Initial boundary-value problem for the spherically symmetric Einstein equations with fluids with tangential pressure

TL;DR

This paper proves the local existence and uniqueness of solutions to the Einstein equations for spherically symmetric fluids with tangential pressure, including an application to elastic fluids matched with vacuum exterior.

Contribution

It establishes a rigorous mathematical framework for spherically symmetric Einstein-fluid systems with tangential pressure, including boundary conditions and an application to elastic fluids.

Findings

Existence and uniqueness of local solutions near the boundary.

Application to elastic fluid interiors matched with vacuum exterior.

Mathematical formulation of boundary-value problem for Einstein equations.

Abstract

We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial spacelike hypersurface with a timelike boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior.