New shear-free relativistic models with heat flow

TL;DR

This paper develops a method using Lie group theory to generate infinite families of new shear-free relativistic models with heat flow, expanding the solution space of Einstein's equations.

Contribution

It introduces a five-parameter transformation family that maps existing solutions to new ones, including two novel classes of solutions derived from Lie infinitesimal generators.

Findings

Generated infinite solution families from known solutions.

Developed two new classes of shear-free heat flow models.

Provided a systematic Lie group approach to Einstein equations.

Abstract

We study shear-free spherically symmetric relativistic models with heat flow. Our analysis is based on Lie's theory of extended groups applied to the governing field equations. In particular, we generate a five-parameter family of transformations which enables us to map existing solutions to new solutions. All known solutions of Einstein equations with heat flow can therefore produce infinite families of new solutions. In addition, we provide two new classes of solutions utilising the Lie infinitesimal generators. These solutions generate an infinite class of solutions given any one of the two unknown metric functions.