The Gravitational and Electrostatic Fields Far from an Isolated Einstein-Maxwell Source

TL;DR

This paper analyzes the exterior gravitational and electrostatic fields of a charged, massive source as a deviation from the Reissner-Nordström metric, deriving solutions and exploring special cases.

Contribution

It derives coupled differential equations for the potentials and provides explicit solutions, including a multipole expansion with hypergeometric functions, extending previous neutral source results.

Findings

Explicit solutions for coupled potentials are obtained.

A multipole expansion with hypergeometric dependence is derived.

Results recover known neutral case solutions.

Abstract

The exterior solution for an arbitrary charged, massive source, is studied as a static deviation from the Reissner-Nordstr\o m metric. This is reduced to two coupled ordinary differential equations for the gravitational and electrostatic potential functions. The homogeneous equations are explicitly solved in the particular case $q^2=m^2$, obtaining a multipole expansion with radial hypergeometric dependence for both potentials. In the limiting case of a neutral source, the equations are shown to coincide with recent results by Bondi and Rindler.