Cosmological solutions of the Vlasov-Einstein system with spherical, plane, and hyperbolic symmetry

Abstract

The Vlasov-Einstein system describes a self-gravitating, collisionless gas within the framework of general relativity. We investigate the initial value problem in a cosmological setting with spherical, plane, or hyperbolic symmetry and prove that for small initial data solutions exist up to a spacetime singularity which is a curvature and a crushing singularity. An important tool in the analysis is a local existence result with a continuation criterion saying that solutions can be extended as long as the momenta in the support of the phase-space distribution of the matter remain bounded.

32 pages, LaTeX, report 941

References in corpus (4)

• Global Properties of Locally Spatially Homogeneous Cosmological Models with Matter
• Static solutions of the spherically symmetric Vlasov-Einstein system
• Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting
• A regularity theorem for solutions of the spherically symmetric Vlasov-Einstein system

Cited by in corpus (20)

• The Einstein-Vlasov System/Kinetic Theory
• The Einstein-Vlasov system/Kinetic theory
• Theorems on existence and global dynamics for the Einstein equations
• Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant
• Dynamics of spatially homogeneous locally rotationally symmetric solutions of the Einstein-Vlasov equations
• Global dynamics of the mixmaster model
• Describing general cosmological singularities in Iwasawa variables
• Dynamical systems approach to G2 cosmology
• A regime of linear stability for the Einstein-scalar field system with applications to nonlinear Big Bang formation
• Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless matter
• The Einstein-Vlasov sytem/Kinetic theory
• A class of plane symmetric perfect-fluid cosmologies with a Kasner-like singularity
• The maximal development of near-FLRW data for the Einstein-scalar field system with spatial topology ${\mathbb{S}}^3$
• Global Prescribed Mean Curvature foliations in cosmological spacetimes with matter, Part I
• Local Prescribed Mean Curvature foliations in cosmological spacetimes
• Local and global existence theorems for the Einstein equations
• Global Prescribed Mean Curvature foliations in cosmological spacetimes with matter, Part II
• Structure of solutions near the initial singularity for the surface-symmetric Einstein-Vlasov system
• Future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a cosmological constant
• Recollapsing spacetimes with $\Lambda <0$