Applications of Lie Symmetries to Higher Dimensional Gravitating Fluid

TL;DR

This paper systematically applies Lie symmetry methods to find new solutions of Einstein's equations for higher-dimensional radiating shear-free spherically symmetric spacetimes, generalizing previous four-dimensional results.

Contribution

It introduces a Lie symmetry-based approach to derive new solutions in higher dimensions, extending known four-dimensional solutions and revealing infinite families of solutions.

Findings

Found new solutions using Lie symmetries

Reduced equations to Riccati form

Generalized four-dimensional results to higher dimensions

Abstract

We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein's equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie point symmetries of the fundamental field equation, we obtain either an implicit solution or we can reduce the governing equations to a Riccati equation. We show that known solutions of the Einstein equations can produce infinite families of new solutions. Earlier results in four dimensions are shown to be special cases of our generalised results.