The Einstein-Vlasov System/Kinetic Theory

2011/05/27 by Håkan Andréasson · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Effective field theory #Field (mathematics) #Focus (optics) #Gas Dynamics and Kinetic Theory #Kinetic energy #Kinetic term #Kinetic theory #Newtonian fluid #Statistical Mechanics and Entropy #Thermoelastic and Magnetoelastic Phenomena #gr-qc #math-ph #math.MP

paper · pdf · doi:10.12942/lrr-2011-4

published as Living Rev.Rel.14:4,2011 · Published version http://www.livingreviews.org/lrr-2011-4

openalex publication_date 2011/05/27 · arxiv created 2011/06/07 · arxiv updated 2015/05/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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 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.

Citations

• A Review of Mathematical Topics in Collisional Kinetic Theory
• Global solutions for the relativistic Boltzmann equation in the homogeneous case on the Minkowski space-time
• Classical Solutions and the Glassey-Strauss Theorem for the 3D Vlasov-Maxwell System
• Global existence and asymptotic behaviour in the future for the Einstein--Vlasov system with positive cosmological constant
• Global weak solutions of Vlasov‐Maxwell systems
• Global Foliations of Matter Spacetimes¶with Gowdy Symmetry
• Global Existence Proof for Relativistic Boltzmann Equation with Hard Interactions
• Examples of Naked Singularity Formation in the Gravitational Collapse of a Scalar Field
• Absence of shocks in an initially dilute collisionless plasma
• Zur Theorie der Gravitation vom Standpunkt des Relativitätsprinzips
• On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation
• Static shells for the Vlasov-Poisson and Vlasov-Einstein systems
• The classical limit of the relativistic Vlasov-Maxwell system
• Singularity formation in a collisionless plasma could occur only at high velocities
• Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric
• Dynamics of the spatially homogeneous Bianchi type I Einstein–Vlasov equations
• On global existence for the spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates
• Global Existence for the Spherically Symmetric Einstein–Vlasov System with Outgoing Matter
• The Instability of Naked Singularities in the Gravitational Collapse of a Scalar Field
• Strong cosmic censorship for T²-symmetric cosmological spacetimes with collisionless matter

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