Bubbles in Kaluza-Klein theories with space- or time-like internal dimensions

TL;DR

This paper classifies and analyzes bubble solutions in 5D Kaluza-Klein theories with space- or time-like internal dimensions, revealing their properties, stability, and potential instabilities related to monopoles and cosmic strings.

Contribution

It provides a comprehensive analysis of static, spherically symmetric bubbles in 5D Kaluza-Klein theory, including their regularity conditions, properties, and implications for vacuum stability.

Findings

Regular bubbles can only be neutral or magnetically charged.

Non-singular massless monopoles exist in two-timing theories, indicating possible new pathologies.

Constructed instantons describe bubble formation at cosmic string ends.

Abstract

Bubbles are point-like regular solutions of the higher-dimensional Kaluza-Klein equations that appear as naked singularities in four dimensions. We analyze all such possible solutions in 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 space-like as well as time-like. Since bubbles do not have horizons, they have no entropy, nor do they emit any thermal radiation, but they are, in general, non-extremal objects. In the two-timing case, it is remarkable that non-singular 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.