eng
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
Living Reviews in Relativity
1433-8351
2011-05-27
14
4
10.12942/lrr-2011-4
lrr-2011-4
article
The Einstein-Vlasov System/Kinetic Theory
Håkan Andréasson
1
Department of Mathematics, Chalmers University of Technology, S-41296 Göteborg, Sweden
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.
http://www.livingreviews.org/lrr-2011-4
Kinetic theory
Einstein-Vlasov system
Vlasov-Poisson system
Global existence
Nordström-Vlasov system