The Einstein-Vlasov system/Kinetic theory
Artikel i vetenskaplig tidskrift, 2011

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.

Kinetic theory

Einstein-Vlasov system

Vlasov-Poisson system

Nordström-Vlasov system

Global existence


Håkan Andreasson

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Living Reviews in Relativity

1433-8351 (ISSN)

Vol. 14 Art. no. 4-