(In)finite extent of stationary perfect fluids in Newtonian theory

TL;DR

This paper establishes criteria based on the equation of state and motion laws that determine whether stationary perfect fluids in Newtonian gravity have finite or infinite spatial extent, generalizing static results without symmetry assumptions.

Contribution

It provides new criteria for the extent of stationary perfect fluids in Newtonian gravity, including conditions that exclude hollow configurations and generalizing static case results without symmetry.

Findings

Criteria for finite or infinite extent of fluids

Exclusion of hollow configurations under certain conditions

Generalization of static case results to non-symmetric scenarios

Abstract

For stationary, barotropic fluids in Newtonian gravity we give simple criteria on the equation of state and the "law of motion" which guarantee finite or infinite extent of the fluid region (providing a priori estimates for the corresponding stationary Newton-Euler system). Under more restrictive conditions, we can also exclude the presence of "hollow" configurations. Our main result, which does not assume axial symmetry, uses the virial theorem as the key ingredient and generalises a known result in the static case. In the axially symmetric case stronger results are obtained and examples are discussed.