A fifth order differential equation for charged perfect fluids

TL;DR

This paper derives and analyzes a novel fifth order differential equation governing shear-free spherically symmetric charged fluids, using Lie symmetry methods to reduce it to quadratures and unify previous results.

Contribution

It introduces a new fifth order differential equation for charged fluids and applies Lie symmetry analysis to systematically reduce and solve it.

Findings

Derived a fifth order differential equation for charged fluids.

Reduced the equation to quadratures using Lie symmetry analysis.

Unified earlier results within a general framework.

Abstract

We investigate the master nonlinear partial differential equation that governs the evolution of shear-free spherically symmetric charged fluids. We use an approach which has not been considered previously for the underlying equation in shear-free spherically symmetric spacetimes. We derive a fifth order purely differential equation that must be satisfied for the underlying equation to admit a Lie point symmetry. We then perform a comprehensive analysis of this equation utilising the Lie symmetry analysis and direct integration. This enables us to reduce the fifth order equation to quadratures. Earlier results are shown to be contained in our general treatment.