The surface-symmetric Einstein-Vlasov system with cosmological constant

TL;DR

This paper extends local existence results for the Einstein-Vlasov system to include a positive cosmological constant, demonstrating global existence and inflationary behavior for certain initial data in spherically symmetric cases.

Contribution

It generalizes previous work by incorporating a non-zero cosmological constant and analyzes late-time behavior of the energy-momentum tensor.

Findings

Existence of a large class of initial data with global solutions

Inflationary asymptotics in the future for spherically symmetric case

Analysis of energy-momentum tensor behavior at late times

Abstract

The results on local existence and continuation criteria obtained by G. Rein in [4] are extended to the case with a non-zero cosmological constant. It is also shown that for the spherically symmetric case and a positive cosmological constant there is a large class of initial data with global existence and inflationary asymptotics in the future as in the case of plane or hyperbolic symmetry treated in [7]. Furthermore we analyze the behaviour of the energy-momentum tensor at late times.