Higher-dimensional Kaluza–Klein monopoles

Abstract

It is well known that the Kaluza–Klein monopole of Sorkin, Gross and Perry can be obtained from the Euclidean Taub–NUT solution with an extra compact fifth spatial dimension via Kaluza–Klein reduction. In this paper we consider Taub–NUT-like solutions of the vacuum Einstein field equations, with or without cosmological constant, in five dimensions and higher, and similarly perform Kaluza–Klein reductions to obtain new magnetic KK brane solutions in higher dimensions, as well as further sphere reductions to magnetic monopoles in four dimensions. In six dimensions we also employ spatial and timelike Hopf dualities to untwist the circle fibration characteristic to these spaces and obtain charged strings. A variation of these methods in ten dimensions leads to a non-uniform electric string in five dimensions.