Fate of the Kaluza-Klein bubble

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 bubble space-time, where the bubble expands infinitely, the subsequent evolutions of the Brill-Horowitz momentarily static initial data show that the bubble will expand in terms of the area. At first glance, this result may support the Corley-Jacobson conjecture that the bubble will expand forever as well as 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 the appearance of a naked singularity as the final fate of this space-time.