All static spherically symmetric perfect fluid solutions of Einstein's Equations

TL;DR

This paper introduces an algorithm that systematically generates all regular static spherically symmetric perfect fluid solutions to Einstein's equations, producing new physically relevant solutions through a functional approach.

Contribution

It presents a novel algorithm based on a single monotone function to generate all such solutions, including many previously unknown physically interesting cases.

Findings

Generated an infinite number of new exact solutions.

Demonstrated the algorithm's effectiveness with physically relevant solutions.

Established inequalities necessary for physical relevance.

Abstract

An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect fluid solutions of Einstein's equations. For physically relevant solutions the generating functions must be restricted by non-trivial integral-differential inequalities. Nonetheless, the algorithm is demonstrated here by the construction of an infinite number of previously unknown physically interesting exact solutions.