The Einstein-Vlasov sytem/Kinetic theory

Abstract

The main purpose of this article is to guide the reader 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 where the main focus has been on nonrelativistic- and special relativistic physics, e.g. 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 (e.g. fluid models). The first part of this paper gives an introduction 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 in order to get a good comprehension of kinetic theory in general relativity.

31 pages. This article has been submitted to Living Rev. Relativity (http://www.livingreviews.org)

References in corpus (10)

• Critical phenomena in gravitational collapse
• Cosmological models and centre manifold theory
• On the Einstein-Vlasov system with hyperbolic symmetry
• Critical phenomena at the threshold of black hole formation for collisionless matter in spherical symmetry
• The Vlasov-Poisson system with radiation damping
• Self-similar spherically symmetric solutions of the massless Einstein-Vlasov system
• Global Prescribed Mean Curvature foliations in cosmological spacetimes with matter, Part I
• Local Prescribed Mean Curvature foliations in cosmological spacetimes
• Existence of CMC and constant areal time foliations in T^2 symmetric spacetimes with Vlasov matter
• Global Prescribed Mean Curvature foliations in cosmological spacetimes with matter, Part II

Cited by in corpus (9)

• Asymptotic behaviour of the Einstein-Vlasov system with a positive cosmological constant
• Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless matter
• The Stability of the Minkowski space for the Einstein-Vlasov system
• Ohm's Law in the Fast Lane: General Relativistic Charge Dynamics
• Global Existence of Solutions for the Einstein-Boltzmann System in a Bianchi Type I Space-Time
• Existence of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system
• Future attractors of Bianchi types II and V cosmologies with massless Vlasov matter
• A Birman-Schwinger principle in galactic dynamics
• A Collision Operator for Field-Mediated Interactions in General Relativistic Kinetic Theory