The Einstein-Vlasov System/Kinetic Theory
The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein’s equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focu...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2011-05-01
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| Series: | Living Reviews in Relativity |
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| Online Access: | http://www.livingreviews.org/lrr-2011-4 |
| _version_ | 1818554762463805440 |
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| author | Håkan Andréasson |
| author_facet | Håkan Andréasson |
| author_sort | Håkan Andréasson |
| collection | DOAJ |
| description | The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein’s equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein–Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity. |
| first_indexed | 2024-12-12T09:44:21Z |
| format | Article |
| id | doaj.art-96d02801868f48048370ddaff3a8159a |
| institution | Directory Open Access Journal |
| issn | 1433-8351 |
| language | English |
| last_indexed | 2024-12-12T09:44:21Z |
| publishDate | 2011-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Living Reviews in Relativity |
| spelling | doaj.art-96d02801868f48048370ddaff3a8159a2022-12-22T00:28:27ZengSpringerOpenLiving Reviews in Relativity1433-83512011-05-01144The Einstein-Vlasov System/Kinetic TheoryHåkan AndréassonThe main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein’s equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein–Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity.http://www.livingreviews.org/lrr-2011-4Einstein-Vlasov systemGlobal existenceNordström-Vlasov systemKinetic theoryVlasov-Poisson system |
| spellingShingle | Håkan Andréasson The Einstein-Vlasov System/Kinetic Theory Living Reviews in Relativity Einstein-Vlasov system Global existence Nordström-Vlasov system Kinetic theory Vlasov-Poisson system |
| title | The Einstein-Vlasov System/Kinetic Theory |
| title_full | The Einstein-Vlasov System/Kinetic Theory |
| title_fullStr | The Einstein-Vlasov System/Kinetic Theory |
| title_full_unstemmed | The Einstein-Vlasov System/Kinetic Theory |
| title_short | The Einstein-Vlasov System/Kinetic Theory |
| title_sort | einstein vlasov system kinetic theory |
| topic | Einstein-Vlasov system Global existence Nordström-Vlasov system Kinetic theory Vlasov-Poisson system |
| url | http://www.livingreviews.org/lrr-2011-4 |
| work_keys_str_mv | AT hakanandreasson theeinsteinvlasovsystemkinetictheory AT hakanandreasson einsteinvlasovsystemkinetictheory |