Lie symmetries for a conformally flat radiating star

TL;DR

This paper applies Lie symmetry analysis to a nonlinear PDE governing a radiating star in conformally flat spacetime, deriving exact solutions and classifying them based on symmetry reductions.

Contribution

It identifies Lie symmetries of the boundary condition PDE and generates new exact solutions for radiating stars in conformally flat spacetimes.

Findings

Derived new classes of exact solutions for the boundary PDE.

Reduced the PDE to ODEs using symmetry methods.

Classified solutions into self-similar and separable types.

Abstract

We consider a relativistic radiating spherical star in conformally flat spacetimes. In particular we study the junction condition relating the radial pressure to the heat flux at the boundary of the star which is a nonlinear partial differential equation. The Lie symmetry generators that leave the equation invariant are identified and we generate an optimal system. Each element of the optimal system is used to reduce the partial differential equation to an ordinary differential equation which is further analysed. We identify new categories of exact solutions to the boundary conditions. Two classes of solutions are of interest. The first class depends on a self similar variable. The second class is separable in the spacetime variables.