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 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.

Published version http://www.livingreviews.org/lrr-2011-4

References in corpus (82)

• Sharp bounds on the critical stability radius for relativistic charged spheres
• Sharp bounds on $2m/r$ of general spherically symmetric static objects
• On classical solutions to the 3D relativistic Vlasov-Maxwell system: Glassey-Strauss' theorem revisited
• Spherically symmetric spacetimes with a trapped surface
• Global Properties of Locally Spatially Homogeneous Cosmological Models with Matter
• Global Foliations of Vacuum Spacetimes with $T^2$ Isometry
• Asymptotic behaviour of the Einstein-Vlasov system with a positive cosmological constant
• Crushing singularities in spacetimes with spherical, plane and hyperbolic symmetry
• Global foliations of matter spacetimes with Gowdy symmetry
• Cosmological models and centre manifold theory
• Existence of constant mean curvature foliations in spacetimes with two-dimensional local symmetry
• On the Einstein-Vlasov system with hyperbolic symmetry
• Isotropic cosmological singularities 2: The Einstein-Vlasov system
• Compact support of spherically symmetric equilibria in non-relativistic and relativistic galactic dynamics
• Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric
• Isotropic cosmological singularities 3: The Cauchy problem for the inhomogeneous conformal Einstein-Vlasov equations
• Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant
• The Stability of the Irrotational Euler-Einstein System with a Positive Cosmological Constant
• The Cosmic No-Hair Theorem and the Nonlinear Stability of Homogeneous Newtonian Cosmological Models
• Dynamics of spatially homogeneous locally rotationally symmetric solutions of the Einstein-Vlasov equations
• Existence of maximal hypersurfaces in some spherically symmetric spacetimes
• Cosmological solutions of the Vlasov-Einstein system with spherical, plane, and hyperbolic symmetry
• Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials
• On the area of the symmetry orbits in $T^2$ symmetric spacetimes with Vlasov matter
• Inextendibility of expanding cosmological models with symmetry
• Critical collapse of collisionless matter - a numerical investigation
• Global Newtonian limit for the Relativistic Boltzmann Equation near Vacuum
• A numerical investigation of the steady states of the spherically symmetric Einstein-Vlasov-Maxwell system
• A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system
• Strong cosmic censorship for T^2-symmetric spacetimes with cosmological constant and matter
• On future geodesic completeness for the Einstein-Vlasov system with hyperbolic symmetry
• The Newtonian Limit for Asymptotically Flat Solutions of the Vlasov-Einstein System
• Spherically symmetric steady states of galactic dynamics in scalar gravity
• Static solutions of the spherically symmetric Vlasov-Einstein system
• On the steady states of the spherically symmetric Einstein-Vlasov system
• Coordinates in the relativistic Boltzmann theory
• On static shells and the Buchdahl inequality for the spherically symmetric Einstein-Vlasov system
• Sharp bounds on 2m/r for static spherical objects
• Critical phenomena at the threshold of black hole formation for collisionless matter in spherical symmetry
• Absolute Stability Limit for Relativistic Charged Spheres
• Bounds on 2m/R for static spherical objects
• The Vlasov-Poisson system with radiation damping
• Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models
• Existence of axially symmetric static solutions of the Einstein-Vlasov system
• A regularity theorem for solutions of the spherically symmetric Vlasov-Einstein system
• Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless matter
• The initial singularity in solutions of the Einstein-Vlasov system of Bianchi type I
• Dynamics of the spatially homogeneous Bianchi type I Einstein-Vlasov equations
• An extension principle for the Einstein-Vlasov system in spherical symmetry
• The Newtonian limit of the relativistic Boltzmann equation
• Global Existence of Solutions for the Einstein-Boltzmann System in a Bianchi Type I Space-Time
• Static self-gravitating elastic bodies in Einstein gravity
• Self-similar spherically symmetric solutions of the massless Einstein-Vlasov system
• Global classical solutions to the 3D Nordström-Vlasov system
• The formation of black holes in spherically symmetric gravitational collapse
• Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data
• Rotating elastic bodies in Einstein gravity
• Global Prescribed Mean Curvature foliations in cosmological spacetimes with matter, Part I
• On the Buchdahl inequality for spherically symmetric static shells
• Local Prescribed Mean Curvature foliations in cosmological spacetimes
• Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter
• Cosmological spacetimes not covered by a constant mean curvature slicing
• Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system
• Strong cosmic censorship for T^2-symmetric cosmological spacetimes with collisionless matter
• Multipole radiation in a collisonless gas coupled to electromagnetism or scalar gravitation
• Dynamics of Bianchi type I solutions of the Einstein equations with anisotropic matter
• The Einstein-Vlasov-Maxwell(EVM) System with Spherical Symmetry
• Global Prescribed Mean Curvature foliations in cosmological spacetimes with matter, Part II
• Global Existence Proof for Relativistic Boltzmann Equation with Hard Interactions
• Self-gravitating stationary spherically symmetric systems in relativistic galactic dynamics
• The asymptotic behaviour in Schwarzschild time of Vlasov matter in spherically symmetric gravitational collapse
• Existence of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system
• Local Existence and Continuation Criterion for Solutions of the Spherically Symmetric Einstein-Vlasov-Maxwell System
• Asymptotic behavior and orbital stability of galactic dynamics in relativistic scalar gravity
• Global solutions for the relativistic Boltzmann equation in the homogeneous case on the Minkowski space-time
• On global existence for the spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates
• On the area of the symmetry orbits of cosmological spacetimes with toroidal or hyperbolic symmetry
• Structure of solutions near the initial singularity for the surface-symmetric Einstein-Vlasov system
• Global existence and future asymptotic behaviour for solutions of the Einstein-Vlasov-scalar field system with surface symmetry
• Regularity results for the spherically symmetric Einstein-Vlasov system
• On the nature of initial singularities for solutions of the Einstein-Vlasov-scalar field system with surface symmetry
• On surface-symmetric spacetimes with collisionless and charged matter

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• Accretion of the relativistic Vlasov gas onto a moving Schwarzschild black hole: Exact solutions
• The Newtonian limit of the relativistic Boltzmann equation
• Chaotic blowup in the 3D incompressible Euler equations on a logarithmic lattice
• Accretion of the Vlasov gas onto a Schwarzschild-like black hole
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• Boson stars and their relatives in semiclassical gravity
• A proof of the instability of AdS for the Einstein--null dust system with an inner mirror
• Accretion of the Vlasov gas on Reissner-Nordström black holes
• Relic neutrinos: Physically consistent treatment of effective number of neutrinos and neutrino mass
• Accretion of the relativistic Vlasov gas in the equatorial plane of the Kerr black hole
• On Axisymmetric and Stationary Solutions of the Self-Gravitating Vlasov System
• The kinetic gas universe
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• On the oscillations and future asymptotics of locally rotationally symmetric Bianchi type III cosmologies with a massive scalar field
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• Spherically symmetric steady states of John elastic bodies in general relativity
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• Cosmic String and Black Hole Limits of Toroidal Vlasov Bodies in General Relativity
• Stability for the spherically symmetric Einstein-Vlasov system - a coercivity estimate
• Scalar field dark matter in hybrid approach
• A numerical stability analysis for the Einstein-Vlasov system
• An Inverse Problem for the Relativistic Boltzmann Equation
• Isotropization of Slowly Expanding Spacetimes
• Collisionless equilibria in general relativity: stable configurations beyond the first binding energy maximum
• On the Hoop conjecture and the weak cosmic censorship conjecture for the axisymmetric Einstein-Vlasov system
• Axisymmetric, stationary collisionless gas configurations surrounding black holes
• Open problems in mathematical physics
• Einstein gravity of a diffusing fluid
• On the origin of cosmic web
• Kantowski-Sachs cosmology with Vlasov matter
• General relativistic non-ideal fluid equations for dark matter from a truncated cumulant expansion
• Field-theoretic approach to large-scale structure formation
• Cosmological Landsberg Finsler spacetimes
• A stellar model with diffusion in general relativity
• The Schr$\ddot{o}$dinger-Poisson equations as the large-N limit of the Newtonian N-body system: applications to the large scale dark matter dynamics
• General field theory and weak Euler-Lagrange equation for classical particle-field systems in plasma physics
• On the future of solutions to the massless Einstein-Vlasov system in a Bianchi I cosmology
• Accretion of a Vlasov gas by a Kerr black hole
• Axisymmetric, stationary collisionless gas clouds trapped in a Newtonian potential
• Asymptotic behavior of a matter filled universe with exotic topology
• Spherical accretion of a collisionless kinetic gas into a generic static black hole
• Thermal equilibrium states and instability of self-gravitating particles in an asymptotically AdS spacetime
• Evolution of thin shells in D-dimensional General Relativity
• From kinetic gases to an exponentially expanding universe - The Finsler-Friedmann equation
• Cosmology of Einstein-Vlasov system in a weak modification of general relativity
• Static solutions to the spherically symmetric Einstein-Vlasov system: a particle-number-Casimir approach
• The Einstein-Vlasov system in spherical symmetry II: spherical perturbations of static solutions
• Quarks to Cosmos: Particles and Plasma in Cosmological evolution
• Distribution functions for a family of general-relativistic Hypervirial models in collisionless regime
• EVStabilityNet: Predicting the Stability of Star Clusters in General Relativity
• A Birman-Schwinger Principle in General Relativity: Linearly Stable Shells of Collisionless Matter Surrounding a Black Hole
• The evolution of a spatially homogeneous and isotropic universe filled with a collisionless gas
• A core-halo pattern of entropy creation in gravitational collapse
• Temperature fluctuations in an inhomogeneous diffusive fluid
• Existence of steady states of the massless Einstein-Vlasov system surrounding a Schwarzschild black hole
• Einstein-Vlasov system with equal-angular momenta in ${\text{AdS}}_5$
• Kinetic gases in static spherically symmetric modified dispersion relations