Andréasson Håkan
Department of Mathematics, Chalmers University of Technology, S-41296 Göteborg, Sweden.
Living Rev Relativ. 2002;5(1):7. doi: 10.12942/lrr-2002-7. Epub 2002 Dec 6.
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 nonrelativistic 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. The Vlasov equation describes matter phenomenologically, and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (i.e. fluid models). 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 good comprehension of kinetic theory in general relativity.
本文的主要目的是提供一份关于爱因斯坦 - 弗拉索夫系统解的全局性质定理的指南。该系统将爱因斯坦方程与一个动力学物质模型耦合在一起。几十年来，动力学理论一直是一个重要的研究领域，主要关注非相对论和狭义相对论物理，即对中性气体、等离子体和牛顿自引力系统的动力学进行建模。1990年，伦德尔和赖因开始了对爱因斯坦 - 弗拉索夫系统的数学研究。从那时起，关于该系统解的全局性质的许多定理已经被建立。弗拉索夫方程从现象学角度描述物质，需要强调的是，本文中呈现的大多数定理目前对于其他此类物质模型（即流体模型）并不适用。本文首先介绍非弯曲时空中的动力学理论，然后引入爱因斯坦 - 弗拉索夫系统。我们认为，对非弯曲时空中动力学理论的良好理解是全面理解广义相对论中动力学理论的基础。
