Radiating stars with exponential Lie symmetries

TL;DR

This paper applies Lie symmetry analysis to a nonlinear PDE in general relativity, deriving new exact solutions for radiating star models with exponential symmetry properties, extending previous models and including special cases.

Contribution

It introduces new Lie symmetry solutions for radiating star models, expanding the set of known exact solutions and generalizing earlier Euclidean star models.

Findings

New exponential Lie symmetry solutions for gravitational potentials

Derivation of exact solutions to the boundary Riccati equation

Recovery of Euclidean star models as special cases

Abstract

We analyze the general model of a radiating star in general relativity. A group analysis of the under determined, nonlinear partial differential equation governing the model's gravitational potentials is performed. This analysis is an extension of previous group analyses carried out and produces new group invariant solutions. We find that the gravitational potentials depend on exponential functions owing to the choice of the Lie symmetry generator. The fundamental boundary equation to be solved is in general a Riccati equation. Several new exact families of solutions to the boundary condition are generated. Earlier models of Euclidean stars and generalized Euclidean stellar models are regained as special cases. Linear equations of state can be found for shear-free and shearing spacetimes.