Static perfect fluids with Pant-Sah equations of state

TL;DR

This paper studies a family of exact, static, spherically symmetric perfect fluid solutions in Einstein's gravity with Pant-Sah equations of state, highlighting their geometric characterization, physical realism, and symmetry properties.

Contribution

It introduces a geometric characterization of Pant-Sah equations of state and proves spherical symmetry of solutions, extending understanding of these physically realistic models.

Findings

Solutions have finite radius and are physically realistic.

The equations of state are characterized by constant scalar curvature of a conformally rescaled metric.

Spherical symmetry of asymptotically flat solutions is proven.

Abstract

We analyze the 3-parameter family of exact, regular, static, spherically symmetric perfect fluid solutions of Einstein's equations (corresponding to a 2-parameter family of equations of state) due to Pant and Sah and "rediscovered" by Rosquist and the present author. Except for the Buchdahl solutions which are contained as a limiting case, the fluids have finite radius and are physically realistic for suitable parameter ranges. The equations of state can be characterized geometrically by the property that the 3-metric on the static slices, rescaled conformally with the fourth power of any linear function of the norm of the static Killing vector, has constant scalar curvature. This local property does not require spherical symmetry; in fact it simplifies the the proof of spherical symmetry of asymptotically flat solutions which we recall here for the Pant-Sah equations of state. We also consider a model in Newtonian theory with analogous geometric and physical properties, together with a proof of spherical symmetry of the asymptotically flat solutions.