COSMOLOGICAL SOLUTIONS OF THE VLASOV-EINSTEIN SYSTEM WITH SPHERICAL, PLANE, AND HYPERBOLIC SYMMETRY

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