A group theoretic approach to shear-free radiating stars

TL;DR

This paper employs Lie symmetry methods to analyze and solve the complex junction conditions in shear-free radiating stars, leading to new exact solutions and insights into relativistic astrophysical models.

Contribution

It introduces a group theoretic approach to transform nonlinear PDEs in stellar models into solvable ODEs, providing new exact solutions and connecting symmetries with physical properties.

Findings

Derived new exact solutions to the junction condition

Identified solutions satisfying linear barotropic equation of state

Recovered conformally flat models as special cases

Abstract

A systematic analysis of the junction condition, relating the radial pressure with the heat flow in a shear-free relativistic radiating star, is undertaken. This is a highly nonlinear partial differential equation in general. We obtain the Lie point symmetries that leave the boundary condition invariant. Using a linear combination of the symmetries, we transform the junction condition into ordinary differential equations. We present several new exact solutions to the junction condition. In each case we can identify the exact solution with a Lie point generator. Some of the solutions obtained satisfy the linear barotropic equation of state. As a special case we regain conformally flat models which were found previously. Our analysis highlights the interplay between Lie algebras, nonlinear differential equations and application to relativistic astrophysics.