# The Einstein–Vlasov System/Kinetic Theory

**Update available:
http://www.livingreviews.org/lrr-2011-4**

**Håkan Andréasson
**

Department of Mathematics

Chalmers University of Technology

S-412 96 Göteborg, Sweden

http://www.math.chalmers.se/~hand

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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.