Vol. 14 (2011) > lrr-2011-4

doi: 10.12942/lrr-2011-4
Living Rev. Relativity 14 (2011), 4

The Einstein-Vlasov System/Kinetic Theory

1 Department of Mathematics, Chalmers University of Technology, S-41296 Göteborg, Sweden

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Article Abstract

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.

Keywords: Kinetic theory, Vlasov-Poisson system, Nordström-Vlasov system, Einstein-Vlasov system, Global existence

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Since a Living Reviews in Relativity article may evolve over time, please cite the access <date>, which uniquely identifies the version of the article you are referring to:

Håkan Andréasson,
"The Einstein-Vlasov System/Kinetic Theory",
Living Rev. Relativity 14,  (2011),  4. URL (cited on <date>):
http://www.livingreviews.org/lrr-2011-4

Article History

ORIGINAL http://www.livingreviews.org/lrr-2002-7
Title The Einstein-Vlasov System/Kinetic Theory
Author Håkan Andréasson
Date accepted 18 October 2002, published 6 December 2002
UPDATE http://www.livingreviews.org/lrr-2005-2
Title The Einstein-Vlasov System/Kinetic Theory
Author Håkan Andréasson
Date accepted 23 February 2005, published 18 March 2005
Changes Updated and extended article: Sections 1.3 and 2.3 added, extended reference list from previous 90 to 121.
UPDATE http://www.livingreviews.org/lrr-2011-4
Title The Einstein-Vlasov System/Kinetic Theory
Author Håkan Andréasson
Date accepted 6 May 2011, published 27 May 2011
Changes This is a revised and updated version of the article from 2005. A number of new sections on the Einstein-Vlasov system have been added, e.g., on the formation of black holes and trapped surfaces, on self-similar solutions, on the structure of static solutions, on Buchdahl type inequalities, on the stability of cosmological solutions, and on axisymmetric solutions. Some of the previous sections have been significantly extended. The number of references has increased from 121 to 197.
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