Local existence and continuation criteria for solutions of the Einstein-Vlasov-scalar field system with surface symmetry

TL;DR

This paper establishes local existence and continuation criteria for solutions to the Einstein-Vlasov-scalar field system with surface symmetry, and demonstrates global existence in the scalar field-only case within general relativity.

Contribution

It provides the first local existence and continuation criteria results for the Einstein-Vlasov-scalar field system with surface symmetry, including a global existence result for scalar field-only scenarios.

Findings

Proved local in time existence for the system under spherical, plane, and hyperbolic symmetry.

Established continuation criteria for cosmological solutions.

Derived a global existence result when only scalar fields are present.

Abstract

We prove in the cases of spherical, plane and hyperbolic symmetry a local in time existence theorem and continuation criteria for cosmological 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. This system describes the evolution of self-gravitating collisionless matter and scalar waves within the context of general relativity. In the case where the only source is a scalar field it is shown that a global existence result can be deduced from the general theorem.