The Einstein-Vlasov system/Kinetic theory

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, {\it 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 ({\it 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.

40 pages, updated version, to appear in Living Reviews in Relativity

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Cited by in corpus (38)

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• Spectral densities for hot QCD plasmas in a leading log approximation
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• Hyperboloidal slicing approach to quasi-normal mode expansions: the Reissner-Nordström case
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
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• Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models
• Existence of axially symmetric static solutions of the Einstein-Vlasov system
• Dynamics of the spatially homogeneous Bianchi type I Einstein-Vlasov equations
• Global classical solutions to the 3D Nordström-Vlasov system
• The formation of black holes in spherically symmetric gravitational collapse
• Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter
• On the relativistic BGK-Boltzmann model: asymptotics and hydrodynamics
• Field theory and weak Euler-Lagrange equation for classical particle-field systems
• Conformal symmetry and non-relativistic second order fluid dynamics
• Bounds on the mass-to-radius ratio for non-compact field configurations
• Description of the evolution of inhomogeneities on a Dark Matter halo with the Vlasov equation
• The asymptotic behaviour in Schwarzschild time of Vlasov matter in spherically symmetric gravitational collapse
• Evolution of the phase-space density and the Jeans scale for dark matter derived from the Vlasov-Einstein equation
• Asymptotic behavior and orbital stability of galactic dynamics in relativistic scalar gravity
• Static cylindrically symmetric spacetimes
• On global existence for the spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates
• On the dynamics of thin shells of counter rotating particles
• A class of dust-like self-similar solutions of the massless Einstein-Vlasov system
• Static spherically symmetric Einstein-Vlasov shells made up of particles with a discrete set of values of their angular momentum
• Regularity results for the spherically symmetric Einstein-Vlasov system
• An Approach for Modelling Tachyons with Gravitation
• On surface-symmetric spacetimes with collisionless and charged matter
• Dispersive behavior in Galactic Dynamics
• Virial inequalities for steady states in relativistic galactic dynamics
• Relatively non-degenerate integrated decay estimates for massless Vlasov fields on Schwarzschild spacetimes
• Well-posedness of anisotropic and homogeneous solutions to the Einstein-Boltzmann system with a conformal-gauge singularity