Non-linear Electrodynamics derived from the Kaluza-Klein Theory

TL;DR

This paper derives a non-linear extension of Maxwell's equations from five-dimensional Kaluza-Klein theory, incorporating the quadratic Gauss-Bonnet invariant, and explores static solutions and their qualitative behavior.

Contribution

It introduces a novel non-linear electrodynamics framework derived from Kaluza-Klein theory including the Gauss-Bonnet term, expanding the theoretical landscape.

Findings

Derived non-linear equations generalizing Maxwell's system

Presented the possibility of static solutions

Discussed the qualitative behavior of these solutions

Abstract

The lagrangian of the Kaluza-Klein theory, in its simplest five-dimensional version, should include not only the scalar curvature R, but also the quadratic Gauss-Bonnet invariant. The general lagrangian is computed and the resulting non-linear equations which generalize Maxwell's system in a quite unique way are investigated. The possibility of the existence of static solutions is presented, and the qualitative behaviour of such solutions is discussed.