Introduction to general relativity:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific Publ.
2007
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 342 S. graph. Darst. |
| ISBN: | 9789812705853 9812705856 9789812705846 9812705848 |
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MARC
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| 100 | 1 | |a Walecka, John Dirk |d 1932- |e Verfasser |0 (DE-588)132844788 |4 aut | |
| 245 | 1 | 0 | |a Introduction to general relativity |c John Dirk Walecka |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific Publ. |c 2007 | |
| 300 | |a XII, 342 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Relativité générale (Physique) - Mathématiques | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a General relativity (Physics) |x Mathematics | |
| 650 | 0 | 7 | |a Allgemeine Relativitätstheorie |0 (DE-588)4112491-1 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-015679405 | ||
Record in the Search Index
| _version_ | 1804136559497183232 |
|---|---|
| adam_text | Contents
Preface vii
1.
Introduction
1
2.
Partiele
on a Two-Dimensional
Surface
9
2.1
Infinitesimal Displacements
.................. 10
2.2
Lagrange s Equations
...................... 12
2.3
Reciprocal Basis
........................ 14
2.4
Geodesic Motion
........................ 19
2.5
Role of Coordinates
...................... 24
3.
Curvilinear Coordinate Systems
27
3.1
Line Element
.......................... 27
3.2
Reciprocal Basis
........................ 29
3.3
Metric
.............................. 29
3.4
Vectors
............................. 30
3.5
Tensors
............................. 31
3.6
Change of Basis
......................... 33
3.7
Transformation Law
...................... 36
3.8
Affine
Connection
........................ 39
3.9
Example: Polar Coordinates
.................. 41
4.
Particle on a Two-Dimensional Surface
—
Revisited
43
4.1
Motion in Three-Dimensional Euclidian Space
........ 43
4.2
Parallel Displacement
..................... 46
x
Introduction
to General Relativity
5.
Some Tensor Analysis
51
5.1
Covariant Derivative
...................... 51
5.2
The Riemann Curvature Tensor
................ 54
5.3
Second Covariant Derivative
.................. 60
5.4
Covariant Differentiation
.................... 64
5.5
Symmetry Properties of the Riemann Tensor
........ 67
5.6
Bianchi
Identities
........................ 68
5.7
The Einstein Tensor
...................... 69
5.8
Example
—
Surface of a Sphere
................. 72
5.9
Volume element
......................... 76
6.
Special Relativity
87
6.1
Basic Principles
......................... 87
6.2
Four-Vectors
.......................... 88
6.3
Relativistic Particle Motion
.................. 91
6.4
Lorentz
Transformations
.................... 98
6.5
General Tensor Transformation Law
............. 109
6.6
Relativistic Hydrodynamics
..................
Ill
6.7
Transition to General Relativity
................ 120
7.
General Relativity
123
7.1
Einstein s Theory
........................ 123
7.2
Newtonian Limit
........................ 126
7.3
The Equivalence Principle
................... 131
7.4
Local Freely Falling Frame (LF3)
............... 133
7.5
Spherically Symmetric Solution to Field Equations
..... 135
7.6
Solution in Vacuum
...................... 143
7.7
Interpretation of
Schwarzschild
Metric
............ 148
7.8
A Few Applications
....................... 152
8.
Precession of Perihelion
155
8.1
Lagrangian
........................... 156
8.2
Equations of Motion
...................... 159
8.3
Equilibrium Circular Orbits
.................. 163
8.4
Small Oscillations About Circular Orbits
........... 164
8.5
Some Numbers and Comparison with Experiment
...... 169
8.6
Deflection of Light
....................... 171
Contents xi
9.
Gravitational Redshift
173
9.1 Basic
Observation .......................
174
9.2
Frequency Shift
......................... 174
9.3
Propagation of Light
...................... 176
9.4
A Cyclic Process
........................ 178
10.
Neutron Stars
181
10.1
Hydrodynamics in General Relativity
............ 181
10.2
Tolman-Oppenheimer-Volkoff
(TOV)
Equations
....... 190
10.3
Relativistic Mean Field Theory of Nuclear Matter (RMFT)
201
10.4
Neutron Stars and Black Holes
................ 210
11.
Cosmology
217
11.1
Uniform Mass Background
.................. 218
11.2
Robertson-Walker Metric with
к
= 0............. 220
11.3
Solution to Einstein s Equations
............... 225
11.4
Interpretation
.......................... 229
11.5
Cosmological Redshift
..................... 233
11.6
Horizon
............................. 237
11.7
Some Comments
........................ 239
12.
Gravitational Radiation
241
12.1
Linearized Theory
....................... 241
12.2
Auxiliary
(Lorentz)
Condition
................. 245
12.3
Plane-Wave Solution to the Einstein Field Equations
.... 250
12.4
Interpretation
.......................... 253
12.5
Detection
............................ 257
13.
Special Topics
263
13.1
Einstein-Hilbert Lagrangian
.................. 264
13.2
Cosmological Constant
..................... 267
13.3
Additional Scalar Field
..................... 268
13.4
Robertson-Walker Metric with
к
φ
0............. 270
13.5
Inflation
............................. 275
14.
Problems
281
Appendix A Reduction of
дџ
δϋμιι
to covariant divergences
321
xii
Introduction
to
General
Relativity
Appendix
В
Robertson-Walker Metric with
к
φ
О
325
Bibliography
327
Index
331
|
| adam_txt |
Contents
Preface vii
1.
Introduction
1
2.
Partiele
on a Two-Dimensional
Surface
9
2.1
Infinitesimal Displacements
. 10
2.2
Lagrange's Equations
. 12
2.3
Reciprocal Basis
. 14
2.4
Geodesic Motion
. 19
2.5
Role of Coordinates
. 24
3.
Curvilinear Coordinate Systems
27
3.1
Line Element
. 27
3.2
Reciprocal Basis
. 29
3.3
Metric
. 29
3.4
Vectors
. 30
3.5
Tensors
. 31
3.6
Change of Basis
. 33
3.7
Transformation Law
. 36
3.8
Affine
Connection
. 39
3.9
Example: Polar Coordinates
. 41
4.
Particle on a Two-Dimensional Surface
—
Revisited
43
4.1
Motion in Three-Dimensional Euclidian Space
. 43
4.2
Parallel Displacement
. 46
x
Introduction
to General Relativity
5.
Some Tensor Analysis
51
5.1
Covariant Derivative
. 51
5.2
The Riemann Curvature Tensor
. 54
5.3
Second Covariant Derivative
. 60
5.4
Covariant Differentiation
. 64
5.5
Symmetry Properties of the Riemann Tensor
. 67
5.6
Bianchi
Identities
. 68
5.7
The Einstein Tensor
. 69
5.8
Example
—
Surface of a Sphere
. 72
5.9
Volume element
. 76
6.
Special Relativity
87
6.1
Basic Principles
. 87
6.2
Four-Vectors
. 88
6.3
Relativistic Particle Motion
. 91
6.4
Lorentz
Transformations
. 98
6.5
General Tensor Transformation Law
. 109
6.6
Relativistic Hydrodynamics
.
Ill
6.7
Transition to General Relativity
. 120
7.
General Relativity
123
7.1
Einstein's Theory
. 123
7.2
Newtonian Limit
. 126
7.3
The Equivalence Principle
. 131
7.4
Local Freely Falling Frame (LF3)
. 133
7.5
Spherically Symmetric Solution to Field Equations
. 135
7.6
Solution in Vacuum
. 143
7.7
Interpretation of
Schwarzschild
Metric
. 148
7.8
A Few Applications
. 152
8.
Precession of Perihelion
155
8.1
Lagrangian
. 156
8.2
Equations of Motion
. 159
8.3
Equilibrium Circular Orbits
. 163
8.4
Small Oscillations About Circular Orbits
. 164
8.5
Some Numbers and Comparison with Experiment
. 169
8.6
Deflection of Light
. 171
Contents xi
9.
Gravitational Redshift
173
9.1 Basic
Observation .
174
9.2
Frequency Shift
. 174
9.3
Propagation of Light
. 176
9.4
A Cyclic Process
. 178
10.
Neutron Stars
181
10.1
Hydrodynamics in General Relativity
. 181
10.2
Tolman-Oppenheimer-Volkoff
(TOV)
Equations
. 190
10.3
Relativistic Mean Field Theory of Nuclear Matter (RMFT)
201
10.4
Neutron Stars and Black Holes
. 210
11.
Cosmology
217
11.1
Uniform Mass Background
. 218
11.2
Robertson-Walker Metric with
к
= 0. 220
11.3
Solution to Einstein's Equations
. 225
11.4
Interpretation
. 229
11.5
Cosmological Redshift
. 233
11.6
Horizon
. 237
11.7
Some Comments
. 239
12.
Gravitational Radiation
241
12.1
Linearized Theory
. 241
12.2
Auxiliary
(Lorentz)
Condition
. 245
12.3
Plane-Wave Solution to the Einstein Field Equations
. 250
12.4
Interpretation
. 253
12.5
Detection
. 257
13.
Special Topics
263
13.1
Einstein-Hilbert Lagrangian
. 264
13.2
Cosmological Constant
. 267
13.3
Additional Scalar Field
. 268
13.4
Robertson-Walker Metric with
к
φ
0. 270
13.5
Inflation
. 275
14.
Problems
281
Appendix A Reduction of
дџ"
δϋμιι
to covariant divergences
321
xii
Introduction
to
General
Relativity
Appendix
В
Robertson-Walker Metric with
к
φ
О
325
Bibliography
327
Index
331 |
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| id | DE-604.BV022471935 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:44:58Z |
| indexdate | 2024-07-09T20:58:20Z |
| institution | BVB |
| isbn | 9789812705853 9812705856 9789812705846 9812705848 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015679405 |
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| physical | XII, 342 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
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| publisher | World Scientific Publ. |
| record_format | marc |
| spelling | Walecka, John Dirk 1932- Verfasser (DE-588)132844788 aut Introduction to general relativity John Dirk Walecka Singapore [u.a.] World Scientific Publ. 2007 XII, 342 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Relativité générale (Physique) - Mathématiques Mathematik General relativity (Physics) Mathematics Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015679405&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Walecka, John Dirk 1932- Introduction to general relativity Relativité générale (Physique) - Mathématiques Mathematik General relativity (Physics) Mathematics Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| subject_GND | (DE-588)4112491-1 |
| title | Introduction to general relativity |
| title_auth | Introduction to general relativity |
| title_exact_search | Introduction to general relativity |
| title_exact_search_txtP | Introduction to general relativity |
| title_full | Introduction to general relativity John Dirk Walecka |
| title_fullStr | Introduction to general relativity John Dirk Walecka |
| title_full_unstemmed | Introduction to general relativity John Dirk Walecka |
| title_short | Introduction to general relativity |
| title_sort | introduction to general relativity |
| topic | Relativité générale (Physique) - Mathématiques Mathematik General relativity (Physics) Mathematics Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| topic_facet | Relativité générale (Physique) - Mathématiques Mathematik General relativity (Physics) Mathematics Allgemeine Relativitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015679405&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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