Bubbles in Kaluza-Klein theories with spacelike or timelike internal dimensions

Abstract

Bubbles are pointlike regular solutions of the higher-dimensional Kaluza-Klein equations that appear as naked singularities in four dimensions. We analyze all such possible solutions in five-dimensional (5D) Kaluza-Klein theory that are static and spherically symmetric. We show that they can be obtained by taking unusual choices of the parameters in the dyonic black hole solutions, and find that regularity can only be achieved if their electric charge is zero. However, they can be neutral or possess magnetic charge. We study some of their properties, both in theories where the internal dimension is spacelike as well as timelike. Since bubbles do not have horizons, they have no entropy, nor do they emit any thermal radiation, but they are, in general, nonextremal objects. In the two-timing case, it is remarkable that nonsingular massless monopoles are possible, probably signaling a new pathology of these theories. These two-timing monopoles connect two asymptotically flat regions, and matter can flow from one region to the other. We also present a $C$-type solution that describes neutral bubbles in uniform acceleration, and we use it to construct an instanton that mediates the breaking of a cosmic string by forming bubbles at its ends. The rate for this process is also calculated. Finally, we argue that a similar solution can be constructed for magnetic bubbles, and that it can be used to describe a semiclassical instability of the two-timing vacuum against production of massless monopole pairs.