Isothermal spherical perfect fluid model: Uniqueness and Conformal mapping

TL;DR

This paper establishes a condition under which spherically symmetric spacetimes can be modeled as isothermal perfect fluids, showing they are conformally related to minimally curved spacetimes, with implications for understanding gravitational and fluid dynamics.

Contribution

It proves a necessary and sufficient condition linking isothermal perfect fluid models to conformal mappings of minimally curved spacetimes, advancing theoretical understanding.

Findings

Characterizes isothermal perfect fluid spacetimes via conformal relations.

Identifies conditions for spherically symmetric solutions without boundary.

Links fluid models to minimally curved spacetime geometries.

Abstract

We prove the theorem: The necessary and sufficient condition for a spherically symmetric spacetime to represent an isothermal perfect fluid (barotropic equation of state with density falling off as inverse square of the curvature radius) distribution without boundary is that it is conformal to the ``minimally'' curved (gravitation only manifesting in tidal acceleration and being absent in particle trajectory) spacetime.