Global existence and future asymptotic behaviour for solutions of the Einstein-Vlasov-scalar field system with surface symmetry

TL;DR

This paper establishes global existence and future asymptotic behavior of solutions to the Einstein-Vlasov-scalar field system with surface symmetry, demonstrating geodesic completeness in certain symmetric cases.

Contribution

It provides the first proof of global in time existence and geodesic completeness for these coupled systems under plane and hyperbolic symmetries.

Findings

Future geodesic completeness in plane symmetry with scalar field

Global existence results for hyperbolic and plane symmetric solutions

Causal geodesics are future complete in homogeneous cases

Abstract

We prove in the cases of plane and hyperbolic symmetries a global in time existence result in the future for comological solutions of the Einstein-Vlasov-scalar field system, with the sources generated by a distribution function and a scalar field, subject to the Vlasov and wave equations respectively. The spacetime is future geodesically complete in the special case of plane symmetry with only a scalar field. Causal geodesics are also shown to be future complete for homogeneous solutions of the Einstein-Vlasov-scalar field system with plane and hyperbolic symmetry.