Exact interior solutions
261
10.7
Realistic stars and gravitational collapse
264
10.8
Bibliography
270
10.9
Exercises
271
Contents
11 Schwarzschild
geometry
and black holes
275
11.1
Trajectories in the
Schwarzschild
spacetime
275
11.2
Nature of the surface
г=2М
288
11.3
More-general black holes
294
11.4
Quantum mechanical emission of radiation by black holes: The
Hawking process
305
11.5
Bibliography
310
11.6
Exercises
311
12
Cosmology
318
12.1
What is cosmology?
318
12.2
General-relativistic cosmological models
322
12.3
Cosmological observations
329
12.4
Physical cosmology
334
12.5
Bibliography
338
12.6
Exercises
338
Appendix A:
Summary of linear algebra
342
Appendix B:
Hints and solutions to selected exercises
346
References
359
Index
367 |
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| isbn | 9780521277037 |
| language | English |
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| spelling | Schutz, Bernard F. 1946- Verfasser (DE-588)1012853179 aut A first course in general relativity Bernard F. Schutz 20. print. Cambridge [u.a.] Cambridge Univ. Press 2008 XIV, 376 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Allgemeine Relativitätstheorie (DE-588)4112491-1 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016813893&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 | Schutz, Bernard F. 1946- A first course in general relativity Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| subject_GND | (DE-588)4112491-1 (DE-588)4123623-3 |
| title | A first course in general relativity |
| title_auth | A first course in general relativity |
| title_exact_search | A first course in general relativity |
| title_exact_search_txtP | A first course in general relativity |
| title_full | A first course in general relativity Bernard F. Schutz |
| title_fullStr | A first course in general relativity Bernard F. Schutz |
| title_full_unstemmed | A first course in general relativity Bernard F. Schutz |
| title_short | A first course in general relativity |
| title_sort | a first course in general relativity |
| topic | Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| topic_facet | Allgemeine Relativitätstheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016813893&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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