Higher dimensional charged shear-free relativistic models with heat flux

TL;DR

This paper develops higher-dimensional shear-free relativistic models with heat flux and electric charge, solving Einstein-Maxwell equations using Lie symmetries, and explores their physical properties including temperature behavior.

Contribution

It introduces exact solutions for higher-dimensional charged shear-free models using Lie symmetry methods, extending previous four-dimensional results and analyzing temperature effects.

Findings

Derived new exact solutions for higher-dimensional models.

Extended previous four-dimensional solutions to higher dimensions.

Analyzed temperature profiles and their dependence on spacetime dimension.

Abstract

We analyse shear-free spherically symmetric relativistic models of gravitating fluids with heat flow and electric charge defined on higher dimensional manifolds. The solution to the Einstein-Maxwell system is governed by the pressure isotropy condition which depends on the spacetime dimension. We study this highly nonlinear partial differential equation using Lie's group theoretic approach. The Lie symmetry generators that leave the equation invariant are determined. We provide exact solutions to the gravitational potentials using the first symmetry admitted by the equation. Our new exact solutions contain the earlier results for the four-dimensional case. Using the other Lie generators, we are able to provide solutions to the gravitational potentials or reduce the order of the master equation to a first order nonlinear differential equation. We derive the temperature transport equation in higher dimensions and find expressions for the causal and Eckart temperatures showing their explicit dependance on the dimension. We analyse a particular solution, obtained via group techniques, to show its physical applicability.