The Erwin Schrr Odinger International Institute for Mathematical Physics Cosmological Solutions of the Vlasov{einstein System with Spherical, Plane, and Hyperbolic Symmetry 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.

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