Collapse of Kaluza-Klein Bubbles

TL;DR

This paper investigates the stability and evolution of Kaluza-Klein bubble configurations, revealing that negative energy bubbles tend to expand and are unlikely to collapse into singularities.

Contribution

It demonstrates that all negative energy Kaluza-Klein bubbles initially expand, providing insights into their stability and evolution, which was not previously understood.

Findings

Negative energy bubbles start expanding from time symmetry.

Positive energy bubbles can expand or contract initially.

Negative energy bubbles are unlikely to form naked singularities.

Abstract

Kaluza-Klein theory admits ``bubble" configurations, in which the circumference of the fifth dimension shrinks to zero on some compact surface. A three parameter family of such bubble initial data at a moment of time-symmetry (some including a magnetic field) has been found by Brill and Horowitz, generalizing the (zero-energy) ``Witten bubble" solution. Some of these data have negative total energy. We show here that all the negative energy bubble solutions start out expanding away from the moment of time symmetry, while the positive energy bubbles can start out either expanding or contracting. Thus it is unlikely that the negative energy bubbles would collapse and produce a naked singularity.