The Evolution Problem in General Relativity:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2003
|
| Schriftenreihe: | Progress in Mathematical Physics
25 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The main goal of this work is to revisit the proof of the global stability of Minkowski space by D. Christodoulou and S. Klainerman, [Ch-KI]. We provide a new self-contained proof of the main part of that result, which concerns the full solution of the radiation problem in vacuum, for arbitrary asymptotically flat initial data sets. This can also be interpreted as a proof of the global stability of the external region of Schwarzschild spacetime. The proof, which is a significant modification of the arguments in [Ch-Kl], is based on a double null foliation of spacetime instead of the mixed null-maximal foliation used in [Ch-Kl]. This approach is more naturally adapted to the radiation features of the Einstein equations and leads to important technical simplifications. In the first chapter we review some basic notions of differential geometry that are sys tematically used in all the remaining chapters. We then introduce the Einstein equations and the initial data sets and discuss some of the basic features of the initial value problem in general relativity. We shall review, without proofs, well-established results concerning local and global existence and uniqueness and formulate our main result. The second chapter provides the technical motivation for the proof of our main theorem |
| Beschreibung: | 1 Online-Ressource (400p. 20 illus) |
| ISBN: | 9781461220848 9780817642549 |
| DOI: | 10.1007/978-1-4612-2084-8 |
Internformat
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| 500 | |a The main goal of this work is to revisit the proof of the global stability of Minkowski space by D. Christodoulou and S. Klainerman, [Ch-KI]. We provide a new self-contained proof of the main part of that result, which concerns the full solution of the radiation problem in vacuum, for arbitrary asymptotically flat initial data sets. This can also be interpreted as a proof of the global stability of the external region of Schwarzschild spacetime. The proof, which is a significant modification of the arguments in [Ch-Kl], is based on a double null foliation of spacetime instead of the mixed null-maximal foliation used in [Ch-Kl]. This approach is more naturally adapted to the radiation features of the Einstein equations and leads to important technical simplifications. In the first chapter we review some basic notions of differential geometry that are sys tematically used in all the remaining chapters. We then introduce the Einstein equations and the initial data sets and discuss some of the basic features of the initial value problem in general relativity. We shall review, without proofs, well-established results concerning local and global existence and uniqueness and formulate our main result. The second chapter provides the technical motivation for the proof of our main theorem | ||
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| author | Klainerman, Sergiu |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-2084-8 |
| format | Electronic eBook |
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| isbn | 9781461220848 9780817642549 |
| language | English |
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| spelling | Klainerman, Sergiu Verfasser aut The Evolution Problem in General Relativity by Sergiu Klainerman, Francesco Nicolò Boston, MA Birkhäuser Boston 2003 1 Online-Ressource (400p. 20 illus) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematical Physics 25 The main goal of this work is to revisit the proof of the global stability of Minkowski space by D. Christodoulou and S. Klainerman, [Ch-KI]. We provide a new self-contained proof of the main part of that result, which concerns the full solution of the radiation problem in vacuum, for arbitrary asymptotically flat initial data sets. This can also be interpreted as a proof of the global stability of the external region of Schwarzschild spacetime. The proof, which is a significant modification of the arguments in [Ch-Kl], is based on a double null foliation of spacetime instead of the mixed null-maximal foliation used in [Ch-Kl]. This approach is more naturally adapted to the radiation features of the Einstein equations and leads to important technical simplifications. In the first chapter we review some basic notions of differential geometry that are sys tematically used in all the remaining chapters. We then introduce the Einstein equations and the initial data sets and discuss some of the basic features of the initial value problem in general relativity. We shall review, without proofs, well-established results concerning local and global existence and uniqueness and formulate our main result. The second chapter provides the technical motivation for the proof of our main theorem Mathematics Differential equations, partial Global differential geometry Mathematical physics Applications of Mathematics Partial Differential Equations Differential Geometry Mathematical Methods in Physics Mathematik Mathematische Physik Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 s Evolutionsgleichung (DE-588)4129061-6 s 1\p DE-604 Nicolò, Francesco Sonstige oth https://doi.org/10.1007/978-1-4612-2084-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Klainerman, Sergiu The Evolution Problem in General Relativity Mathematics Differential equations, partial Global differential geometry Mathematical physics Applications of Mathematics Partial Differential Equations Differential Geometry Mathematical Methods in Physics Mathematik Mathematische Physik Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| subject_GND | (DE-588)4112491-1 (DE-588)4129061-6 |
| title | The Evolution Problem in General Relativity |
| title_auth | The Evolution Problem in General Relativity |
| title_exact_search | The Evolution Problem in General Relativity |
| title_full | The Evolution Problem in General Relativity by Sergiu Klainerman, Francesco Nicolò |
| title_fullStr | The Evolution Problem in General Relativity by Sergiu Klainerman, Francesco Nicolò |
| title_full_unstemmed | The Evolution Problem in General Relativity by Sergiu Klainerman, Francesco Nicolò |
| title_short | The Evolution Problem in General Relativity |
| title_sort | the evolution problem in general relativity |
| topic | Mathematics Differential equations, partial Global differential geometry Mathematical physics Applications of Mathematics Partial Differential Equations Differential Geometry Mathematical Methods in Physics Mathematik Mathematische Physik Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| topic_facet | Mathematics Differential equations, partial Global differential geometry Mathematical physics Applications of Mathematics Partial Differential Equations Differential Geometry Mathematical Methods in Physics Mathematik Mathematische Physik Allgemeine Relativitätstheorie Evolutionsgleichung |
| url | https://doi.org/10.1007/978-1-4612-2084-8 |
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