5-Dimensional Kaluza-Klein Theory with a Source

TL;DR

This paper demonstrates how a 5-dimensional dust field in Kaluza-Klein theory can generate electromagnetic fields in 4D after dimensional reduction, linking matter and electromagnetism geometrically.

Contribution

It introduces a model where 5D dust acts as a source for electromagnetic fields in 4D Kaluza-Klein theory, providing a geometric unification of matter and electromagnetism.

Findings

Dust field curves 5D spacetime to produce electromagnetic source.

Dimensional reduction yields electromagnetic fields from 5D matter.

Model offers a geometric explanation for electromagnetic sources.

Abstract

A free test particle in 5-dimensional Kaluza-Klein spacetime will show its electricity in the reduced 4-dimensional spacetime when it moves along the fifth dimension. In the light of this observation, we study the coupling of a 5-dimensional dust field with the Kaluza-Klein gravity. It turns out that the dust field can curve the 5-dimensional spacetime in such a way that it provides exactly the source of the electromagnetic field in the 4-dimensional spacetime after the dimensional reduction.