Initial data for fluid bodies in general relativity

TL;DR

This paper constructs initial data sets for Einstein's equations describing isolated fluid bodies with specific boundary properties, advancing the understanding of fluid configurations in general relativity.

Contribution

It introduces a method to generate asymptotically flat initial data for fluid bodies with positive density and smooth boundary conditions, filling a gap in initial data construction.

Findings

Existence of asymptotically flat initial data for fluid bodies.

Fluid density is positive and constant at the boundary.

Initial data are smooth except at the boundary.

Abstract

We show that there exist asymptotically flat almost-smooth initial data for Einstein-perfect fluid's equation that represent an isolated liquid-type body. By liquid-type body we mean that the fluid energy density has compact support and takes a strictly positive constant value at its boundary. By almost-smooth we mean that all initial data fields are smooth everywhere on the initial hypersurface except at the body boundary, where tangential derivatives of any order are continuous at that boundary. PACS: 04.20.Ex, 04.40.Nr, 02.30.Jr