Gravitation: foundations and frontiers
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
|
| Ausgabe: | Reprinted with corr. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024595271&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XXVIII, 700 S. graph. Darst. |
| ISBN: | 9780521882231 |
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| 250 | |a Reprinted with corr. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2010 | |
| 300 | |a XXVIII, 700 S. |b graph. Darst. | ||
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-024595271 | |
Datensatz im Suchindex
| _version_ | 1819349106662834176 |
|---|---|
| adam_text | Contents
List of exercises page
xiii
List of projects
xix
Preface
xxi
How to use this book
xxvii
1
Special relativity
1
1.1
Introduction
1
1.2
The principles of special relativity
1
1.3
Transformation of coordinates and velocities
6
1.3.1
Lorentz
transformation
8
1.3.2
Transformation of velocities
10
1.3.3
Lorentz
boost in an arbitrary direction
11
1.4
Four-vectors
13
1.4.1
Four-velocity and acceleration
17
1.5
Tensors
19
1.6
Tensors as geometrical objects
23
1.7
Volume and surface integrals in four dimensions
26
1.8
Particle dynamics
29
1.9
The distribution function and its moments
35
1.10
The
Lorentz
group and
Pauli
matrices
45
2
Scalar and electromagnetic fields in special relativity
54
2.1
Introduction
54
2.2
External fields of force
54
2.3
Classical scalar field
55
2.3.1
Dynamics of a particle interacting with a scalar field
55
2.3.2
Action and dynamics of the scalar field
57
2.3.3
Energy-momentum tensor for the scalar field
60
2.3.4
Free field and the wave solutions
62
vu
viii Contents
2.3.5
Why does the scalar field lead to an attractive force?
64
2.4
Electromagnetic field
66
2.4.1
Charged particle in an electromagnetic field
67
2.4.2
Lorentz
transformation of electric and magnetic fields
71
2.4.3
Current vector
73
2.5
Motion in the Coulomb field
75
2.6
Motion in a constant electric field
79
2.7
Action principle for the vector field
81
2.8
Maxwell s equations
83
2.9
Energy and momentum of the electromagnetic field
90
2.10
Radiation from an accelerated charge
95
2.11
Larmor formula and radiation reaction
100
3
Gravity and spacetime geometry: the inescapable connection
107
3.1
Introduction
107
3.2
Field theoretic approaches to gravity
107
3.3
Gravity as a scalar field
108
3.4
Second rank tensor theory of gravity
113
3.5
The principle of equivalence and the geometrical description
of gravity
125
3.5.1
Uniformly accelerated observer
126
3.5.2
Gravity and the flow of time
128
4
Metric tensor, geodesies and covariant derivative
136
4.1
Introduction
136
4.2
Metric tensor and gravity
136
4.3
Tensor algebra in curved spacetime
141
4.4
Volume and surface integrals
146
4.5
Geodesic curves
149
4.5.1
Properties of geodesic curves
154
4.5.2 Affine
parameter and null geodesies
156
4.6
Covariant derivative
162
4.6.1
Geometrical interpretation of the covariant derivative
163
4.6.2
Manipulation of covariant derivatives
167
4.7
Parallel transport
170
4.8
Lie transport and Killing vectors
173
4.9
Fermi-Walker transport
181
5
Curvature of spacetime
189
5.1
Introduction
189
5.2
Three perspectives on the spacetime curvature
189
5.2.1
Parallel transport around a closed curve
189
5.2.2
Non-commutativity of covariant derivatives
192
Contents ix
5.2.3
Tidal acceleration produced by gravity
196
5.3
Properties of the curvature tensor
200
5.3.1
Algebraic properties
200
5.3.2
Bianchi
identity
203
5.3.3
Ricci
tensor, Weyl tensor and
conformai
transformations
204
5.4
Physics in curved spacetime
208
5.4.1
Particles and photons in curved spacetime
209
5.4.2
Ideal fluid in curved spacetime
210
5.4.3
Classical field theory in curved spacetime
217
5.4.4
Geometrical optics in curved spacetime
221
5.5
Geodesic congruence and Raychaudhuri s equation
224
5.5.1
Timelike congruence
225
5.5.2
Null congruence
228
5.5.3
Integration on null surfaces
230
5.6
Classification of spacetime curvature
231
5.6.1
Curvature in two dimensions
232
5.6.2
Curvature in three dimensions
233
5.6.3
Curvature in four dimensions
234
Einstein s field equations and gravitational dynamics
239
6.1
Introduction
239
6.2
Action and gravitational field equations
239
6.2.1
Properties of the gravitational action
242
6.2.2
Variation of the gravitational action
244
6.2.3
A digression on an alternative form of action functional
247
6.2.4
Variation of the matter action
250
6.2.5
Gravitational field equations
258
6.3
General properties of gravitational field equations
261
6.4
The weak field limit of gravity
268
6.4.1
Metric of a stationary source in linearized theory
271
6.4.2
Metric of a light beam in linearized theory
276
6.5
Gravitational energy-momentum pseudo-tensor
279
Spherically symmetric geometry
293
7.1
Introduction
293
7.2
Metric of a spherically symmetric spacetime
293
7.2.1
Static geometry and Birkoff s theorem
296
7.2.2
Interior solution to the
Schwarzschild
metric
304
7.2.3
Embedding diagrams to visualize geometry
311
7.3
Vaidya metric of a radiating source
ЗІЗ
7.4
Orbits in the
Schwarzschild
metric
314
7.4.1
Precession of the perihelion
318
x
Contents
7.4.2
Deflection of an ultra-relativistic particle
323
7.4.3
Precession of a gyroscope
326
7.5
Effective potential for orbits in the Schwarzschild metric
329
7.6
Gravitational collapse of a dust sphere
334
8
Black holes
340
8.1
Introduction
340
8.2
Horizons in spherically symmetric metrics
340
8.3
Kruskal-Szekeres coordinates
343
8.3.1
Radial
infall
in different coordinates
350
8.3.2
General properties of maximal extension
356
8.4
Penrose-Carter diagrams
358
8.5
Rotating black holes and the Kerr metric
365
8.5.1
Event horizon and infinite redshift surface
368
8.5.2
Static limit
372
8.5.3
Penrose process and the area of the event horizon
374
8.5.4
Particle orbits in the Kerr metric
378
8.6
Super-radiance in Kerr geometry
381
8.7
Horizons as null surfaces
385
9
Gravitational waves
399
9.1
Introduction
399
9.2
Propagating modes of gravity
399
9.3
Gravitational waves in a flat spacetime background
402
9.3.1
Effect of the gravitational wave on a system of particles
409
9.4
Propagation of gravitational waves in the curved spacetime
413
9.5
Energy and momentum of the gravitational wave
416
9.6
Generation of gravitational waves
422
9.6.1
Quadrupole formula for the gravitational radiation
427
9.6.2
Back reaction due to the emission of gravitational
waves
429
9.7
General relativistic effects in binary systems
434
9.7.1
Gravitational radiation from binary pulsars
434
9.7.2
Observational aspects of binary pulsars
438
9.7.3
Gravitational radiation from coalescing binaries
443
10
Relativistic cosmology
452
10.1
Introduction
452
10.2
The
Friedmann
spacetime
452
10.3
Kinematics of the
Friedmann
model
457
10.3.1
The redshifting of the momentum
458
10.3.2
Distribution functions for particles and photons
461
10.3.3
Measures of distance
462
Contents xi
10.4 Dynamics
of the
Friedmann
model
466
10.5 The de
Sitter spacetime
479
10.6
Brief thermal history of the universe
483
10.6.1
Decoupling of matter and radiation
484
10.7
Gravitational lensing
487
10.8
Killing vectors and the symmetries of the space
493
10.8.1
Maximally symmetric spaces
494
10.8.2
Homogeneous spaces
496
11
Differential forms and exterior calculus
502
11.1
Introduction
502
11.2
Vectors and
1
-forms
502
11.3
Differential forms
510
11.4
Integration of forms
513
11.5
The Hodge duality
516
11.6
Spin connection and the curvature 2-forms
519
11.6.1
Einstein-Hilbert action and curvature 2-forms
523
11.6.2
Gauge theories in the language of forms
526
12
Hamiltonian structure of general relativity
530
12.1
Introduction
530
12.2
Einstein s equations in
(1+3
)-f
orm
530
12.3
Gauss-Codazzi
equations
535
12.4
Gravitational action in (l+3)-form
540
12.4.1
The Hamiltonian for general relativity
542
12.4.2
The surface term and the extrinsic curvature
545
12.4.3
Variation of the action and canonical momenta
547
12.5
Junction conditions
552
12.5.1
Collapse of a dust sphere and thin-shell
554
13
Evolution of cosmological perturbations
560
13.1
Introduction
560
13.2
Structure formation and linear perturbation theory
560
13.3
Perturbation equations and gauge transformations
562
13.3.1
Evolution equations for the source
569
13.4
Perturbations in dark matter and radiation
572
13.4.1
Evolution of modes with A ~>
du 573
13.4.2
Evolution of modes with
A
<C
d#
in the radiation
dominated phase
574
13.4.3
Evolution in the matter dominated phase
577
13.4.4
An alternative description of the matter-radiation
system
578
13.5
Transfer function for the matter perturbations
582
xii
Contents
13.6
Application: temperature anisotropies of
CMBR
584
13.6.1
The Sachs-Wolfe effect
586
14
Quantum field theory in curved spacetime
591
14.1
Introduction
591
14.2
Review of some key results in quantum field theory
591
14.2.1
Bogolyubov transformations and the particle concept
596
14.2.2
Path integrals and Euclidean time
598
14.3
Exponential redshift and the thermal spectrum
602
14.4
Vacuum state in the presence of horizons
605
14.5
Vacuum functional from a path integral
609
14.6
Hawking radiation from black holes
618
14.7
Quantum field theory in
a
Friedmann
universe
625
14.7.1
General formalism
625
14.7.2
Application: power law expansion
628
14.8
Generation of initial perturbations from inflation
631
14.8.1
Background evolution
632
14.8.2
Perturbations in the inflationary models
634
15
Gravity in higher and lower dimensions
643
15.1
Introduction
643
15.2
Gravity in lower dimensions
644
15.2.1
Gravity and black hole solutions in
(1 + 2)
dimensions
644
15.2.2
Gravity in two dimensions
646
15.3
Gravity in higher dimensions
646
15.3.1
Black holes in higher dimensions
648
15.3.2
Brane
world models
648
15.4
Actions with holography
653
15.5
Surface term and the entropy of the horizon
663
16
Gravity as an emergent phenomenon
670
16.1
Introduction
670
16.2
The notion of an emergent phenomenon
671
16.3
Some intriguing features of gravitational dynamics
673
16.3.1
Einstein s equations as a thermodynamic identity
673
16.3.2
Gravitational entropy and the boundary term in the
action
676
16.3.3
Horizon thermodynamics and Lanczos-Lovelock
theories
677
16.4
An alternative perspective on gravitational dynamics
679
Notes
689
Index
695
|
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| author | Padmanabhan, Thanu 1957- |
| author_GND | (DE-588)124930522 |
| author_facet | Padmanabhan, Thanu 1957- |
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| id | DE-604.BV039747747 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:01:25Z |
| institution | BVB |
| isbn | 9780521882231 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024595271 |
| oclc_num | 712588695 |
| open_access_boolean | |
| owner | DE-703 DE-19 DE-BY-UBM |
| owner_facet | DE-703 DE-19 DE-BY-UBM |
| physical | XXVIII, 700 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spellingShingle | Padmanabhan, Thanu 1957- Gravitation foundations and frontiers Gravitation (DE-588)4021908-2 gnd Gravitationstheorie (DE-588)4158117-9 gnd |
| subject_GND | (DE-588)4021908-2 (DE-588)4158117-9 |
| title | Gravitation foundations and frontiers |
| title_auth | Gravitation foundations and frontiers |
| title_exact_search | Gravitation foundations and frontiers |
| title_full | Gravitation foundations and frontiers T. Padmanabhan |
| title_fullStr | Gravitation foundations and frontiers T. Padmanabhan |
| title_full_unstemmed | Gravitation foundations and frontiers T. Padmanabhan |
| title_short | Gravitation |
| title_sort | gravitation foundations and frontiers |
| title_sub | foundations and frontiers |
| topic | Gravitation (DE-588)4021908-2 gnd Gravitationstheorie (DE-588)4158117-9 gnd |
| topic_facet | Gravitation Gravitationstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024595271&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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