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

The Gross-Perry-Sorkin spacetime, formed by the Euclidean Taub-Newman-Unti-Tamburino space with the time trivially added, is the appropriate background of the Dirac magnetic monopole without an explicit mass term. We show 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-Newman-Unti-Tamburino space are preserved. This leads to an Abelian Kaluza-Klein theory whose metric appears as a combination 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.