Gerhard Rein
Cosmological Solutions of the Vlasov-Einstein System with Spherical, Plane, and Hyperbolic Symmetry
The paper is published: Math. Proc. Camb. Philos. Soc. 119, 4 (1996) 739-762

MSC:

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

35Q75 PDE in relativity

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.

Keywords: Vlasov-Einstein system, initial value problem, symmetry