Relativity, gravitation and cosmology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2010
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | 312 S. Ill., graph. Darst. |
| ISBN: | 9780521761192 9780521131384 |
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| adam_text | Contents
RELATIVITY,
GRAVITATION
AND COSMOLOGY
Introduction
9
Chapter I Special relativity and spacetime I I
Introduction
11
1.1
Basic concepts of special relativity
12
1.1.1
Events, frames of reference and observers
12
1.1.2
The postulates of special relativity
14
1.2
Coordinate transformations
16
1.2.1
The Galilean transformations
16
1.2.2
The
Lorentz
transformations
18
1.2.3
A derivation of the
Lorentz
transformations
21
1.2.4
Intervals and their transformation rules
23
1.3
Consequences of the
Lorentz
transformations
24
1.3.1
Time dilation
24
1.3.2
Length contraction
26
1.3.3
The relativity of simultaneity
27
1.3.4
The
Doppler
effect
28
1.3.5
The velocity transformation
29
1.4
Minkowski spacetime
31
1.4.1
Spacetime diagrams, lightcones and causality
31
1.4.2
Spacetime separation and the Minkowski metric
35
1.4.3
The twin effect
38
Chapter
2
Special relativity and physical laws
45
Introduction
45
2.1
Invariants and physical laws
46
2.1.1
The
invariance
of physical quantities
46
2.1.2
The
invariance
of physical laws
47
2.2
The laws of mechanics
49
2.2.1
Relativistic momentum
49
2.2.2
Relativistic kinetic energy
52
2.2.3
Total relativistic energy and mass energy
54
2.2.4
Four-momentum
56
2.2.5
The energy-momentum relation
58
2.2.6
The conservation of energy and momentum
60
2.2.7
Four-force
61
2.2.8
Four-vectors
62
2.3
The laws of
electromagnetism
67
Contents
2.3.1 The
conservation
of
charge
67
2.3.2
The
Lorentz
force law
68
2.3.3
The transformation of electric and magnetic fields
73
2.3.4
The Maxwell equations
74
2.3.5
Four-tensors
75
Chapter
3
Geometry and curved spacetime
80
Introduction
80
3.1
Line elements and differential geometry
82
3.1.1
Line elements in a plane
82
3.1.2
Curved surfaces
85
3.2
Metrics and connections
90
3.2.1
Metrics and Riemannian geometry
90
3.2.2
Connections and parallel transport
92
3.3
Geodesies
97
3.3.1
Most direct route between two points
97
3.3.2
Shortest distance between two points
98
3.4
Curvature
100
3.4.1
Curvature of a curve in a plane
101
3.4.2
Gaussian curvature of a two-dimensional surface
102
3.4.3
Curvature in spaces of higher dimensions
104
3.4.4
Curvature of spacetime
106
Chapter
4
General relativity and gravitation I
10
Introduction
110
4.1
The founding principles of general relativity
111
4.1.1
The principle of equivalence
112
4.1.2
The principle of general covariance
116
4.1.3
The principle of consistency
124
4.2
The basic ingredients of general relativity
126
4.2.1
The energy-momentum tensor
126
4.2.2
The Einstein tensor
132
4.3
Einstein s field equations and geodesic motion
133
4.3.1
The Einstein field equations
134
4.3.2
Geodesic motion
136
4.3.3
The Newtonian limit of Einstein s field equations
138
4.3.4
The cosmological constant
139
Chapter
5 Schwarzschild
spacetime 1
44
Introduction
144
5.1
The metric of
Schwarzschild
spacetime
145
5.1.1 The Schwarzschild
metric
145
5.1.2
Derivation of the
Schwarzschild
metric
146
5.2
Properties of
Schwarzschild
spacetime
151
5.2.1
Spherical symmetry
151
5.2.2
Asymptotic flatness
152
5.2.3
Time-independence
152
5.2.4
Singularity
153
5.2.5
Generality
154
5.3
Coordinates and measurements in
Schwarzschild
spacetime
154
5.3.1
Frames and observers
155
5.3.2
Proper time and gravitational time dilation
156
5.3.3
Proper distance
159
5.4
Geodesic motion in
Schwarzschild
spacetime
160
5.4.1
The geodesic equations
161
5.4.2
Constants of the motion in
Schwarzschild
spacetime
162
5.4.3
Orbital motion in
Schwarzschild
spacetime
166
Chapter
6
Black holes 1
7
1
Introduction
171
6.1
Introducing black holes
171
6.1.1
A black hole and its event horizon
171
6.1.2
A brief history of black holes
172
6.1.3
The classification of black holes
175
6.2
Non-rotating black holes
176
6.2.1
Falling into a non-rotating black hole
177
6.2.2
Observing a fall from far away
179
6.2.3
Tidal effects near a non-rotating black hole
183
6.2.4
The deflection of light near a non-rotating black hole
186
6.2.5
The event horizon and beyond
187
6.3
Rotating black holes
192
6.3.1
The Kerr solution and rotating black holes
192
6.3.2
Motion near a rotating black hole
194
6.4
Quantum physics and black holes
198
6.4.1
Hawking radiation
198
6.4.2
Singularities and quantum physics
200
Chapter
7
Testing general relativity
204
Introduction
204
7.1
The classic tests of general relativity
204
7.1.1
Precession of the perihelion of Mercury
204
ontents
7.1.2
Deflection of light by the Sun
205
7.1.3
Gravitational redshif
t
and gravitational time dilation
206
7.1.4
Time delay of signals passing the Sun
211
7.2
Satellite-based tests
213
7.2.1
Geodesic gyroscope precession
213
7.2.2
Frame dragging
214
7.2.3
The LAGEOS satellites
215
7.2.4
Gravity Probe
В
216
7.3
Astronomical observations
217
7.3.1
Black holes
217
7.3.2
Gravitational lensing
223
7.4
Gravitational waves
226
7.4.1
Gravitational waves and the Einstein field equations
226
7.4.2
Methods of detecting gravitational waves
229
7.4.3
Likely sources of gravitational waves
231
Chapter
8
Relativistic cosmology
234
Introduction
234
8.1
Basic principles and supporting observations
235
8.1.1
The applicability of general relativity
235
8.1.2
The cosmological principle
236
8.1.3
Weyl s postulate
240
8.2
Robertson-Walker spacetime
242
8.2.1
The Robertson-Walker metric
243
8.2.2
Proper distances and velocities in cosmic spacetime
245
8.2.3
The cosmic geometry of space and spacetime
247
8.3
The
Friedmann
equations and cosmic evolution
251
8.3.1
The energy-momentum tensor of the cosmos
251
8.3.2
The
Friedmann
equations
254
8.3.3
Three cosmological models with
к
= 0 256
8.3.4 Friedmann-Robertson-Walker
models in general
259
8.4
Friedmann-Robertson-Walker models and observations
263
8.4.1
Cosmological redshift and cosmic expansion
263
8.4.2
Density parameters and the age of the Universe
269
8.4.3
Horizons and limits
270
Appendix
277
Solutions
279
Acknowledgements
308
Index
309
Relativity,
Gravitation
and Cosmology
Aimed at advanced undergraduates, this self-contained textbook covers the key ideas of
special and general relativity together with their applications.
The textbook introduces students to basic geometric concepts, such as metrics,
connections and curvature, before examining general relativity in more detail. It shows
the observational evidence supporting the theory, and the description general relativity
provides of black holes and cosmological spacetimes.
■
In full colour, with numerous worked examples and exercises with solutions
■
Key points and equations are highlighted for easy identification
■
Each chapter ends with a summary list of important concepts and results
Relativity. Gravitation and Cosmology provides the essential background for an
up-to-date discussion of modern observational cosmology. Each chapter builds on the
previous one as concepts are developed, making it ideal for self-study.
Robert J. A. Lambourne is Director of the Physics Innovation Centre for Excellence
in Teaching and Learning (piCETL) in the Department of Physics and Astronomy. The
Open University. In
2002
he was awarded the Bragg medal and prize of the Institute of
Physics for his contributions to physics education, and was made a National Teaching
Fellow in
2006.
The author team has done a great job of
producing a text suitable for upper level
undergrads
and even first year astronomy
graduate students. The graphics are very good
and I particularly appreciate the concise chapter
summaries and the exercises with solutions.
Students will love this text. I will definitely use it in
my upper division classes.
Professor John Huchra, Harvard University
The presentation of special and general relativity
is remarkably clear, with explicit derivations and
explanations accompanied by useful and relevant
exercises. This text strikes a nice balance between
theory and applications and does a commendable
job of bringing undergraduates up to speed on a
challenging topic. I highly recommend this text for
a first undergraduate course in general relativity.
Dr
Jeremy Darling, University of Colorado
CAMBRIDGE
UNIVERSITY PRESS
www.cambridge.org
ISBN
978-0-521-76119-2
9 780521 761192
|
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| spelling | Lambourne, Robert J. Verfasser (DE-588)141658177 aut Relativity, gravitation and cosmology author: Robert J. A. Lambourne 1. publ. Cambridge Cambridge Univ. Press 2010 312 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Relativity (Physics) Gravitation Cosmology Relativitätstheorie (DE-588)4049363-5 gnd rswk-swf Gravitation (DE-588)4021908-2 gnd rswk-swf Kosmologie (DE-588)4114294-9 gnd rswk-swf Relativitätstheorie (DE-588)4049363-5 s Gravitation (DE-588)4021908-2 s Kosmologie (DE-588)4114294-9 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=018804807&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018804807&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Lambourne, Robert J. Relativity, gravitation and cosmology Relativity (Physics) Gravitation Cosmology Relativitätstheorie (DE-588)4049363-5 gnd Gravitation (DE-588)4021908-2 gnd Kosmologie (DE-588)4114294-9 gnd |
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| title | Relativity, gravitation and cosmology |
| title_auth | Relativity, gravitation and cosmology |
| title_exact_search | Relativity, gravitation and cosmology |
| title_full | Relativity, gravitation and cosmology author: Robert J. A. Lambourne |
| title_fullStr | Relativity, gravitation and cosmology author: Robert J. A. Lambourne |
| title_full_unstemmed | Relativity, gravitation and cosmology author: Robert J. A. Lambourne |
| title_short | Relativity, gravitation and cosmology |
| title_sort | relativity gravitation and cosmology |
| topic | Relativity (Physics) Gravitation Cosmology Relativitätstheorie (DE-588)4049363-5 gnd Gravitation (DE-588)4021908-2 gnd Kosmologie (DE-588)4114294-9 gnd |
| topic_facet | Relativity (Physics) Gravitation Cosmology Relativitätstheorie Kosmologie |
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