Discussions on a special static spherically symmetric perfect fluid solution of Einstein's equations

TL;DR

This paper presents a unique static spherically symmetric perfect fluid solution to Einstein's equations, highlighting its singularities, energy condition satisfaction, and coordinate transformations to avoid certain singularities.

Contribution

It introduces a novel perfect fluid solution with specific divergence properties and discusses methods to handle its singularities using isotropic coordinates.

Findings

Pressure and density diverge at the origin.

The solution satisfies all energy conditions.

Singularities can be avoided with coordinate transformations.

Abstract

In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to give positive pressure but nevertheless, it satisfies all energy conditions. In this new spacetime geometry, the metric becomes singular at some finite value of radial coordinate although, by using isotropic coordinates, this singularity could be avoided, as has been shown here. Some characteristics of this solution are also discussed.