Sources for the Majumdar-Papapetrou Space-Times

TL;DR

This paper presents exact solutions to Einstein's field equations for static charged dust distributions, generalizing Majumdar-Papapetrou metrics and revealing a direct relation between charge and mass densities.

Contribution

It introduces a nonlinear Poisson-like equation for static charged dust, extending the class of known solutions in Einstein-Maxwell theory.

Findings

Charge density equals mass density in solutions

Solutions generalize Majumdar-Papapetrou metrics

Einstein equations reduce to a nonlinear Poisson equation

Abstract

Einstein's field equations are solved exactly for static charged dust distributions. These solutions generalize the Majumdar Papapetrou metrics. Maxwell's equations lead to the equality of charge and mass densities of the dust distribution. Einstein's equatins reduce to a nonlinear version of Poisson's equation.