Transforming the Einstein static Universe into physically acceptable static fluid spheres

TL;DR

This paper explores transforming the Einstein static Universe into physically acceptable static fluid spheres using solution generating techniques, emphasizing the role of integration constants in obtaining realistic models.

Contribution

It introduces a method to generate new static fluid sphere solutions from the Einstein static Universe, highlighting the significance of integration constants in these solutions.

Findings

New exact solutions for static fluid spheres are derived.

The properties of these solutions are analyzed in detail.

Integration constants play a crucial role in the physical acceptability of solutions.

Abstract

The staid subject of exact static spherically symmetric perfect fluid solutions of Einstein's equations has been reinvigorated in the last decade. We now have several solution generating techniques which give rise to new exact solutions. Here the Einstein static Universe is transformed into a physically acceptable solution the properties of which are examined in detail. The emphasis here is on the importance of the integration constants that these generating techniques introduce.