A six dimensional analysis of Maxwell's Field Equations

TL;DR

This paper extends Kaluza's five-dimensional unification to a six-dimensional framework, deriving Maxwell's equations solely from Einstein's field equations, and naturally incorporating magnetic monopoles.

Contribution

It introduces a six-dimensional model that unifies electromagnetism with gravity and derives Maxwell's equations from Einstein's equations alone, including magnetic monopoles.

Findings

Unified derivation of Maxwell's equations from Einstein's field equations.

Symmetric wave equations for potentials.

Natural inclusion of magnetic monopoles without singularities.

Abstract

A framework based on an extension of Kaluza's original idea of using a five dimensional space to unify gravity with electromagnetism is used to analyze Maxwell\'{}s field equations. The extension consists in the use of a six dimensional space in which all equations of electromagnetism may be obtained using only Einstein's field equation. Two major advantages of this approach to electromagnetism are discussed, a full symmetric derivation for the wave equations for the potentials and a natural inclusion of magnetic monopoles without using any argument based on singularities.