The Einstein-Vlasov System/Kinetic Theory
H{\aa}kan Andr\'easson
TL;DR
This paper reviews mathematical theorems on the global behavior of solutions to the Einstein-Vlasov system, a coupled set of Einstein's equations and kinetic matter models, highlighting progress since 1990.
Contribution
It provides a comprehensive guide to theorems on the global properties of solutions to the Einstein-Vlasov system, summarizing key mathematical results since 1990.
Findings
Many theorems on global solutions have been established since 1990
The Einstein-Vlasov system models relativistic kinetic matter in general relativity
Progress has been made in understanding the global behavior of solutions
Abstract
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.
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