# On the relationship between charge and mass in General Relativity

## TL;DR

This paper explores the connection between mass and charge in General Relativity by constructing 5D Einstein-Maxwell solutions, revealing how mass variations affect electric fields and charge, with results consistent with Coulomb's law at large distances.

## Contribution

It introduces explicit 5D Einstein-Maxwell solutions linking mass and charge, showing how mass changes influence electric fields and charge equivalence.

## Key findings

- Mass variations alter electric field strength.
- Different masses can produce identical electric fields.
- Large-distance behavior matches Coulomb's law.

## Abstract

This paper demonstrates a relationship between mass and charge through explicit construction of exact Einstein-Maxwell spacetimes by embedding the Schwarzschild and Kerr instantons in 5 dimensions. It is shown further how by varying only the mass of an object, its electric field or apparent "charge" changes, while making it possible for two different mass values to yield the same electric field strength. The 5-dimensional solution, however, reduces to the familiar Coulomb limit $1/r^2$ for large distances.