Remarks on a five-dimensional Kaluza-Klein theory of the massive Dirac monopole

TL;DR

This paper introduces a new five-dimensional vacuum solution in Kaluza-Klein theory that models massive magnetic monopoles, preserving key symmetries and affecting test particle motion.

Contribution

It presents a simple exact five-dimensional vacuum metric for massive monopoles with preserved isometries, extending the Gross-Perry-Sorkin solution.

Findings

New exact five-dimensional vacuum solution for massive monopoles

Preserves isometry properties of Euclidean Taub-NUT space

Analyzes scalar charged test particle motion with gravitational and magnetic effects

Abstract

The Gross-Perry-Sorkin spacetime, formed by the Euclidean Taub-NUT space with the time trivially added, is the appropriate background of the Dirac magnetic monopole without an explicit mass term. One remarks that there exists a very simple five-dimensional metric of spacetimes carrying massive magnetic monopoles that is an exact solution of the vacuum Einstein equations. Moreover, the same isometry properties as the original Euclidean Taub-NUT space are preserved. This leads to an Abelian Kaluza-Klein theory whose metric appears as a combinations between the Gross-Perry-Sorkin and Schwarzschild ones. The asymptotic motion of the scalar charged test particles is discussed, now by accounting for the mixing between the gravitational and magnetic effects.