The Deng algorithm in higher dimensions

TL;DR

This paper generalizes Deng's algorithm to higher-dimensional spherically symmetric spacetimes, enabling the generation of exact solutions to Einstein's equations for shear-free cosmological models with heat flow, and verifies their physical plausibility.

Contribution

It extends Deng's algorithm to higher dimensions, providing a method to find exact solutions for shear-free heat-flow cosmological models in higher-dimensional gravity.

Findings

Identified three new higher-dimensional metrics including four-dimensional cases

Matter variables are well-behaved in the solutions

Speed of sound remains causal in the models

Abstract

We extend an algorithm of Deng in spherically symmetric spacetimes to higher dimensions. We show that it is possible to integrate the generalised condition of pressure isotropy and generate exact solutions to the Einstein field equations for a shear-free cosmological model with heat flow in higher dimensions. Three new metrics are identified which contain results of four dimensions as special cases. We show graphically that the matter variables are well behaved and the speed of sound is causal.