Transforming the Einstein static Universe into physically acceptable static fluid spheres II: A two - fold infinity of exact solutions

TL;DR

This paper introduces a method to generate an infinite class of exact, physically acceptable static fluid solutions in Einstein's equations, extending the Tolman IV solution without explicit isotropic or curvature coordinate forms.

Contribution

It presents a novel solution-generating technique that produces an infinite class of exact static fluid solutions, generalizing the Tolman IV solution in Einstein's gravity.

Findings

Generated an infinite class of solutions

Most solutions lack explicit coordinate representations

Solutions generalize the Tolman IV model

Abstract

Following a solution generating technique introduced recently by one of us, we transform the Einstein static Universe into a two - fold infinity class of physically acceptable exact perfect fluid solutions of Einstein's equations. Whereas the entire class of solutions can be considered as generalizations of the familiar Tolman IV solution, no member of the class can be written explicitly in isotropic coordinates. Further, except for a set of measure zero, no member of the class can be written explicitly in curvature coordinates either.