Cauchy problem on two characteristic hypersurfaces for the Einstein-Vlasov-Scalar field equations in temporal gauge

TL;DR

This paper addresses the initial value problem for Einstein-Vlasov-Scalar equations on intersecting characteristic hypersurfaces, establishing global solutions for initial data constraints and local solutions for evolution in the temporal gauge.

Contribution

It provides a novel approach to solving the initial data constraints globally and the evolution locally for Einstein-Vlasov-Scalar equations in the temporal gauge with characteristic initial data.

Findings

Global solution for initial data constraints

Local existence of evolution problem

Initial data on intersecting hypersurfaces

Abstract

In this paper, we consider the initial value problem for the Einstein-Vlasov-Scalar field equations in temporal gauge, where the initial data are prescribed on two characteristic smooth intersecting hypersurfaces. From a suitable choice of some free data, the initial data constraints's problem is solved globally, then the evolution problem relative to the deduced initial data is solved locally in time.