Structure of solutions near the initial singularity for the surface-symmetric Einstein-Vlasov system

Abstract

Results on the behaviour in the past time direction of cosmological models with collisionless matter and a cosmological constant $\Lambda$ are presented. It is shown that under the assumption of non-positive $\Lambda$ and spherical or plane symmetry the area radius goes to zero at the initial singularity. Under a smallness assumption on the initial data, these properties hold in the case of hyperbolic symmetry and negative $\Lambda$ as well as in the positive $\Lambda$ case. Furthermore in the latter cases past global existence of spatially homogeneous solutions is proved for generic initial data. The early-time asymptotics is shown to be Kasner-like for small data.

17 pages

Cited by in corpus (4)

• The Einstein-Vlasov System/Kinetic Theory
• The Einstein-Vlasov system/Kinetic theory
• Theorems on existence and global dynamics for the Einstein equations
• Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless matter