Kaluza-Klein Monopole

Abstract

By adding the trivial term $\ensuremath{-}d{t}^{2}$ one can convert the four-dimensional (positive-definite) Newman-Unti-Tamburino line element into a static solution of the five-dimensional vacuum Einstein equations. Interpreted $\stackrel{`}{a}\mathrm{la}$ Kaluza and Klein, the solution describes a monopole with a charge-to-mass ratio of $\sqrt{2}$ in rationalized Planck units. Although it is a perfectly regular five-geometry it appears singular from a four-dimensional perspective.