Lecture notes on the general theory of relativity: from Newton's attractive gravity to the repulsive gravity of vacuum energy
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2009
|
| Series: | Lecture notes in physics
772 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 248 S. Ill., graph. Darst. |
| ISBN: | 9780387881331 |
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MARC
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| 245 | 1 | 0 | |a Lecture notes on the general theory of relativity |b from Newton's attractive gravity to the repulsive gravity of vacuum energy |c Ø. Grøn |
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a XI, 248 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in physics |v 772 | |
| 650 | 4 | |a Relativity (Physics) | |
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Record in the Search Index
| _version_ | 1804138554799947776 |
|---|---|
| adam_text | Contents
1
Newton s Law of Universal Gravitation
........................... 1
1.1
The Force Law of Gravitation
................................ 1
1.2
Newton s Law of Gravitation in Its Local Form
................. 2
1.3
Tidal Forces
............................................... 5
1
.4
The Principle of Equivalence
................................. 9
1
.5
The General Principle of Relativity
............................ 10
1
.6
The Covariance Principle
....................................
II
1.7
Mach s Principle
........................................... 12
Problems
...................................................... 13
References
..................................................... 16
2
The Special Theory of Relativity
................................. 17
2.1
Coordinate Systems and Minkowski Diagrams
.................. 17
2.2
Synchronization of Clocks
................................... 19
2.3
The
Doppler
Effect
......................................... 20
2.4
Relativistic Time Dilation
.................................... 22
2.5
The Relativity of Simultaneity
................................ 23
2.6
The
Lorentz
Contraction
..................................... 26
2.7
The
Lorentz
Transformation
................................. 27
2.8
Lorentz-Invariant Interval
.................................... 29
2.9
The Twin Paradox
.......................................... 32
2.10
Hyperbolic Motion
......................................... 33
2.11
Energy and Mass
........................................... 36
2.1 2
Relativistic Increase of Mass
................................. 37
2.13
Tachyons
................................................. 38
2.14
Magnetism as a Relativistic Second-Order Effect
................ 39
Problems
...................................................... 42
Reference
...................................................... 49
3
Vectors, Tensors and Forms
..................................... ? 1
3.1
Vectors
................................................... 51
3.1.1
4-Veetors
........................................... 52
3.1.2
Tantient Vector Fields and Coordinate Vectors
............ 54
Contents
3.1.3
Coordinate Transformations
........................... 58
3.1.4
Structure Coefficients
................................. 61
3.2
Tensors
................................................... 63
3.2.1
Transformation of Tensor Components
.................. 65
3.2.2
Transformation of Basis
1
-Forms
....................... 65
3.2.3
The Metric Tensor
................................... 66
3.3
Forms
.................................................... 69
Problems
...................................................... 71
Reference
...................................................... 75
Accelerated Reference Frames
................................... 77
4.1
Rotating Reference Frames
.................................. 77
4.1.1
The Spatial Metric Tensor
............................. 77
4.1.2
Angular Acceleration in the Rotating Frame
.............. 81
4.1.3
Gravitational Time Dilation
............................ 83
4.1.4
Path of Photons Emitted from Axes in the Rotating
Reference Frame (RF)
................................ 84
4.1.5
The Sagnac Effect
................................... 85
4.2
Hyperbolically Accelerated Reference Frames
.................. 86
Problems
...................................................... 92
Covariant Differentiation
....................................... 97
5.1
Differentiation of Forms
..................................... 97
5.1.1
Exterior Differentiation
............................... 97
5.1.2
Covariant Derivative
................................. 99
5.2
The
Christoffel
Symbols
..................................... 101
5.3
Geodesic Curves
........................................... 104
5.4
The Covariant Euler-Lagrange Equations
...................... 105
5.5
Application of the Lagrangian Formalism to Free Particles
........ 107
5.5.1
Equation of Motion from Lagrange s Equations
........... 107
5.5.2
Geodesic World Lines in Spacetime
..................... 108
5.5.3
Gravitational
Doppler
Effect
........................... 117
5.6
The
Koszul
Connection
..................................... 119
5.7
Connection Coefficients
Γ^ν
and Structure Coefficients c^v
...... 121
5.8
Covariant Differentiation of Vectors, Forms and Tensors
.......... 122
5.8.1
Covariant Differentiation of a Vector in an Arbitrary Basis
.. 122
5.8.2
Covariant Differentiation of Forms
...................... 123
5.8.3
Generalization for Tensors of Higher Rank
............... 124
5.9
The Cartan Connection
...................................... 125
Problems
...................................................... 128
Reference
...................................................... 132
Contents
Curvature
.....................................................133
6.1
The Riemann Curvature Tensor
...............................133
6.2
Differential Geometry of Surfaces
.............................137
6.2.1
Surface Curvature Using the Cartan Formalism
...........140
6.3
The
Ricci
Identity
..........................................141
6.4
Bianchi s
1st
Identity
.......................................142
6.5
Bianchi s
2nd
Identity
.......................................143
Problems
......................................................144
Einstein s Field Equations
.......................................149
7.1
Energy-Momentum Conservation
.............................149
7.1.1
Newtonian Fluid
.....................................149
7.1.2
Perfect Fluids
.......................................151
7.2
Einstein s Curvature Tensor
..................................151
7.3
Einstein s Field Equations
...................................152
7.4
The Geodesic Postulate as a Consequence of the Field Equations
. 154
Problems
......................................................155
The
Schwarzschild Spacetime................................... 159
8.1
Schwarzschild s Exterior Solution
............................. 159
8.2
Radial Free Fall in
Schwarzschild Spacetime ................... 163
8.3
Light Cones in
Schwarzschild Spacetime....................... 165
8.4
Analytical Extension of the
Schwarzschild
Coordinates
........... 167
8.5
Embedding of the
Schwarzschild
Metric
....................... 169
8.6
Deceleration of Light
....................................... 170
8.7
Particle Trajectories in
Schwarzschild 3-Space.................. 171
8.7.1
Motion in the Equatorial Plane
......................... 173
8.8
Classical Tests of Einstein s General Theory of Relativity
.........
1
75
8.8.1
The Hafele-Keating Experiment
.......................175
8.8.2
Mercury s Perihelion Precession
........................176
8.8.3
Deflection of Light
...................................177
Problems
......................................................179
Reference
......................................................185
Black Holes
...................................................187
9.1
Surface Gravity : Gravitational Acceleration on the Horizon of a
Black Hole
................................................187
9.2
Hawking Radiation: Radiation from a Black Hole
...............188
9.3
Rotating Black Holes: The Kerr Metric
........................189
9.3.1
Zero-Angular-Momentum-Observers
....................190
9.3.2
Does the Kerr Space Have a Horizon?
...................191
Problems
......................................................
192
x
Contents
10
Schwa
rzschild s
Interior Solution
................................199
10.1
Newtonian Incompressible Star
...............................199
10.2
The Pressure Contribution to the
Gravitati
onal Mass of a Static.
Spherically Symmetric System
...............................201
10.3
The Tolman-Oppenheimer-Volkoff Equat ion
...................202
10.4
An Exact Solution for Incompressible Stars
-
Schwarzschild s
Interior Solution
...........................................204
Problems
......................................................205
11
Cosmology
....................................................207
1
I
.
I Comoving Coordinate System
................................207
I 1
.2
Curvature Isotropy
-
The Robertson-Walker Metric
..............208
I 1
.3
Cosmic Dynamics
..........................................209
11.3.1
Hubble s Law
.......................................209
1 1.3.2
Cosmological Redshift of Light
........................209
I
1.3.3
Cosmic Fluids
.......................................211
I
1.3.4
Isotropie
and Homogeneous Universe Models
............212
I
1.4
Some Cosmological Models
.........._......................215
1 1.4.1
Radiation-Dominated Model
....-......................215
I 1
.4.2
Dust-Dominated Model
...............................216
1
1
.4.3
Transition from Radiation
-
To Matter-Dominated
Universe
....................-......................220
1
1.4.4
Friedmann-Lemaître
Model
.... -......................221
I
1.5
Inflationary Cosmology
.....................................230
I 1
.5.1
Problems with the Big Bang Models
....................230
1 1.5.2
Cosmic Inflation
.....................................232
Problems
......................................................237
Reference
...............................-......................244
Index
.............................................................245
|
| any_adam_object | 1 |
| author | Grøn, Øyvind |
| author_GND | (DE-588)133721140 |
| author_facet | Grøn, Øyvind |
| author_role | aut |
| author_sort | Grøn, Øyvind |
| author_variant | ø g øg |
| building | Verbundindex |
| bvnumber | BV035268339 |
| callnumber-first | Q - Science |
| callnumber-label | QC173 |
| callnumber-raw | QC173.55 |
| callnumber-search | QC173.55 |
| callnumber-sort | QC 3173.55 |
| callnumber-subject | QC - Physics |
| classification_rvk | UD 8220 |
| ctrlnum | (OCoLC)339320970 (DE-599)DNB990247244 |
| dewey-full | 530.11 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.11 |
| dewey-search | 530.11 |
| dewey-sort | 3530.11 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV035268339 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:30:02Z |
| institution | BVB |
| isbn | 9780387881331 |
| language | English |
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| physical | XI, 248 S. Ill., graph. Darst. |
| publishDate | 2009 |
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| publisher | Springer |
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| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Grøn, Øyvind Verfasser (DE-588)133721140 aut Lecture notes on the general theory of relativity from Newton's attractive gravity to the repulsive gravity of vacuum energy Ø. Grøn New York, NY Springer 2009 XI, 248 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 772 Relativity (Physics) Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Gravitationstheorie (DE-588)4158117-9 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 s Gravitationstheorie (DE-588)4158117-9 s DE-604 Erscheint auch als Online-Ausgabe 978-0-387-88134-8 Lecture notes in physics 772 (DE-604)BV000003166 772 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017073756&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grøn, Øyvind Lecture notes on the general theory of relativity from Newton's attractive gravity to the repulsive gravity of vacuum energy Lecture notes in physics Relativity (Physics) Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Gravitationstheorie (DE-588)4158117-9 gnd |
| subject_GND | (DE-588)4112491-1 (DE-588)4158117-9 |
| title | Lecture notes on the general theory of relativity from Newton's attractive gravity to the repulsive gravity of vacuum energy |
| title_auth | Lecture notes on the general theory of relativity from Newton's attractive gravity to the repulsive gravity of vacuum energy |
| title_exact_search | Lecture notes on the general theory of relativity from Newton's attractive gravity to the repulsive gravity of vacuum energy |
| title_full | Lecture notes on the general theory of relativity from Newton's attractive gravity to the repulsive gravity of vacuum energy Ø. Grøn |
| title_fullStr | Lecture notes on the general theory of relativity from Newton's attractive gravity to the repulsive gravity of vacuum energy Ø. Grøn |
| title_full_unstemmed | Lecture notes on the general theory of relativity from Newton's attractive gravity to the repulsive gravity of vacuum energy Ø. Grøn |
| title_short | Lecture notes on the general theory of relativity |
| title_sort | lecture notes on the general theory of relativity from newton s attractive gravity to the repulsive gravity of vacuum energy |
| title_sub | from Newton's attractive gravity to the repulsive gravity of vacuum energy |
| topic | Relativity (Physics) Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Gravitationstheorie (DE-588)4158117-9 gnd |
| topic_facet | Relativity (Physics) Allgemeine Relativitätstheorie Gravitationstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017073756&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003166 |
| work_keys_str_mv | AT grønøyvind lecturenotesonthegeneraltheoryofrelativityfromnewtonsattractivegravitytotherepulsivegravityofvacuumenergy |