Wormholes and Flux Tubes in 5D Kaluza-Klein Theory

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 $G_{5ϕ}$ 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.