# The Einstein-Vlasov system/Kinetic theory

**Living Reviews in Relativity**(1433-8351). Vol. 14 (2011), p. Art. no. 4.

[Artikel, refereegranskad vetenskaplig]

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.

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

*Update (27 May 2011): 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 signifcantly extended. The number of references has increased from 121 to 197.*

Denna post skapades 2012-01-19. Senast ändrad 2016-07-14.

CPL Pubid: 153819