Lie symmetry approach to the time-dependent Karmarkar condition

TL;DR

This paper applies Lie symmetry methods to find solutions of the time-dependent Einstein Field Equations satisfying the Karmarkar condition, leading to new models of radiating stars and potential cosmological applications.

Contribution

First application of Lie symmetry techniques to generate solutions satisfying the Karmarkar condition in dynamic spacetimes, including radiating stellar models.

Findings

Derived a radiating stellar model satisfying heat-flux boundary conditions.

Generated solutions that may be useful for cosmological models.

Highlighted the viability of Lie symmetry methods in this context.

Abstract

We obtain solutions of the time-dependent Einstein Field Equations which satisfy the Karmarkar condition via the method of Lie symmetries. Spherically symmetric spacetime metrics are used with metric functions set to impose conformal flatness, Weyl-free collapse and shear-free collapse. In particular, a solution was found which satisfies the heat-flux boundary condition of Santos, and a radiating stellar model was then obtained and investigated. Solutions obtained which do not allow for the application of the junction conditions at a boundary surface may lend themselves to cosmological models. This is a first attempt in generating solutions satisfying the Karmarkar condition via the method of Lie symmetries and our example of a radiating model highlights the viability of this method.