The Einstein-Vlasov system/kinetic theory

DOI10.12942/lrr-2002-1zbMath1024.83008OpenAlexW2137202140WikidataQ37599432 ScholiaQ37599432MaRDI QIDQ5906964

Håakan Andréasson

Publication date: 17 July 2003

Published in: Living Reviews in Relativity (Search for Journal in Brave)

Full work available at URL: http://www.livingreviews.org/lrr-2002-7

zbMATH Keywords

Einstein's equationsEinstein-Vlasov systemglobal propertieskinetic matter modelNewtonian self-gravitating systems

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory (83-02) Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) (83C55) PDEs in connection with relativity and gravitational theory (35Q75) Einstein-Maxwell equations (83C22)

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Global weak solutions to the Nordström-Vlasov system, Gravitational collapse and the formation of black holes for the spherically symmetric Einstein-Vlasov system, Global solutions to the Cauchy problem for the relativistic Boltzmann equation with near-vacuum data, Global classical solutions to the 3D Nordström-Vlasov system, Decay estimates for the \(3D\) relativistic and non-relativistic Vlasov-Poisson systems, Regularity results for the spherically symmetric Einstein-Vlasov system, On the spatially homogeneous and isotropic Einstein-Vlasov-Fokker-Planck system with cosmological scalar field, Theoretical cosmology, Accretion disks around naked singularities, Future attractors of Bianchi types II and V cosmologies with massless Vlasov matter, Mathematical general relativity, A class of dust-like self-similar solutions of the massless Einstein-Vlasov system, Strong Cosmic Censorship for Surface-Symmetric Cosmological Spacetimes with Collisionless Matter, The stability of the Minkowski space for the Einstein-Vlasov system, Asymptotic behavior and orbital stability of galactic dynamics in relativistic scalar gravity, Nonlinear stability of the Milne model with matter, Low Dimensional Born-Infeld Equations Coupled with a Collisionless Matter Model, A Birman–Schwinger principle in galactic dynamics: ESI, Vienna, 07–11 February 2022

Cites Work

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• Asymptotic behaviour of the gravitational field and the nature of singularities in Gowdy spacetimes
• The existence of a black hole due to condensation of matter
• On space-times with U(1)\(\times U(1)\) symmetric compact Cauchy surfaces
• A numerical analysis of chaotic behaviour in Bianchi IX models
• Reduction of Einstein's equations for vacuum space-times with spacelike U(1) isometry groups
• Chaos in the long-term behavior of some Bianchi-type VIII models
• Homothetic and conformal symmetries of solutions to Einstein's equations
• On static and radiative space-times
• Singular space-times
• The instability of naked singularities in the gravitational collapse of a scalar field.
• Global foliations of vacuum spacetimes with \(T^2\) isometry
• On ``asymptotically flat space-times with \(G_2\)-invariant Cauchy surfaces
• Mass inflation and chaotic behaviour inside hairy black holes
• The inner structure of black holes
• A mathematical theory of gravitational collapse
• Detection of computer generated gravitational waves in numerical cosmologies
• The formation of black holes in nonspherical collapse and cosmic censorship
• Critical phenomena in nonlinear sigma models
• Manufacture of Gowdy spacetimes with spikes
• Chaos in Superstring Cosmology
• Physical aspects of a naked singularity explosion: how does a naked singularity explode?
• Hoop conjecture for apparent horizon formation
• New algorithm for Mixmaster dynamics
• The Mixmaster cosmology as a dynamical system
• Strong cosmic censorship in polarised Gowdy spacetimes
• General theory of fractal path integrals with applications to many-body theories and statistical physics
• The hoop conjecture and the Gibbons-Penrose construction of trapped surfaces
• A fully -dimensional Regge calculus model of the Kasner cosmology
• Asymptotic states of magnetic Bianchi I cosmologies
• Global dynamics of the mixmaster model
• Black hole formation from massive scalar fields
• Nonlinear gravitational effect
• Inner structure of a charged black hole: An exact mass-inflation solution
• Formation of naked singularities: The violation of cosmic censorship
• Black hole in three-dimensional spacetime
• Structure of the singularity inside a realistic rotating black hole
• Black Hole Singularities: A Numerical Approach
• Choptuik Spacetime as an Eigenvalue Problem
• Structure of the Black Hole's Cauchy-Horizon Singularity
• Cosmic Censorship: As Strong As Ever
• Chaos in the Einstein-Yang-Mills Equations
• Oscillatory Null Singularity inside Realistic Spinning Black Holes
• On crossing the Cauchy horizon of a Reissner–Nordström black-hole
• Curvature blow up in Bianchi VIII and IX vacuum spacetimes
• Dispersion and collapse of wave maps
• The singularities of gravitational collapse and cosmology
• No chaos in brane-world cosmology
• Trapped surfaces in prolate collapse in the Gibbons - Penrose construction
• How to avoid artificial boundaries in the numerical calculation of black hole spacetimes
• The Gowdy cosmologies revisited
• Asymptotic behavior in polarized T2-symmetric vacuum space–times
• Asymptotically flat space-times have no conformal Killing fields
• Asymptotic states of magnetic Bianchi VI cosmologies
• Asymptotic behaviour in polarized and half-polarized U (1) symmetric vacuum spacetimes
• On the general behaviour of the universe near the cosmological singularity
• Structure of the charged spherical black hole interior
• The spherically symmetric collapse of a massless scalar field
• Comment on the `chaotic' singularity in some magnetic Bianchi cosmologies
• Continuous self-similarity and S -duality
• Symmetry-seeking spacetime coordinates
• Analytic description of singularities in Gowdy spacetimes
• Dynamics of magnetic Bianchi VI ₀ cosmologies
• Generic Isolated Horizons and Their Applications
• The occurrence of singularities in cosmology. ɪɪɪ. Causality and singularities
• Mixmaster Universe
• The Large Scale Structure of Space-Time
• General Relativity
• Critical phenomena in gravitational collapse
• Computational cosmology: from the early universe to the large scale structure
• Critical phenomena in gravitational collapse
• Numerical approaches to spacetime singularities
• Empty space-times admitting a three parameter group of motions
• Ocillatory behaviour in homogeneous string cosmology models
• Mixmaster chaos
• Quiescent cosmological singularities
• The Bianchi IX attractor