The initial singularity in solutions of the Einstein-Vlasov system of Bianchi type I

TL;DR

This paper investigates the behavior of solutions to the Einstein-Vlasov system with Bianchi I symmetry, focusing on the nature of the initial singularity and late-time dynamics for massive and massless particles.

Contribution

It provides new insights into the asymptotic behavior near the initial singularity and demonstrates a unique solution with massless particles that differs from perfect fluid models.

Findings

Solutions tend to isotropic dust solutions at late times for massive particles.

The initial singularity exhibits a limited set of possible behaviors.

A specific solution with massless particles shows matter remains significant near the singularity.

Abstract

The dynamics of solutions of the Einstein-Vlasov system with Bianchi I symmetry is discussed in the case of massive or massless particles. It is shown that in the case of massive particles the solutions are asymptotic to isotropic dust solutions at late times. The initial singularity is more difficult to analyse. It is shown that the asymptotic behaviour there must be one of a small set of possibilities but it is not clear whether all of these possibilities are realized. One solution is exhibited in the case of massless particles which behaves quite differently near the singularity from any Bianchi I solution with perfect fluid as matter model. In particular the matter is not dynamically negligeable near the singularity for this solution.