The Einstein-Vlasov System/Kinetic Theory

doi:doi:10.12942/lrr-2005-2

url: http://www.livingreviews.org/lrr-2005-2

doi: 10.12942/lrr-2005-2

Living Rev. Relativity 8 (2005), 2

The Einstein-Vlasov System/Kinetic Theory

Håkan Andréasson

Affiliation(s)

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 nonrelativistic 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. The Vlasov equation describes matter phenomenologically, and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (i.e. fluid models). 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 good comprehension of kinetic theory in general relativity.

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"The Einstein-Vlasov System/Kinetic Theory",
Living Rev. Relativity 8, (2005), 2. URL (cited on <date>):
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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.