Relativity, gravitation, and cosmology: a basic introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Oxford Univ. Press
2006
|
| Ausgabe: | Reprint. |
| Schriftenreihe: | Oxford master series in physics
11 : Particle physics, astrophysics, and cosmology |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIII, 340 S. Ill., graph. Darst. |
| ISBN: | 9780198529569 |
Internformat
MARC
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| 100 | 1 | |a Cheng, Ta-Pei |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Relativity, gravitation, and cosmology |b a basic introduction |c Ta-Pei Cheng |
| 250 | |a Reprint. | ||
| 264 | 1 | |a New York [u.a.] |b Oxford Univ. Press |c 2006 | |
| 300 | |a XIII, 340 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Oxford master series in physics |v 11 : Particle physics, astrophysics, and cosmology | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a aGeneral relativity (Physics) |a vTextbooks | |
| 650 | 4 | |a aSpace and time | |
| 650 | 4 | |a aGravity | |
| 650 | 4 | |a aCosmology | |
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Datensatz im Suchindex
| _version_ | 1804137764896112640 |
|---|---|
| adam_text | Contents
Parti RELATIVITY Metric Description of
Spacetime
1
Introduction and overview
3
1.1
Relativity as a coordinate symmetry
5
1.1.1
From Newtonian relativity to aether
5
1.1.2
Einsteinian relativity
6
1.1.3
Coordinate symmetry transformations
7
1.1.4
New kinematics and dynamics
7
1.2
GR as a gravitational field theory
8
1.2.1
Einstein s motivations for the general theory
8
1.2.2
Geometry as gravity
10
1.2.3
Mathematical language of relativity
11
1.2.4
GR is the framework for cosmology
12
Review questions
12
2
Special relativity and the flat spacetime
14
2.1
Coordinate symmetries
14
2.1.1
Rotational symmetry
14
2.1.2
Newtonian physics and Galilean symmetry
16
2.1.3
Electrodynamics and
Lorentz
symmetry
17
2.1.4
Velocity addition rale amended
18
2.2
The new kinematics of space and time
19
2.2.1
Relativity of spatial equilocality
20
2.2.2
Relativity of simultaneity
—
the new
kinematics
20
2.2.3
The invariant space-time interval
22
2.3
Geometric formulation of SR
24
2.3.1
General coordinates and the metric tensor
24
2.3.2
Derivation of
Lorentz
transformation
28
2.3.3
The spacetime diagram
30
2.3.4
Time-dilation and length contraction
32
Review questions
35
Problems
35
3
The principle of equivalence
38
3.1
Newtonian gravitation potential
—
a review
38
3.2
EP introduced
39
3.2.1
Inertia! mass vs. gravitational mass
40
3.2.2
EP and its significance
41
χ
Contents
3.3
Implications
of the strong
EP 43
3.3.1
Gravitational redshift and time dilation
43
3.3.2
Light ray deflection calculated
48
3.3.3
Energy considerations of a gravitating
light pulse
51
3.3.4
Einstein s inference of a curved spacetime
52
Review questions
53
Problems
53
Metric description of a curved space
55
4.1
Gaussian coordinates
56
4.2
Metric tensor
57
4.2.1
Geodesic as the shortest curve
59
4.2.2
Local Euclidean coordinates
61
4.3
Curvature
63
4.3.1
Gaussian curvature
63
4.3.2
Spaces with constant curvature
64
4.3.3
Curvature measures deviation from Euclidean
relations
66
Review questions
68
Problems
69
GR as a geometric theory of gravity
-
1
71
5.1
Geometry as gravity
71
5.1.1
EP physics and a warped spacetime
73
5.1.2
Curved spacetime as gravitational field
74
5.2
Geodesic equation as GR equation of motion
75
5.2.1
The Newtonian limit
76
5.2.2
Gravitational redshift revisited
78
5.3
The curvature of spacetime
79
5.3.1
Tidal force as the curvature of spacetime
80
5.3.2
The GR field equation described
83
Review questions
85
Problems
85
Spacetime outside a spherical star
87
6.1
Description of
Schwarzschild
spacetime
87
6.1.1
Spherically symmetric metric tensor
88
6.1.2 Schwarzschild
geometry
90
6.2
Gravitational lensing
92
6.2.1
Light ray deflection revisited
93
6.2.2
The lens equation
93
6.3
Precession of Mercury s perihelion
97
6.4
Black holes
102
6.4.1
Singularities of the
Schwarzschild
metric
102
6.4.2
Time measurements in the
Schwarzschild
spacetime
102
6.4.3
Lightcones of the
Schwarzschild
black hole
105
Contents xi
6.4.4 Orbit
of an object around a black hole
108
6.4.5
Physical reality of black holes
108
Review questions
111
Problems
112
Partii
COSMOLOGY
7
The homogeneous and
isotropie
universe
115
7.1
The cosmos observed
116
7.1.1
Matter distribution on the cosmic
distance scale
116
7.1.2
Cosmological redshift: Hubble s law
116
7.1.3
Age of the universe
120
7.1.4
Dark matter and mass density
of the universe
121
7.2
The cosmological principle
125
7.3
The Robertson-Walker metric
127
7.3.1
Proper distance in the RW geometry
129
7.3.2
Redshift and luminosity distance
130
Review questions
133
Problems
134
The expanding universe and thermal relics
136
8.1 Friedmann
equations
137
8.1.1
The quasi-Newtonian interpretation
139
8.2
Time evolution of model universes
142
8.3
Big bang cosmology
145
8.3.1
Scale-dependence of radiation
temperature
145
8.3.2
Different thermal equilibrium stages
147
8.4
Primordial nucleosynthesis
149
8.5
Photon decoupling and the CMB
152
8.5.1
Universe became transparent to photons
153
8.5.2
The discovery of CMB radiation
154
8.5.3
Photons, neutrinos, and the radiation-matter
equality time
155
8.5.4
CMB temperature fluctuation
159
Review questions
162
Problems
163
Inflation and the accelerating universe
165
9.1
The cosmological constant
166
9.1.1
Vacuum-energy as source of gravitational
repulsion
167
9.1.2
The static universe
168
9.2
The inflationary epoch
170
9.2.1
Initial conditions for the standard
big bang model
171
xii Contents
9.2.2
The inflation scenario
173
9.2.3
Inflation and the conditions it left behind
175
9.3
CMB anisotropy and evidence for
k
= 0 178
9.3.1
Three regions ofthe angular power spectrum
179
9.3.2
The primary peak and spatial geometry
of the universe
181
9.4
The accelerating universe in the present epoch
183
9.4.1
Distant
supernovae
and the
1998
discovery
184
9.4.2
Transition from deceleration to
acceleration
187
9.5
The concordant picture
189
Review questions
193
Problems
193
Part III RELATIVITY Full Tensor Formulation
10
Tensors in special relativity
197
10.1
General coordinate systems
197
10.2
Four-vectors in Minkowski spacetime
200
10.3
Manifestly covariant formalism for E&M
205
10.3.1
The electromagnetic field tensor
205
10.3.2
Electric charge conservation
208
10.4
Energy-momentum tensors
208
Review questions
213
Problems
213
11
Tensors in general relativity
215
11.1
Derivatives
ina
curved space
215
11.1.1
General coordinate transformations
216
11.1.2
Covariant differentiation
218
11.1.3 Christoffel
symbols and metric tensor
220
11.2
Parallel transport
222
11.2.1
Component changes under parallel
transport
222
11.2.2
The geodesic as the straightest
possible curve
224
11.3
Riemannian curvature tensor
225
11.3.1
The curvature tensor in an n-dimensional
space
226
11.3.2
Symmetries and contractions of the
curvature tensor
228
Review questions
230
Problems
231
12
GR as a geometric theory of gravity
-
II
233
12.1
The principle of general covariance
233
12.1.1
Geodesic equation from SR equation
of motion
235
Contents xiii
12.2 Einstein
field equation
236
12.2.1
Finding the relativistic gravitational field
equation
236
12.2.2
Newtonian limit of the Einstein equation
237
12.3
The
Schwarzschild
exterior solution
239
12.4
The Einstein equation for cosmology
244
12.4.1
Solution for a homogeneous and
isotropie
3D
space
244
12.4.2 Friedmann
equations
246
12.4.3
Einstein equation with a cosmological
constant term
247
Review questions
248
Problems
248
13
Linearized theory and gravitational waves
250
13.1
The linearized Einstein theory
251
13.1.1
The coordinate change called gauge
transformation
252
13.1.2
The wave equation in the
Lorentz
gauge
253
13.2
Plane waves and the polarization tensor
254
13.3
Gravitational wave detection
255
13.3.1
Effect of gravitational waves on test
particles
255
13.3.2
Gravitational wave interferometers
257
13.4
Evidence for gravitational wave
259
13.4.1
Energy flux in linearized gravitational
waves
260
13.4.2
Emission of gravitational radiation
262
13.4.3
Binary pulsar PSR
1913+16 264
Review questions
268
Problems
269
A Supplementary notes
271
A.
1
The twin paradox (Section
2.3.4) 271
A.2 A glimpse of advanced topics in black hole physics
(Section
6.4) 275
A.3 False vacuum and hidden symmetry
(Section
9.2.2) 279
A.4 The problem of quantum vacuum energy as
Λ
(Section
9.4) 280
В
Answer keys to review questions
283
С
Solutions of selected problems
293
References
330
Bibliography
333
Index
335
|
| adam_txt |
Contents
Parti RELATIVITY Metric Description of
Spacetime
1
Introduction and overview
3
1.1
Relativity as a coordinate symmetry
5
1.1.1
From Newtonian relativity to aether
5
1.1.2
Einsteinian relativity
6
1.1.3
Coordinate symmetry transformations
7
1.1.4
New kinematics and dynamics
7
1.2
GR as a gravitational field theory
8
1.2.1
Einstein's motivations for the general theory
8
1.2.2
Geometry as gravity
10
1.2.3
Mathematical language of relativity
11
1.2.4
GR is the framework for cosmology
12
Review questions
12
2
Special relativity and the flat spacetime
14
2.1
Coordinate symmetries
14
2.1.1
Rotational symmetry
14
2.1.2
Newtonian physics and Galilean symmetry
16
2.1.3
Electrodynamics and
Lorentz
symmetry
17
2.1.4
Velocity addition rale amended
18
2.2
The new kinematics of space and time
19
2.2.1
Relativity of spatial equilocality
20
2.2.2
Relativity of simultaneity
—
the new
kinematics
20
2.2.3
The invariant space-time interval
22
2.3
Geometric formulation of SR
24
2.3.1
General coordinates and the metric tensor
24
2.3.2
Derivation of
Lorentz
transformation
28
2.3.3
The spacetime diagram
30
2.3.4
Time-dilation and length contraction
32
Review questions
35
Problems
35
3
The principle of equivalence
38
3.1
Newtonian gravitation potential
—
a review
38
3.2
EP introduced
39
3.2.1
Inertia! mass vs. gravitational mass
40
3.2.2
EP and its significance
41
χ
Contents
3.3
Implications
of the strong
EP 43
3.3.1
Gravitational redshift and time dilation
43
3.3.2
Light ray deflection calculated
48
3.3.3
Energy considerations of a gravitating
light pulse
51
3.3.4
Einstein's inference of a curved spacetime
52
Review questions
53
Problems
53
Metric description of a curved space
55
4.1
Gaussian coordinates
56
4.2
Metric tensor
57
4.2.1
Geodesic as the shortest curve
59
4.2.2
Local Euclidean coordinates
61
4.3
Curvature
63
4.3.1
Gaussian curvature
63
4.3.2
Spaces with constant curvature
64
4.3.3
Curvature measures deviation from Euclidean
relations
66
Review questions
68
Problems
69
GR as a geometric theory of gravity
-
1
71
5.1
Geometry as gravity
71
5.1.1
EP physics and a warped spacetime
73
5.1.2
Curved spacetime as gravitational field
74
5.2
Geodesic equation as GR equation of motion
75
5.2.1
The Newtonian limit
76
5.2.2
Gravitational redshift revisited
78
5.3
The curvature of spacetime
79
5.3.1
Tidal force as the curvature of spacetime
80
5.3.2
The GR field equation described
83
Review questions
85
Problems
85
Spacetime outside a spherical star
87
6.1
Description of
Schwarzschild
spacetime
87
6.1.1
Spherically symmetric metric tensor
88
6.1.2 Schwarzschild
geometry
90
6.2
Gravitational lensing
92
6.2.1
Light ray deflection revisited
93
6.2.2
The lens equation
93
6.3
Precession of Mercury's perihelion
97
6.4
Black holes
102
6.4.1
Singularities of the
Schwarzschild
metric
102
6.4.2
Time measurements in the
Schwarzschild
spacetime
102
6.4.3
Lightcones of the
Schwarzschild
black hole
105
Contents xi
6.4.4 Orbit
of an object around a black hole
108
6.4.5
Physical reality of black holes
108
Review questions
111
Problems
112
Partii
COSMOLOGY
7
The homogeneous and
isotropie
universe
115
7.1
The cosmos observed
116
7.1.1
Matter distribution on the cosmic
distance scale
116
7.1.2
Cosmological redshift: Hubble's law
116
7.1.3
Age of the universe
120
7.1.4
Dark matter and mass density
of the universe
121
7.2
The cosmological principle
125
7.3
The Robertson-Walker metric
127
7.3.1
Proper distance in the RW geometry
129
7.3.2
Redshift and luminosity distance
130
Review questions
133
Problems
134
The expanding universe and thermal relics
136
8.1 Friedmann
equations
137
8.1.1
The quasi-Newtonian interpretation
139
8.2
Time evolution of model universes
142
8.3
Big bang cosmology
145
8.3.1
Scale-dependence of radiation
temperature
145
8.3.2
Different thermal equilibrium stages
147
8.4
Primordial nucleosynthesis
149
8.5
Photon decoupling and the CMB
152
8.5.1
Universe became transparent to photons
153
8.5.2
The discovery of CMB radiation
154
8.5.3
Photons, neutrinos, and the radiation-matter
equality time
155
8.5.4
CMB temperature fluctuation
159
Review questions
162
Problems
163
Inflation and the accelerating universe
165
9.1
The cosmological constant
166
9.1.1
Vacuum-energy as source of gravitational
repulsion
167
9.1.2
The static universe
168
9.2
The inflationary epoch
170
9.2.1
Initial conditions for the standard
big bang model
171
xii Contents
9.2.2
The inflation scenario
173
9.2.3
Inflation and the conditions it left behind
175
9.3
CMB anisotropy and evidence for
k
= 0 178
9.3.1
Three regions ofthe angular power spectrum
179
9.3.2
The primary peak and spatial geometry
of the universe
181
9.4
The accelerating universe in the present epoch
183
9.4.1
Distant
supernovae
and the
1998
discovery
184
9.4.2
Transition from deceleration to
acceleration
187
9.5
The concordant picture
189
Review questions
193
Problems
193
Part III RELATIVITY Full Tensor Formulation
10
Tensors in special relativity
197
10.1
General coordinate systems
197
10.2
Four-vectors in Minkowski spacetime
200
10.3
Manifestly covariant formalism for E&M
205
10.3.1
The electromagnetic field tensor
205
10.3.2
Electric charge conservation
208
10.4
Energy-momentum tensors
208
Review questions
213
Problems
213
11
Tensors in general relativity
215
11.1
Derivatives
ina
curved space
215
11.1.1
General coordinate transformations
216
11.1.2
Covariant differentiation
218
11.1.3 Christoffel
symbols and metric tensor
220
11.2
Parallel transport
222
11.2.1
Component changes under parallel
transport
222
11.2.2
The geodesic as the straightest
possible curve
224
11.3
Riemannian curvature tensor
225
11.3.1
The curvature tensor in an n-dimensional
space
226
11.3.2
Symmetries and contractions of the
curvature tensor
228
Review questions
230
Problems
231
12
GR as a geometric theory of gravity
-
II
233
12.1
The principle of general covariance
233
12.1.1
Geodesic equation from SR equation
of motion
235
Contents xiii
12.2 Einstein
field equation
236
12.2.1
Finding the relativistic gravitational field
equation
236
12.2.2
Newtonian limit of the Einstein equation
237
12.3
The
Schwarzschild
exterior solution
239
12.4
The Einstein equation for cosmology
244
12.4.1
Solution for a homogeneous and
isotropie
3D
space
244
12.4.2 Friedmann
equations
246
12.4.3
Einstein equation with a cosmological
constant term
247
Review questions
248
Problems
248
13
Linearized theory and gravitational waves
250
13.1
The linearized Einstein theory
251
13.1.1
The coordinate change called gauge
transformation
252
13.1.2
The wave equation in the
Lorentz
gauge
253
13.2
Plane waves and the polarization tensor
254
13.3
Gravitational wave detection
255
13.3.1
Effect of gravitational waves on test
particles
255
13.3.2
Gravitational wave interferometers
257
13.4
Evidence for gravitational wave
259
13.4.1
Energy flux in linearized gravitational
waves
260
13.4.2
Emission of gravitational radiation
262
13.4.3
Binary pulsar PSR
1913+16 264
Review questions
268
Problems
269
A Supplementary notes
271
A.
1
The twin paradox (Section
2.3.4) 271
A.2 A glimpse of advanced topics in black hole physics
(Section
6.4) 275
A.3 False vacuum and hidden symmetry
(Section
9.2.2) 279
A.4 The problem of quantum vacuum energy as
Λ
(Section
9.4) 280
В
Answer keys to review questions
283
С
Solutions of selected problems
293
References
330
Bibliography
333
Index
335 |
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| id | DE-604.BV023388795 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:19:03Z |
| indexdate | 2024-07-09T21:17:29Z |
| institution | BVB |
| isbn | 9780198529569 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016571765 |
| oclc_num | 634199568 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-20 DE-83 |
| owner_facet | DE-355 DE-BY-UBR DE-20 DE-83 |
| physical | XIII, 340 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | Oxford master series in physics |
| series2 | Oxford master series in physics |
| spelling | Cheng, Ta-Pei Verfasser aut Relativity, gravitation, and cosmology a basic introduction Ta-Pei Cheng Reprint. New York [u.a.] Oxford Univ. Press 2006 XIII, 340 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford master series in physics 11 : Particle physics, astrophysics, and cosmology Includes bibliographical references and index aGeneral relativity (Physics) vTextbooks aSpace and time aGravity aCosmology Kosmologie (DE-588)4114294-9 gnd rswk-swf Gravitationstheorie (DE-588)4158117-9 gnd rswk-swf Relativitätstheorie (DE-588)4049363-5 gnd rswk-swf Gravitation (DE-588)4021908-2 gnd rswk-swf Gravitationstheorie (DE-588)4158117-9 s DE-604 Relativitätstheorie (DE-588)4049363-5 s Gravitation (DE-588)4021908-2 s Kosmologie (DE-588)4114294-9 s 1\p DE-604 Oxford master series in physics 11 : Particle physics, astrophysics, and cosmology (DE-604)BV017064373 11 http://www.loc.gov/catdir/toc/ecip0422/2004019733.html Verlag Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016571765&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 | Cheng, Ta-Pei Relativity, gravitation, and cosmology a basic introduction Oxford master series in physics aGeneral relativity (Physics) vTextbooks aSpace and time aGravity aCosmology Kosmologie (DE-588)4114294-9 gnd Gravitationstheorie (DE-588)4158117-9 gnd Relativitätstheorie (DE-588)4049363-5 gnd Gravitation (DE-588)4021908-2 gnd |
| subject_GND | (DE-588)4114294-9 (DE-588)4158117-9 (DE-588)4049363-5 (DE-588)4021908-2 |
| title | Relativity, gravitation, and cosmology a basic introduction |
| title_auth | Relativity, gravitation, and cosmology a basic introduction |
| title_exact_search | Relativity, gravitation, and cosmology a basic introduction |
| title_exact_search_txtP | Relativity, gravitation, and cosmology a basic introduction |
| title_full | Relativity, gravitation, and cosmology a basic introduction Ta-Pei Cheng |
| title_fullStr | Relativity, gravitation, and cosmology a basic introduction Ta-Pei Cheng |
| title_full_unstemmed | Relativity, gravitation, and cosmology a basic introduction Ta-Pei Cheng |
| title_short | Relativity, gravitation, and cosmology |
| title_sort | relativity gravitation and cosmology a basic introduction |
| title_sub | a basic introduction |
| topic | aGeneral relativity (Physics) vTextbooks aSpace and time aGravity aCosmology Kosmologie (DE-588)4114294-9 gnd Gravitationstheorie (DE-588)4158117-9 gnd Relativitätstheorie (DE-588)4049363-5 gnd Gravitation (DE-588)4021908-2 gnd |
| topic_facet | aGeneral relativity (Physics) vTextbooks aSpace and time aGravity aCosmology Kosmologie Gravitationstheorie Relativitätstheorie Gravitation |
| url | http://www.loc.gov/catdir/toc/ecip0422/2004019733.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016571765&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV017064373 |
| work_keys_str_mv | AT chengtapei relativitygravitationandcosmologyabasicintroduction |
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