Fate of Kaluza-Klein Bubble

TL;DR

This paper uses numerical simulations to study the evolution of Kaluza-Klein bubbles with negative energy, revealing potential naked singularities instead of eternal expansion.

Contribution

It provides the first numerical analysis of the time evolution of negative-energy Kaluza-Klein bubbles, challenging the expectation of eternal expansion.

Findings

Bubbles initially expand in area, similar to Witten's bubble.

Irregularities in the lapse function and divergence of the Kretschmann invariant observed.

No apparent horizon forms, suggesting possible naked singularity formation.

Abstract

We numerically study classical time evolutions of Kaluza-Klein bubble space-time which has negative energy after a decay of vacuum. As the zero energy Witten's bubble space-time, where the bubble expands infinitely, the subsequent evolutions of Brill and Horowitz's momentarily static initial data show that the bubble will expand in terms of the area. At first glance, this result may support Corley and Jacobson's conjecture that the bubble will expand forever as well as the Witten's bubble. The irregular signatures, however, can be seen in the behavior of the lapse function in the maximal slicing gauge and the divergence of the Kretchman invariant. Since there is no appearance of the apparent horizon, we suspect an appearance of a naked singularity as the final fate of this space-time.