Exact space times in Einstein's general relativity:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2012
|
| Ausgabe: | Repr. with corr. and updates, 1. paperback ed. |
| Schriftenreihe: | Cambridge monographs on mathematical physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XVIII, 528 S. Ill., graph. Darst. |
| ISBN: | 9780521889278 9781107406186 |
Internformat
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| 020 | |a 9781107406186 |c paperback |9 978-1-107-40618-6 | ||
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| 100 | 1 | |a Griffiths, Jeremy B. |d 1947- |e Verfasser |0 (DE-588)137355262 |4 aut | |
| 245 | 1 | 0 | |a Exact space times in Einstein's general relativity |c Jerry B. Griffiths ; Jiří Podolský |
| 250 | |a Repr. with corr. and updates, 1. paperback ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2012 | |
| 300 | |a XVIII, 528 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Cambridge monographs on mathematical physics | |
| 650 | 4 | |a General relativity (Physics) | |
| 650 | 4 | |a Space and time | |
| 650 | 0 | 7 | |a Raum-Zeit |0 (DE-588)4302626-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Allgemeine Relativitätstheorie |0 (DE-588)4112491-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Allgemeine Relativitätstheorie |0 (DE-588)4112491-1 |D s |
| 689 | 0 | 1 | |a Raum-Zeit |0 (DE-588)4302626-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Podolský, Jiří |d 1963- |e Verfasser |0 (DE-588)139917357 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025399592&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025399592&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-025399592 | |
Datensatz im Suchindex
| _version_ | 1826921930255499264 |
|---|---|
| adam_text |
Contents
Preface
page
xv
1
Introduction
1
2
Basic tools and concepts
5
2.1
Local geometry
5
2.1.1
Curvature
6
2.1.2
Algebraic classification
8
2.1.3
Geodesies and geometrical optics
10
2.1.4
Symmetries
15
2.1.5
Continuity
16
2.2
Matter content
17
2.2.1
Electromagnetic field
17
2.2.2
Perfect fluid and pure radiation
19
2.3
Global structure
20
2.3.1
Singularities
21
2.3.2
Horizons
23
2.3.3
Causal and
conformai
relations
25
3
Minkowski space-time
27
3.1
Coordinate representations
27
3.2
An aside on the Einstein static universe
29
3.3
Conformai
structure of Minkowski space
31
3.4
A simple model for a cosmic string
35
3.4.1
A spinning cosmic string
36
3.5
Coordinates adapted to uniform acceleration
37
3.6
Other representations of Minkowski space
40
4
de
Sitter space-time
41
4.1
Global representation
41
4.2
Conformai
structure
43
vii
viii Contents
4.3
Spherical coordinates and horizons
44
4.4
Other standard coordinates
48
4.4.1
Conformally flat coordinates
48
4.4.2
Coordinates with a negative spatial curvature
50
4.4.3
Constant-curvature coordinates
51
4.4.4
Bianchi
III and Kantowski-Sachs coordinates
53
4.5
Remarks and references
54
5
Anti-de Sitter space-time
55
5.1
Global representation
55
5.2
Conformai
structure
58
5.3
Other standard coordinates
61
5.4
Remarks and references
66
6
Friedmann-Lemaître—
Robertson—Walker space-times
67
6.1
Geometry and standard coordinates
68
6.2
Matter content and dynamics
71
6.3
Explicit solutions
74
6.3.1
Vacuum FLRW space-times
75
6.3.2
FLRW space-times without
Λ
76
6.3.3
FLRW space-times with
Λ
77
6.4
Conformai
structure
80
6.4.1
FLRW space-times without
Λ
80
6.4.2
FLRW space-times with
Λ
85
6.5
Some principal properties and references
89
7
Electrovacuum and related background space-times
95
7.1
The Bertotti-Robinson solution
95
7.2
Other direct-product space-times
98
7.2.1
Nariai and anti-Nariai space-times
100
7.2.2
Plebański-Hacyan
space-times
101
7.3
The Melvin solution
102
8 Schwarzschild
space-time
106
8.1 Schwarzschild
coordinates
107
8.2
Eddington-Finkelstein coordinates and black holes
110
8.2.1
Outgoing coordinates and white holes
114
8.3
Kruskal-Szekeres coordinates
116
8.4
Conformai
structure
119
8.4.1
The case when
m
< 0 122
8.5
Interior solutions
123
8.6
Exterior solutions
125
Contents ix
9
Space-times related to
Schwarzschild 127
9.1
Other ¿-metrics
127
9.1.1
The ¿//-metrics (e
= -1) 128
9.1.2
The ¿///-metrics
(б
= 0) 133
9.2
The
Reissner-Nordström
solution
136
9.2.1
Singularity and horizons
137
9.2.2
Conformai
structure
142
9.2.3
(Hyper-)extreme
Reissner-Nordström
space-times
146
9.3
The Schwarzschild-Melvin solution
149
9.4
The Schwarzschild-de Sitter solution
150
9.4.1
Black holes in
de
Sitter space-time
151
9.4.2
Extreme holes in
de
Sitter space-time
153
9.4.3
Black holes in anti-de Sitter space-time
155
9.5
Vaidya's radiating
Schwarzschild
solution
156
9.5.1
Radiation from a star
159
9.5.2
The Vaidya solution for incoming radiation
161
9.6
Further generalisations
165
10
Static axially symmetric space-times
169
10.1
The Weyl metric
169
10.1.1
Flat solutions within a Weyl metric
171
10.1.2
The Weyl solutions
172
10.2
Static cylindrically symmetric space-times
173
10.3
The
Schwarzschild
solution
178
10.4
The Zipoy-Voorhees solution
179
10.5
The Curzon-Chazy solution
181
10.6
The Curzon-Chazy two-particle solution
184
10.7
Further comments on the Weyl metrics
186
10.8
Axially symmetric electrovacuuni space-times
188
10.8.1
Equilibrium configurations with distinct sources
191
11
Rotating black holes
194
11.1
The Kerr solution
194
11.1.1
Horizons
196
11.1.2
Curvature singularity and central disc
198
11.1.3
Ergoregions
201
11.1.4
Conformai
diagrams
204
11.1.5
Further comments on the Kerr solution
207
11.2
The Kerr-Newman solution
209
11.3
The Kerr-Newnian-(anti-)de Sitter solution
210
x
Contents
12
Taub-NUT space-time
213
12.1
The NUT solution
214
12.1.1
The NUT regions in Weyl coordinates
216
12.1.2
The
Taub
region
217
12.1.3
The singularity on the axis and a gravitomagnetic
interpretation
218
12.1.4
The occurrence of closed timelike curves
221
12.1.5
Conformai
structure
222
12.2
Misner's construction of a singularity-free solution
225
12.2.1
Conformai
structure in Misner's interpretation
227
12.3
The wider family of NUT solutions
229
12.3.1
The case
e
= -1 230
12.3.2
Thecasee = 0
233
12.4
Further generalisations of the Taub-NUT solutions
235
13
Stationary, axially symmetric space-times
238
13.1
Cylindrically symmetric solutions
238
13.1.1
The Lewis family of vacuum solutions
239
13.1.2
The van Stockum solutions
242
13.1.3
Other cylindrically symmetric solutions
245
13.2
Vacuum, axially symmetric solutions
246
13.2.1
The Ernst equation
246
13.2.2
Some exact solutions
249
13.3
Axially symmetric electrovacuum space-times
252
13.3.1
The Ernst electrovacuum equations
252
13.3.2
Some exact solutions
254
14
Accelerating black holes
258
14.1
The C-metric
259
14.1.1
The
С
-metric in spherical-type coordinates
260
14.1.2
Conformai
diagrams
262
14.1.3
Some geometrical and physical properties
265
14.1.4
The Minkowski limit
268
14.1.5
Global structure of the C-metric
273
14.1.6
Boost-rotation symmetric form
277
14.1.7
Weyl and other coordinates in the static region
278
14.2
Accelerating charged black holes
281
14.2.1
The Ernst solution
282
14.3
Accelerating and rotating black holes
283
14.4
The inclusion of a cosmological constant
286
14.5
Some related topics
290
Contents xi
15
Further solutions for uniformly accelerating particles
291
15.1
Boost-rotation symmetric space-times
292
15.2
Bonnor-Swaminarayan solutions
293
15.2.1
Four particles and a regular axis
295
15.2.2
Four particles with semi-infinite strings
296
15.2.3
Two particles and semi-infinite strings
296
15.2.4
Four particles and a finite string
297
15.2.5
Two particles and a finite string
298
15.2.6
Four particles and two finite strings
298
15.3
Bičák-Hoenselaers-Schmidt
solutions
299
15.3.1
Two particles in an external field
299
15.3.2
Monopole-dipole particles
300
15.3.3
Multipole particles
301
16
Plebański—Demiański
solutions
304
16.1
The
Plebański-Demiański
metric
305
16.2
A general metric for expanding solutions
308
16.3
Generalised black holes
311
16.3.1
The Kerr-Newman-NUT-(anti-)de Sitter solution
314
16.3.2
Accelerating Kerr-Newman-(anti-)de Sitter black
holes
315
16.4
Non-expanding solutions
316
16.4.1
The B-metrics
318
16.5
An alternative extension
319
16.6
The general family of type
D
space-times
320
17
Plane and pp-waves
323
17.1
The class of pp-wave space-times
324
17.2
Focusing properties
325
17.3
Linear superposition and beams of pure radiation
327
17.4
Shock, sandwich and impulsive waves
328
17.5
Plane wave space-times
330
17.5.1
Shock, impulsive and sandwich plane waves
331
17.5.2
Focusing properties of sandwich plane waves
332
17.6
Some related topics
334
18
Kundt solutions
336
18.1
The general class of Kundt space-times
336
18.2
Vacuum and pure radiation Kundt space-times
337
18.3
Type III,
N
and
О
solutions
338
18.3.1
Type III solutions
341
18.3.2
Type
N
solutions
342
xii
Contents
18.3.3
Conformally flat solutions
344
18.4
Geometry of the wave surfaces
346
18.4.1
Kundt waves in a Minkowski background
347
18.4.2
Kundt waves in an (anti-)de Sitter background
349
18.4.3
"pp-waves" in an (anti-)de Sitter background
351
18.4.4
Siklos
waves in an anti-de Sitter background
353
18.5
"Spinning" null matter and "gyratons"
353
18.6
Type
D
(electro)vacuum solutions
357
18.7
Type II solutions
359
19
Robinson-Trautman solutions
361
19.1
Robinson-Trautman vacuum space-times
361
19.2
Type
N
solutions
363
19.2.1
Minkowski background coordinates
365
19.2.2
(Anti-)de Sitter background coordinates
368
19.2.3
Particular type
N
sandwich waves
372
19.3
Type
D
solutions
377
19.4
Type II solutions
379
19.5
Robinson-Trautman space-times with pure radiation
384
19.5.1
Type
D
solutions
385
19.5.2
Kinnersley"*
rocket
386
19.5.3
Type II solutions
388
19.5.4
Bonnor's rocket
389
19.6
Comments on further solutions
390
20
Impulsive waves
392
20.1
Methods of construction
393
20.2
Non-expanding impulsive waves in Minkowski space
394
20.3
Non-expanding impulsive waves in (anti-)de Sitter space
398
20.4
Expanding impulsive waves in Minkowski space
401
20.5
Expanding impulsive waves in (anti-)de Sitter space
407
20.6
Other impulsive wave space-times
410
21
Colliding plane waves
412
21.1
Initial data
413
21.2
The interaction region
415
21.3
The Khan-Penrose solution
418
21.4
The degenerate
Ferrari-Ibáñez
solution
422
21.5
Other type
D
solutions
427
21.5.1
The alternative
Ferrari-Ibáñez
(Schwarzschild)
solution
427
21.5.2
The Chandrasekhar-Xanthopoulos (Kerr) solution
427
Contents xiii
21.5.3 The
Ferrari-Ibáñez (Taub-NUT)
solution
430
21.5.4
Further type D solutions
431
21.6
The Bell-Szekeres (Bertotti-Robinson) solution
433
21.7
Properties of other colliding plane wave space-times
434
22
A final miscellany
438
22.1
Homogeneous
Bianchi
models
439
22.2
Kantowski-Sachs space-times
441
22.3
Cylindrical gravitational waves
442
22.4
Vacuum G2 cosmologies
446
22.5
Majumdar-Papapetrou solutions
448
22.6 Gödel's
rotating universe
450
22.7
Spherically symmetric:
Lemaître
-Tolman
solutions
454
22.8
Szekeres
space-times without symmetry
458
Appendix A 2-spaces of constant curvature
462
Appendix
В
3-spaces of constant curvature
470
References
480
Index
523
Einstein's theory of general relativity is a theory of gravity and, as in the earlier
Newtonian theory, much can be learnt about the character of gravitation and its
effects by investigating particular idealised examples. This book describes die basic
solutions of Einstein's equations with a particular emphasis on what they mean, both
geometrically and physically.
New concepts, such as big bang and big crunch-types of singularities, different kinds of
horizons and gravitational waves are described in the context of the particular space-times
in which the}1 naturally arise. These notions arc initially introduced using the most simple
and symmetric cases. Various important coordinate forms of each solution are presented,
thus enabling the global structure of the corresponding space-time and its other proper¬
ties to be analysed. 'Ihe book is an invaluable resource for both graduate students and
academic researchers working in gravitational physics. |
| any_adam_object | 1 |
| author | Griffiths, Jeremy B. 1947- Podolský, Jiří 1963- |
| author_GND | (DE-588)137355262 (DE-588)139917357 |
| author_facet | Griffiths, Jeremy B. 1947- Podolský, Jiří 1963- |
| author_role | aut aut |
| author_sort | Griffiths, Jeremy B. 1947- |
| author_variant | j b g jb jbg j p jp |
| building | Verbundindex |
| bvnumber | BV040560043 |
| callnumber-first | Q - Science |
| callnumber-label | QC177 |
| callnumber-raw | QC177 |
| callnumber-search | QC177 |
| callnumber-sort | QC 3177 |
| callnumber-subject | QC - Physics |
| classification_rvk | UH 8300 |
| ctrlnum | (OCoLC)820418207 (DE-599)BVBBV040560043 |
| 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 |
| edition | Repr. with corr. and updates, 1. paperback ed. |
| format | Book |
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| id | DE-604.BV040560043 |
| illustrated | Illustrated |
| indexdate | 2025-03-18T09:02:02Z |
| institution | BVB |
| isbn | 9780521889278 9781107406186 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025399592 |
| oclc_num | 820418207 |
| open_access_boolean | |
| owner | DE-384 DE-703 |
| owner_facet | DE-384 DE-703 |
| physical | XVIII, 528 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Cambridge monographs on mathematical physics |
| spelling | Griffiths, Jeremy B. 1947- Verfasser (DE-588)137355262 aut Exact space times in Einstein's general relativity Jerry B. Griffiths ; Jiří Podolský Repr. with corr. and updates, 1. paperback ed. Cambridge [u.a.] Cambridge Univ. Press 2012 XVIII, 528 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on mathematical physics General relativity (Physics) Space and time Raum-Zeit (DE-588)4302626-6 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 s Raum-Zeit (DE-588)4302626-6 s DE-604 Podolský, Jiří 1963- Verfasser (DE-588)139917357 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025399592&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=025399592&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Griffiths, Jeremy B. 1947- Podolský, Jiří 1963- Exact space times in Einstein's general relativity General relativity (Physics) Space and time Raum-Zeit (DE-588)4302626-6 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| subject_GND | (DE-588)4302626-6 (DE-588)4112491-1 |
| title | Exact space times in Einstein's general relativity |
| title_auth | Exact space times in Einstein's general relativity |
| title_exact_search | Exact space times in Einstein's general relativity |
| title_full | Exact space times in Einstein's general relativity Jerry B. Griffiths ; Jiří Podolský |
| title_fullStr | Exact space times in Einstein's general relativity Jerry B. Griffiths ; Jiří Podolský |
| title_full_unstemmed | Exact space times in Einstein's general relativity Jerry B. Griffiths ; Jiří Podolský |
| title_short | Exact space times in Einstein's general relativity |
| title_sort | exact space times in einstein s general relativity |
| topic | General relativity (Physics) Space and time Raum-Zeit (DE-588)4302626-6 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| topic_facet | General relativity (Physics) Space and time Raum-Zeit Allgemeine Relativitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025399592&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025399592&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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