First integrals for charged perfect fluid distributions

TL;DR

This paper introduces a new class of solutions for charged, shear-free, spherically symmetric fluids in general relativity, extending previous neutral fluid models and providing explicit integrals for charged cases.

Contribution

It presents a novel parametric class of solutions to Einstein-Maxwell equations, generalizing earlier neutral fluid results and deriving explicit integrals for charged fluids.

Findings

New parametric solutions to Einstein-Maxwell system

Generalization of uncharged fluid integrals

Explicit first integral for charged fluids

Abstract

We study the evolution of shear-free spherically symmetric charged fluids in general relativity. We find a new parametric class of solutions to the Einstein-Maxwell system of field equations. Our charged results are a generalisation of earlier treatments for neutral relativistic fluids. We regain the first integrals found previously for uncharged matter as a special case. In addition an explicit first integral is found which is necessarily charged.