Criteria for (in)finite extent of static perfect fluids

TL;DR

This paper establishes criteria on the equation of state of static perfect fluids in Newtonian and Einstein theories that determine whether the fluid's spatial extent is finite or infinite, improving previous conditions by relaxing assumptions.

Contribution

It provides a unified framework of criteria for the extent of static perfect fluids, connecting symmetry, asymptotic behavior, and equations of state in both Newtonian and relativistic contexts.

Findings

Criteria for finite or infinite extent of fluids based on the equation of state.

Relaxed asymptotic conditions still guarantee the same extent properties.

Unified approach linking symmetry, asymptotics, and equations of state.

Abstract

In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These criteria are closely related to ones which are known to ensure finite or infinite extent of the fluid region if the assumption of spherical symmetry is replaced by certain asymptotic falloff conditions on the solutions. We improve this result by relaxing the asymptotic asumptions. Our conditions on the equation of state are also related to (but less restrictive than) ones under which it has been shown in Relativity that static, asymptotically flat fluid solutions are spherically symmetric. We present all these results in a unified way.