Remarks on the Einstein-Euler-Entropy system

TL;DR

This paper proves short-time existence for the Einstein-Euler-Entropy system with non-isentropic fluids, using a Lagrangian approach based on Friedrich's techniques, offering a new proof suitable for self-gravitating fluid bodies.

Contribution

It provides a novel proof of short-time existence for the Einstein-Euler-Entropy system using a Lagrangian method, differing from previous approaches by Choquet-Bruhat and Lichnerowicz.

Findings

Short-time existence established for non-isentropic fluids.

Method applicable to both compact and non-compact Cauchy surfaces.

New proof tailored for applications to self-gravitating fluid bodies.

Abstract

We prove short-time existence for the Einstein-Euler-Entropy system for non-isentropic fluids with data in uniformly local Sobolev spaces. The cases of compact as well as non-compact Cauchy surfaces are covered. The method employed uses a Lagrangian description of the fluid flow which is based on techniques developed by Friedrich, hence providing a completely different proof of earlier results of Choquet-Bruhat and Lichnerowicz. This new proof is specially suited for applications to self-gravitating fluid bodies.