Mathematical problems of general relativity: 1
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
European Math. Soc.
(2008)
|
| Series: | Zurich lectures in advanced mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 147 S. graph. Darst. |
| ISBN: | 9783037190050 |
Staff View
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| 245 | 1 | 0 | |a Mathematical problems of general relativity |n 1 |c Demetrios Christodoulou |
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Record in the Search Index
| _version_ | 1804137438146199552 |
|---|---|
| adam_text | Contents
General
introduction
..............................
vii
1
Introduction
................................. 1
2
The laws of General Relativity
....................... 9
2.1
The Einstein equations
......................... 9
2.1.1
Regular ellipticity and regular hyperbolicity
.......... 16
2.2
The Cauchy problem
.......................... 19
2.2.1
Cauchy problem for the Einstein equations: local in time,
existence and uniqueness of solutions
............. 19
2.3
Decomposition of the Einstein equations
............... 31
3
Asymptotic flatness at spacelike infinity and conserved quantities
..... 35
3.1
Conserved quantities
.......................... 35
3.2
Asymptotic flatness
.......................... 54
3.2.1
The maximal time function
................... 58
3.2.2
Positivity
of the energy
..................... 60
3.3
Angular momentum
.......................... 70
3.3.1
Independence from exhaustion
................. 71
3.3.2
Conservation of angular momentum
.............. 71
3.4
The center of mass integrals
...................... 72
3.4.1
Conservation of center of mass integrals
............ 76
4
The global stability of Minkowski spacetime
................ 78
4.1
Statement of the problem
....................... 78
4.1.1
Field theories in a given spacetime
............... 79
4.2
Sketch of the proof of the global stability of Minkowski spacetime
. 103
4.2.1
The problem in General Relativity
-
two main difficulties
... 103
4.2.2
Resolution of the first difficulty
................. 103
4.2.3
Resolution of the second difficulty
............... 109
4.2.4
The controlling quantity
.................... 124
4.2.5
The continuity argument
.................... 127
4.2.6
Estimates for the geometric quantities associated to the maximal
foliation
{Ж,}
.......................... 131
4.2.7
Estimates for the geometric quantities associated to the null
foliation {Cu}
.......................... 132
4.2.8
Decomposition of a Weyl field with respect to the surfaces St,u
137
4.2.9
The borderline error integrals
.................. 139
Bibliography
.................................. 143
Index
...................................... 145
|
| adam_txt |
Contents
General
introduction
.
vii
1
Introduction
. 1
2
The laws of General Relativity
. 9
2.1
The Einstein equations
. 9
2.1.1
Regular ellipticity and regular hyperbolicity
. 16
2.2
The Cauchy problem
. 19
2.2.1
Cauchy problem for the Einstein equations: local in time,
existence and uniqueness of solutions
. 19
2.3
Decomposition of the Einstein equations
. 31
3
Asymptotic flatness at spacelike infinity and conserved quantities
. 35
3.1
Conserved quantities
. 35
3.2
Asymptotic flatness
. 54
3.2.1
The maximal time function
. 58
3.2.2
Positivity
of the energy
. 60
3.3
Angular momentum
. 70
3.3.1
Independence from exhaustion
. 71
3.3.2
Conservation of angular momentum
. 71
3.4
The center of mass integrals
. 72
3.4.1
Conservation of center of mass integrals
. 76
4
The global stability of Minkowski spacetime
. 78
4.1
Statement of the problem
. 78
4.1.1
Field theories in a given spacetime
. 79
4.2
Sketch of the proof of the global stability of Minkowski spacetime
. 103
4.2.1
The problem in General Relativity
-
two main difficulties
. 103
4.2.2
Resolution of the first difficulty
. 103
4.2.3
Resolution of the second difficulty
. 109
4.2.4
The controlling quantity
. 124
4.2.5
The continuity argument
. 127
4.2.6
Estimates for the geometric quantities associated to the maximal
foliation
{Ж,}
. 131
4.2.7
Estimates for the geometric quantities associated to the null
foliation {Cu}
. 132
4.2.8
Decomposition of a Weyl field with respect to the surfaces St,u
137
4.2.9
The borderline error integrals
. 139
Bibliography
. 143
Index
. 145 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T19:59:08Z |
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| institution | BVB |
| isbn | 9783037190050 |
| language | English |
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| physical | X, 147 S. graph. Darst. |
| publishDate | 2008 |
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| series2 | Zurich lectures in advanced mathematics |
| spelling | Christodulu, Dēmētrēs Ch. 1951- Verfasser (DE-588)1049266897 aut Mathematical problems of general relativity 1 Demetrios Christodoulou Zürich European Math. Soc. (2008) X, 147 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Zurich lectures in advanced mathematics Relativitätstheorie (DE-588)4049363-5 gnd rswk-swf Relativitätstheorie (DE-588)4049363-5 s DE-604 (DE-604)BV023174221 1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016360866&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4049363-5 |
| title | Mathematical problems of general relativity |
| title_auth | Mathematical problems of general relativity |
| title_exact_search | Mathematical problems of general relativity |
| title_exact_search_txtP | Mathematical problems of general relativity |
| title_full | Mathematical problems of general relativity 1 Demetrios Christodoulou |
| title_fullStr | Mathematical problems of general relativity 1 Demetrios Christodoulou |
| title_full_unstemmed | Mathematical problems of general relativity 1 Demetrios Christodoulou |
| title_short | Mathematical problems of general relativity |
| title_sort | mathematical problems of general relativity |
| topic | Relativitätstheorie (DE-588)4049363-5 gnd |
| topic_facet | Relativitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016360866&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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