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

Published online by Cambridge University Press:  24 October 2008

Gerhard Rein
Gerhard Rein
Affiliation:
Mathematisches Institut der Universität München, Theresienstr. 39, 80333 München, Germany
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 4 , May 1996 , pp. 739 - 762
Copyright
Copyright © Cambridge Philosophical Society 1996

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