On unbounded bodies with finite mass: asymptotic behaviour

TL;DR

This paper investigates the asymptotic behavior of static Einstein equations coupled with perfect fluids having a specific class of barotropic equations of state that become polytropic of index 5 at low pressure, showing smoothness or analyticity at infinity.

Contribution

It introduces a new class of barotropic EOS and analyzes the asymptotic properties of solutions to Einstein equations with these EOS, extending understanding of unbounded bodies with finite mass.

Findings

Solutions are conformally smooth or analytic at infinity depending on EOS smoothness.

The class of EOS becomes polytropic of index 5 at low pressure.

Asymptotic behavior parallels vacuum solutions under certain conditions.

Abstract

There is introduced a class of barotropic equations of state (EOS) which become polytropic of index $n = 5$ at low pressure. One then studies asymptotically flat solutions of the static Einstein equations coupled to perfect fluids having such an EOS. It is shown that such solutions, in the same manner as the vacuum ones, are conformally smooth or analytic at infinity, when the EOS is smooth or analytic, respectively.