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The Einstein-Vlasov System/Kinetic Theory

Author(s): Håkan Andréasson

Journal: Living Reviews in Relativity
ISSN 1433-8351

Volume: 14;
Start page: 4;
Date: 2011;
Original page

Keywords: Einstein-Vlasov system | Global existence | Nordström-Vlasov system | Kinetic theory | Vlasov-Poisson system

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.
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