Remarks on the Einstein–Euler-Entropy system

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. Along the way, we review some basic definitions and ideas, giving thus a relatively self-contained exposition that also serves as an introduction to many aspects of the problem.