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

Sophonie Blaise Tchapnda
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Abstract

Results on the behaviour in the past time direction of cosmological models with collisionless matter and a cosmological constant $Λ$ are presented. It is shown that under the assumption of non-positive $Λ$ 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 $Λ$ as well as in the positive $Λ$ 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.

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Sophonie Blaise Tchapnda. 2004-07-16. Structure of solutions near the initial singularity for the surface-symmetric Einstein-Vlasov system. https://doi.org/10.1088/0264-9381%2F21%2F23%2F003

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