New charged shear-free relativistic models with heat flux

TL;DR

This paper develops new exact solutions for charged, shear-free relativistic fluids with heat flux, expanding the class of models in general relativity by applying Lie symmetry methods to the Einstein-Maxwell equations.

Contribution

The authors derive new charged shear-free relativistic models with heat flux using Lie symmetry analysis, extending previous uncharged solutions and introducing a systematic way to generate charged models.

Findings

Found Lie symmetry generators for the Einstein-Maxwell system.

Derived exact solutions including charge effects.

Generated new classes of charged Deng models.

Abstract

We study shear-free spherically symmetric relativistic gravitating fluids with heat flow and electric charge. The solution to the Einstein-Maxwell system is governed by the generalised pressure isotropy condition which contains a contribution from the electric field. This condition is a highly nonlinear partial differential equation. We analyse this master equation using Lie's group theoretic approach. The Lie symmetry generators that leave the equation invariant are found. The first generator is independent of the electromagnetic field. The second generator depends critically on the form of the charge, which is determined explicitly in general. We provide exact solutions to the gravitational potentials using the symmetries admitted by the equation. Our new exact solutions contain earlier results without charge. We show that other charged solutions, related to the Lie symmetries, may be generated using the algorithm of Deng. This leads to new classes of charged Deng models which are generalisations of conformally flat metrics.