Solution generating with perfect fluids

TL;DR

This paper applies Stephani's solution-generating technique to Einstein-perfect fluid equations, producing new twisting solutions from seed solutions with specific symmetries and equations of state, expanding the set of known solutions.

Contribution

It demonstrates how to generate twisting perfect fluid solutions using Stephani's method for seed solutions with particular symmetries and equations of state.

Findings

Generated new twisting solutions from simple seed solutions.

Extended solution space for Einstein-perfect fluid equations.

Maintained the same Killing vector and equation of state in new solutions.

Abstract

We apply a technique, due to Stephani, for generating solutions of the Einstein-perfect fluid equations. This technique is similar to the vacuum solution generating techniques of Ehlers, Harrison, Geroch and others. We start with a ``seed'' solution of the Einstein-perfect fluid equations with a Killing vector. The seed solution must either have (i) a spacelike Killing vector and equation of state P=rho or (ii) a timelike Killing vector and equation of state rho+3P=0. The new solution generated by this technique then has the same Killing vector and the same equation of state. We choose several simple seed solutions with these equations of state and where the Killing vector has no twist. The new solutions are twisting versions of the seed solutions.