Wormholes and Flux Tubes in 5D Kaluza-Klein Theory

TL;DR

This paper explores spherically symmetric solutions in 5D Kaluza-Klein theory, revealing how electric and magnetic field interactions shape wormhole-like structures and flux tubes, with implications for exotic matter and confinement phenomena.

Contribution

It demonstrates how varying electric and magnetic fields in 5D Kaluza-Klein theory produce wormholes and flux tubes, connecting higher-dimensional gravity to particle physics concepts.

Findings

Small magnetic fields produce wormhole-like solutions.

Increasing magnetic fields lead to flux tubes similar to QCD flux tubes.

Large electric fields may form wormhole mouths with exotic matter sources.

Abstract

In this paper spherically symmetric solutions to 5D Kaluza-Klein theory, with ``electric'' and/or ``magnetic'' fields are investigated. It is shown that the global structure of the spacetime depends on the relation between the ``electrical'' and ``magnetic'' Kaluza-Klein fields. For small ``magnetic'' field we find a wormhole-like solution. As the strength of the ``magnetic'' field is increased relative to the strength of the ``electrical'' field, the wormhole-like solution evolves into a finite or infinite flux tube depending on the strengths of the two fields. For the large ``electric'' field case we conjecture that this solution can be considered as the mouth of a wormhole, with the $G_{55}$, $G_{5t}$ and $G_{5\phi}$ components of the metric acting as the source of the exotic matter necessary for the formation of the wormhole's mouth. For the large ``magnetic'' field case a 5D flux tube forms, which is similar to the flux tube between two monopoles in Type-II superconductors, or the hypothesized color field flux tube between two quarks in the QCD vacuum.