(In)finiteness of Spherically Symmetric Static Perfect Fluids

TL;DR

This paper investigates conditions under which static, spherically symmetric perfect fluid solutions are finite or infinite in extent, providing new criteria applicable in both Newtonian gravity and General Relativity.

Contribution

It derives improved criteria for the finiteness of perfect fluid solutions, extending previous results in both Newtonian and relativistic contexts.

Findings

Criteria for finiteness based on the equation of state

Extension of results to broader classes of equations of state

Enhanced understanding of fluid solution properties in gravity theories

Abstract

This work is concerned with the finiteness problem for static, spherically symmetric perfect fluids in both Newtonian Gravity and General Relativity. We derive criteria on the barotropic equation of state guaranteeing that the corresponding perfect fluid solutions possess finite/infinite extent. In the Newtonian case, for the large class of monotonic equations of state, and in General Relativity we improve earlier results.