Kinetic theory and the Einstein-Vlasov system

The Vlasov-Einstein equations are a closed self-consistent collision-less system of kinetic equations. They were introduced to model the dynamics of self gravitating multi-particles system. The particles could be a neutral gas, plasma, interstellar dust, stars, galaxies or even clusters of galaxies. In 1990 Rendall and Rein initiated the mathematical study of the Einstein-Vlasov system. Since then many properties of its solution have been established. In General-Relativity hydrodynamic models are commonly used. These models are naive and may give rise to unphysical phenomenas such as shell-crossing singularities. Coupling the Vlasov to the Einestin field equations results in a better description which rules out these singularities. In this paper, I will introduce kinetic theory and then discuss the Vlasov-Einstein system, It’s Lagrangian formalism and properties of its solutions. c ©2003 University of Toronto and the author. For further information, email the author at [email protected]