Generalized Euclidean stars with equation of state

TL;DR

This paper develops a generalized model of radiating relativistic stars using Lie symmetries, deriving solutions that include Euclidean stars as a special case and satisfy physical energy conditions.

Contribution

It introduces a group theoretic approach to find exact solutions for accelerating, expanding, and shearing star models with a linear equation of state, extending previous models.

Findings

Derived Lie symmetry generators for the junction condition.

Obtained explicit solutions for gravitational potentials.

Confirmed physical energy conditions are satisfied.

Abstract

We consider the general case of an accelerating, expanding and shearing model of a radiating relativistic star using Lie symmetries. We obtain the Lie symmetry generators that leave the equation for the junction condition invariant, and find the Lie algebra corresponding to the optimal system of the symmetries. The symmetries in the optimal system allow us to transform the boundary condition to ordinary differential equations. The various cases for which the resulting systems of equations can be solved are identified. For each of these cases the boundary condition is integrated and the gravitational potentials are found explicitly. A particular group invariant solution produces a class of models which contains Euclidean stars as a special case. Our generalized model satisfies a linear equation of state in general. We thus establish a group theoretic basis for our generalized model with an equation of state. By considering a particular example we show that the weak, dominant and strong energy conditions are satisfied.