Partial differential equations in general relativity:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
2008
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Oxford graduate texts in mathematics
16 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 279 S. graph. Darst. |
| ISBN: | 9780199215409 9780199215416 |
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| 100 | 1 | |a Rendall, Alan D. |d 1963- |e Verfasser |0 (DE-588)1034365673 |4 aut | |
| 245 | 1 | 0 | |a Partial differential equations in general relativity |c Alan D. Rendall |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2008 | |
| 300 | |a XVI, 279 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Differential equations, Partial | |
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Datensatz im Suchindex
| _version_ | 1804137482954997760 |
|---|---|
| adam_text | Contents
1
Introduction
1
1.1
Physical
background
1
1.2
Mathematical background
4
1.3
Structure of the book
6
2
General relativity
8
2.1
Basic concepts
8
2.1.1
Lorentzian algebra
8
2.1.2
Lorentzian geometry
11
2.1.3
Geodesic deviation and singularity theorems
16
2.1.4
Volume and integration
20
2.2
The Einstein equations
21
2.3
ТІіеЗ + 1
decomposition
22
2.4
Conformai rescalings
28
2.5
Covering spaces and foliations
29
2.6
Further reading
29
3
Matter models
30
3.1
Scalarfields
33
3.2
The Maxwell and Yang-Mills equations
39
3.3
Continuum mechanics
41
3.4
Kinetic theory
43
3.5
Other matter models
46
3.6
Further reading
49
4
Symmetry classes
50
4.1
Static and stationary models
52
4.2
Spatially homogeneous models
56
Contents
4.3
Surface symmetry
4.4
Τ2
symmetry
4.5
(7(1)
symmetry
4.6
Further reading
61
63
68
69
5
Ordinary differential equations
71
5.1
Existence and uniqueness
73
5.2
Dynamical systems
75
5.3
Formal power series solutions and asymptotic expansions
76
5.4
Linearization and the Hartman-Grobman theorem
79
5.5
Examples
(Bianchi
models)
80
5.5.1
The Wainwright-Hsu system
80
5.5.2
Models of
Bianchi
types II and Vlo
83
5.6
Centre manifolds and the reduction theorem
85
5.7
Further examples
86
5.7.1
Bianchi
types II and Vlo revisited
86
5.7.2
The massive scalar field
88
5.7.3
Bianchi
type III Einstein-Vlasov
90
5.8
Bifurcation theory
93
5.9
Global existence for homogeneous spacetimes
94
5.10
An application to surface symmetry
98
5.11
Further reading
102
6
Functional analysis
103
6.1
Abstract function spaces
103
6.2
Distributions
106
6.3
Concrete function spaces
108
6.4
Littlewood-Paley theory
115
6.5
Pseudodifferential operators
116
6.6
Further reading
118
7
Elliptic equations
119
7.1
The concept of ellipticity
119
7.2
Boundary value problems
122
7.3
Douglis-Nirenberg ellipticity
123
7.4
Fredholm
operators
123
7.5
The Einstein constraints
127
7.6
Further reading
131
Contents
8
Hyperbolic equations
132
8.1
The Cauchy problem
132
8.2
Examples of ill-posed problems
134
8.3
Symmetric hyperbolic systems
136
8.4
Strong hyperbolicity
150
8.5
Leray hyperbolicity
152
8.6
The analytic Cauchy problem
154
8.7
Initial boundary value problems
155
8.8
The null condition
158
8.9
Global difficulties
160
8.10
Comparison with parabolic equations
162
8.11
Fuchsian methods
164
8.12
Further reading
169
9
The Cauchy problem for the Einstein equations
170
170
171
177
179
182
184
10
Global results
186
186
193
199
203
model
203
207
211
11
The Einstein-Vlasov system
213
11.1
Other kinetic equations
213
11.2
Small data global existence
214
11.2.1 Schwarzschild
coordinates
214
11.2.2
Maximal-isotropic and double null coordinates
220
9.1
Coordinate
conditions
9.2
The local Cauchy problem
9.3
Inclusion of matter
9.4
Cosmic censorship
9.5
The BKL picture
9.6
Further reading
Global
results
10.1
Gowdy spacetimes
10.2
Stability of
de
Sitter space
10.3
Stability of Minkowski space
10.4
Stability of the Milne model
10.5
Stability of the flat
Bianchi
type
10.6
The Newtonian limit
10.7
Further reading
Contents
11.
З
Cosmological
solutions
223
11.3.1 Einstein-Vlasov
solutions
with
Τ2
symmetry
224
11.3.2
Τ2
symmetry and CMC time
232
11.3.3
Einstein-Vlasov solutions with surface symmetry
241
11.3.4
Spherical symmetry and CMC time
245
11.3.5
Strong cosmic censorship without full asymptotics
245
11
.4
Isotropie
singularities
248
11
.5
Weak cosmic censorship and internal structure of black
holes
249
11.6
Further reading
250
12
The Einstein-scalar field system
252
252
255
258
260
262
263
Index
277
12.1
Asymptotically flat solutions
12.2
Weak null singularities
12.3
Price s law
12.4
Cosmological solutions
12.5
Further reading
References
|
| adam_txt |
Contents
1
Introduction
1
1.1
Physical
background
1
1.2
Mathematical background
4
1.3
Structure of the book
6
2
General relativity
8
2.1
Basic concepts
8
2.1.1
Lorentzian algebra
8
2.1.2
Lorentzian geometry
11
2.1.3
Geodesic deviation and singularity theorems
16
2.1.4
Volume and integration
20
2.2
The Einstein equations
21
2.3
ТІіеЗ + 1
decomposition
22
2.4
Conformai rescalings
28
2.5
Covering spaces and foliations
29
2.6
Further reading
29
3
Matter models
30
3.1
Scalarfields
33
3.2
The Maxwell and Yang-Mills equations
39
3.3
Continuum mechanics
41
3.4
Kinetic theory
43
3.5
Other matter models
46
3.6
Further reading
49
4
Symmetry classes
50
4.1
Static and stationary models
52
4.2
Spatially homogeneous models
56
Contents
4.3
Surface symmetry
4.4
Τ2
symmetry
4.5
(7(1)
symmetry
4.6
Further reading
61
63
68
69
5
Ordinary differential equations
71
5.1
Existence and uniqueness
73
5.2
Dynamical systems
75
5.3
Formal power series solutions and asymptotic expansions
76
5.4
Linearization and the Hartman-Grobman theorem
79
5.5
Examples
(Bianchi
models)
80
5.5.1
The Wainwright-Hsu system
80
5.5.2
Models of
Bianchi
types II and Vlo
83
5.6
Centre manifolds and the reduction theorem
85
5.7
Further examples
86
5.7.1
Bianchi
types II and Vlo revisited
86
5.7.2
The massive scalar field
88
5.7.3
Bianchi
type III Einstein-Vlasov
90
5.8
Bifurcation theory
93
5.9
Global existence for homogeneous spacetimes
94
5.10
An application to surface symmetry
98
5.11
Further reading
102
6
Functional analysis
103
6.1
Abstract function spaces
103
6.2
Distributions
106
6.3
Concrete function spaces
108
6.4
Littlewood-Paley theory
115
6.5
Pseudodifferential operators
116
6.6
Further reading
118
7
Elliptic equations
119
7.1
The concept of ellipticity
119
7.2
Boundary value problems
122
7.3
Douglis-Nirenberg ellipticity
123
7.4
Fredholm
operators
123
7.5
The Einstein constraints
127
7.6
Further reading
131
Contents
8
Hyperbolic equations
132
8.1
The Cauchy problem
132
8.2
Examples of ill-posed problems
134
8.3
Symmetric hyperbolic systems
136
8.4
Strong hyperbolicity
150
8.5
Leray hyperbolicity
152
8.6
The analytic Cauchy problem
154
8.7
Initial boundary value problems
155
8.8
The null condition
158
8.9
Global difficulties
160
8.10
Comparison with parabolic equations
162
8.11
Fuchsian methods
164
8.12
Further reading
169
9
The Cauchy problem for the Einstein equations
170
170
171
177
179
182
184
10
Global results
186
186
193
199
203
model
203
207
211
11
The Einstein-Vlasov system
213
11.1
Other kinetic equations
213
11.2
Small data global existence
214
11.2.1 Schwarzschild
coordinates
214
11.2.2
Maximal-isotropic and double null coordinates
220
9.1
Coordinate
conditions
9.2
The local Cauchy problem
9.3
Inclusion of matter
9.4
Cosmic censorship
9.5
The BKL picture
9.6
Further reading
Global
results
10.1
Gowdy spacetimes
10.2
Stability of
de
Sitter space
10.3
Stability of Minkowski space
10.4
Stability of the Milne model
10.5
Stability of the flat
Bianchi
type
10.6
The Newtonian limit
10.7
Further reading
Contents
11.
З
Cosmological
solutions
223
11.3.1 Einstein-Vlasov
solutions
with
Τ2
symmetry
224
11.3.2
Τ2
symmetry and CMC time
232
11.3.3
Einstein-Vlasov solutions with surface symmetry
241
11.3.4
Spherical symmetry and CMC time
245
11.3.5
Strong cosmic censorship without full asymptotics
245
11
.4
Isotropie
singularities
248
11
.5
Weak cosmic censorship and internal structure of black
holes
249
11.6
Further reading
250
12
The Einstein-scalar field system
252
252
255
258
260
262
263
Index
277
12.1
Asymptotically flat solutions
12.2
Weak null singularities
12.3
Price's law
12.4
Cosmological solutions
12.5
Further reading
References |
| any_adam_object | 1 |
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| author | Rendall, Alan D. 1963- |
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| callnumber-subject | QC - Physics |
| classification_rvk | SK 540 SK 950 UH 8300 |
| ctrlnum | (OCoLC)226279733 (DE-599)BSZ278200028 |
| 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 Mathematik |
| discipline_str_mv | Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV023204596 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:09:25Z |
| indexdate | 2024-07-09T21:13:00Z |
| institution | BVB |
| isbn | 9780199215409 9780199215416 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016390771 |
| oclc_num | 226279733 |
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| owner_facet | DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-20 DE-83 DE-11 DE-188 |
| physical | XVI, 279 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | Oxford graduate texts in mathematics |
| series2 | Oxford graduate texts in mathematics |
| spelling | Rendall, Alan D. 1963- Verfasser (DE-588)1034365673 aut Partial differential equations in general relativity Alan D. Rendall 1. publ. Oxford Oxford Univ. Press 2008 XVI, 279 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts in mathematics 16 Mathematik Differential equations, Partial General relativity (Physics) Mathematics Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Allgemeine Relativitätstheorie (DE-588)4112491-1 s DE-604 Oxford graduate texts in mathematics 16 (DE-604)BV011416591 16 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016390771&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rendall, Alan D. 1963- Partial differential equations in general relativity Oxford graduate texts in mathematics Mathematik Differential equations, Partial General relativity (Physics) Mathematics Partielle Differentialgleichung (DE-588)4044779-0 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4112491-1 |
| title | Partial differential equations in general relativity |
| title_auth | Partial differential equations in general relativity |
| title_exact_search | Partial differential equations in general relativity |
| title_exact_search_txtP | Partial differential equations in general relativity |
| title_full | Partial differential equations in general relativity Alan D. Rendall |
| title_fullStr | Partial differential equations in general relativity Alan D. Rendall |
| title_full_unstemmed | Partial differential equations in general relativity Alan D. Rendall |
| title_short | Partial differential equations in general relativity |
| title_sort | partial differential equations in general relativity |
| topic | Mathematik Differential equations, Partial General relativity (Physics) Mathematics Partielle Differentialgleichung (DE-588)4044779-0 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| topic_facet | Mathematik Differential equations, Partial General relativity (Physics) Mathematics Partielle Differentialgleichung Allgemeine Relativitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016390771&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011416591 |
| work_keys_str_mv | AT rendallaland partialdifferentialequationsingeneralrelativity |