Point Electric Charge in General Relativity

TL;DR

This paper derives new static spherically symmetric solutions to Einstein-Maxwell equations with a charged point source, revealing regularized potentials and topological corrections to Gauss's law in general relativity.

Contribution

It introduces a three-parameter family of solutions incorporating charge and mass, with regularized potentials and a novel correction to Gauss's theorem due to spacetime topology.

Findings

Solutions depend on mass, charge, and bare mass parameters.

Potential corrections are regular at the center of the point source.

A topological correction to Gauss's theorem is established.

Abstract

Using a proper gauge condition the static spherically symmetric solutions of Einstein-Maxwell equations with charged point source at the center are derived. It is shown that the solutions of the field equations are a three-parameter family depending on the Keplerian mass $M$, the charge $Q$ and the bare mass $M_0$. The result can be interpreted as a correction to Newton's gravitational potential and Coulomb's electric potential which are both regular at the centre where the massive point is placed. A correction to Gauss theorem is derived based on the nontrivial topology of the corresponding spacetime.