A short course in general relativity:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2006
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 292 S. graph. Darst. |
| ISBN: | 9780387260785 0387260781 |
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| 100 | 1 | |a Foster, James |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A short course in general relativity |c James Foster ; J. David Nightingale |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2006 | |
| 300 | |a IX, 292 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Algemene relativiteitstheorie |2 gtt | |
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| 650 | 4 | |a Relativité générale (Physique) | |
| 650 | 4 | |a Relativité générale (Physique) - Problèmes et exercices | |
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| 650 | 4 | |a General relativity (Physics) |v Problems, exercises, etc | |
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Datensatz im Suchindex
| _version_ | 1804135033125994496 |
|---|---|
| adam_text | Contents
Preface
........................................................
v
Introduction
................................................... 1
1
Vector and tensor fields
.................................... 7
1.0
Introduction
............................................ 7
1.1
Coordinate systems in Euclidean space
..................... 7
1.2
Suffix notation
.......................................... 13
1.3
Tangents and gradients
................................... 19
1.4
Coordinate transformations in Euclidean space
.............. 23
1.5
Tensor fields in Euclidean space
........................... 27
1.6
Surfaces in Euclidean space
............................... 30
1.7
Manifolds
.............................................. 35
1.8
Tensor fields on manifolds
................................ 38
1.9
Metric properties
........................................ 43
1.10
What and where are the bases?
........................... 46
Problems
1.................................................. 49
2
The spacetime of general relativity and paths of particles
. . 53
2.0
Introduction
............................................ 53
2.1
Geodesies
.............................................. 56
2.2
Parallel vectors along a curve
............................. 64
2.3
Absolute and covariant differentiation
...................... 71
2.4
Geodesic coordinates
..................................... 79
2.5
The spacetime of general relativity
......................... 82
2.6
Newton s laws of motion
................................. 86
2.7
Gravitational potential and the geodesic
.................... 87
2.8
Newton s law of universal gravitation
...................... 89
2.9
A rotating reference system
............................... 90
Problems
2.................................................. 94
viii
Contents
3
Field equations and curvature
............................. 97
3.0
Introduction
............................................ 97
3.1
The stress tensor and fluid motion
......................... 97
3.2
The curvature tensor and related tensors
...................102
3.3
Curvature and parallel transport
..........................105
3.4
Geodesic deviation
.......................................110
3.5
Einstein s field equations
.................................112
3.6
Einstein s equation compared with Poisson s equation
........115
3.7
The
Schwarzschild
solution
...............................116
Problems
3..................................................119
4
Physics in the vicinity of a massive object
.................123
4.0
Introduction
............................................123
4.1
Length and time
........................................124
4.2
Radar sounding
.........................................129
4.3
Spectral shift
...........................................131
4.4
General particle motion (including photons)
................136
4.5
Perihelion advance
.......................................144
4.6
Bending of light
.........................................146
4.7
Geodesic effect
..........................................149
4.8
Black holes
.............................................152
4.9
Other coordinate systems
.................................157
4.10
Rotating objects; the Kerr solution
........................158
Problems
4..................................................167
5
Gravitational radiation
....................................169
5.0
Introduction
............................................169
5.1
What wiggles?
..........................................170
5.2
Two polarizations
.......................................173
5.3
Simple generation and detection
...........................178
Problems
5..................................................182
6
Elements of cosmology
.....................................183
6.0
Introduction
............................................183
6.1
Robertson Walker line element
............................185
6.2
Field equations
..........................................187
6.3
The Friedmarm models
...................................189
6.4
Redshift. distance, and speed of recession
...................192
6.5
Objects with large redshifts
...............................196
6.6
Comment on Einstein s models; inflation
...................200
6.7
Newtonian dust
.........................................203
Problems
6..................................................206
Appendices
A
Special
relativity
review
...................................211
А.О
Introduction
............................................211
A.I
Lorentz
transformations
..................................214
A.
2
Relativistic addition of velocities
..........................216
A.3 Simultaneity
............................................217
A.
4
Time dilation, length contraction
..........................218
A.
5
Spacetime diagrams
......................................219
A.
6
Some, standard
4-
vectors
..................................222
A.
7
Doppler
effect
...........................................226
A.
8
Electromagnetism
.......................................228
Problems A
. . ...............................................231
В
The Chinese connection
...................................233
B.O Background
.............................................233
B.I Lanchester s transporter on a plane
........................234
B.2 Lanchester s transporter on a surface
.......................237
B.3 A trip at constant latitude
................................240
С
Tensors and Manifolds
.....................................241
CO Introduction
............................................241
C.I Vector spaces
...........................................241
C.2 Dual spaces
.............................................244
C.3 Tensor products
.........................................247
C.4 The space
T¡
...........................................250
С.
5
From tensors to tensor fields
..............................251
C.6 Manifolds
..............................................251
C.7 The tangent space at each point of a manifold
...............254
C.8 Tensor fields on a manifold
...............................256
Solutions
. . . ·...................................................259
References
.....................................................283
Index
..........................................................287
|
| adam_txt |
Contents
Preface
.
v
Introduction
. 1
1
Vector and tensor fields
. 7
1.0
Introduction
. 7
1.1
Coordinate systems in Euclidean space
. 7
1.2
Suffix notation
. 13
1.3
Tangents and gradients
. 19
1.4
Coordinate transformations in Euclidean space
. 23
1.5
Tensor fields in Euclidean space
. 27
1.6
Surfaces in Euclidean space
. 30
1.7
Manifolds
. 35
1.8
Tensor fields on manifolds
. 38
1.9
Metric properties
. 43
1.10
What and where are the bases?
. 46
Problems
1. 49
2
The spacetime of general relativity and paths of particles
. . 53
2.0
Introduction
. 53
2.1
Geodesies
. 56
2.2
Parallel vectors along a curve
. 64
2.3
Absolute and covariant differentiation
. 71
2.4
Geodesic coordinates
. 79
2.5
The spacetime of general relativity
. 82
2.6
Newton's laws of motion
. 86
2.7
Gravitational potential and the geodesic
. 87
2.8
Newton's law of universal gravitation
. 89
2.9
A rotating reference system
. 90
Problems
2. 94
viii
Contents
3
Field equations and curvature
. 97
3.0
Introduction
. 97
3.1
The stress tensor and fluid motion
. 97
3.2
The curvature tensor and related tensors
.102
3.3
Curvature and parallel transport
.105
3.4
Geodesic deviation
.110
3.5
Einstein's field equations
.112
3.6
Einstein's equation compared with Poisson's equation
.115
3.7
The
Schwarzschild
solution
.116
Problems
3.119
4
Physics in the vicinity of a massive object
.123
4.0
Introduction
.123
4.1
Length and time
.124
4.2
Radar sounding
.129
4.3
Spectral shift
.131
4.4
General particle motion (including photons)
.136
4.5
Perihelion advance
.144
4.6
Bending of light
.146
4.7
Geodesic effect
.149
4.8
Black holes
.152
4.9
Other coordinate systems
.157
4.10
Rotating objects; the Kerr solution
.158
Problems
4.167
5
Gravitational radiation
.169
5.0
Introduction
.169
5.1
What wiggles?
.170
5.2
Two polarizations
.173
5.3
Simple generation and detection
.178
Problems
5.182
6
Elements of cosmology
.183
6.0
Introduction
.183
6.1
Robertson Walker line element
.185
6.2
Field equations
.187
6.3
The Friedmarm models
.189
6.4
Redshift. distance, and speed of recession
.192
6.5
Objects with large redshifts
.196
6.6
Comment on Einstein's models; inflation
.200
6.7
Newtonian dust
.203
Problems
6.206
Appendices
A
Special
relativity
review
.211
А.О
Introduction
.211
A.I
Lorentz
transformations
.214
A.
2
Relativistic addition of velocities
.216
A.3 Simultaneity
.217
A.
4
Time dilation, length contraction
.218
A.
5
Spacetime diagrams
.219
A.
6
Some, standard
4-
vectors
.222
A.
7
Doppler
effect
.226
A.
8
Electromagnetism
.228
Problems A
. . .231
В
The Chinese connection
.233
B.O Background
.233
B.I Lanchester's transporter on a plane
.234
B.2 Lanchester's transporter on a surface
.237
B.3 A trip at constant latitude
.240
С
Tensors and Manifolds
.241
CO Introduction
.241
C.I Vector spaces
.241
C.2 Dual spaces
.244
C.3 Tensor products
.247
C.4 The space
T¡
.250
С.
5
From tensors to tensor fields
.251
C.6 Manifolds
.251
C.7 The tangent space at each point of a manifold
.254
C.8 Tensor fields on a manifold
.256
Solutions
. . . ·.259
References
.283
Index
.287 |
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| spelling | Foster, James Verfasser aut A short course in general relativity James Foster ; J. David Nightingale 3. ed. New York [u.a.] Springer 2006 IX, 292 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algemene relativiteitstheorie gtt Relatividade (física) larpcal Relativité générale (Physique) Relativité générale (Physique) - Problèmes et exercices Relativité générale (physique) ram General relativity (Physics) General relativity (Physics) Problems, exercises, etc Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Allgemeine Relativitätstheorie (DE-588)4112491-1 s DE-604 Nightingale, J. David Verfasser aut Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014580645&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 | Foster, James Nightingale, J. David A short course in general relativity Algemene relativiteitstheorie gtt Relatividade (física) larpcal Relativité générale (Physique) Relativité générale (Physique) - Problèmes et exercices Relativité générale (physique) ram General relativity (Physics) General relativity (Physics) Problems, exercises, etc Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| subject_GND | (DE-588)4112491-1 (DE-588)4151278-9 |
| title | A short course in general relativity |
| title_auth | A short course in general relativity |
| title_exact_search | A short course in general relativity |
| title_exact_search_txtP | A short course in general relativity |
| title_full | A short course in general relativity James Foster ; J. David Nightingale |
| title_fullStr | A short course in general relativity James Foster ; J. David Nightingale |
| title_full_unstemmed | A short course in general relativity James Foster ; J. David Nightingale |
| title_short | A short course in general relativity |
| title_sort | a short course in general relativity |
| topic | Algemene relativiteitstheorie gtt Relatividade (física) larpcal Relativité générale (Physique) Relativité générale (Physique) - Problèmes et exercices Relativité générale (physique) ram General relativity (Physics) General relativity (Physics) Problems, exercises, etc Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| topic_facet | Algemene relativiteitstheorie Relatividade (física) Relativité générale (Physique) Relativité générale (Physique) - Problèmes et exercices Relativité générale (physique) General relativity (Physics) General relativity (Physics) Problems, exercises, etc Allgemeine Relativitätstheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014580645&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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