Arbitrarily Negative Energy for Small Kaluza-Klein Bubbles

TL;DR

This paper demonstrates that the energy of small Kaluza-Klein bubbles can be arbitrarily negative, revealing greater instability of the Kaluza-Klein vacuum than previously understood.

Contribution

It provides explicit initial data showing unbounded negative energy for small Kaluza-Klein bubbles, challenging prior assumptions about their stability.

Findings

Energy is unbounded from below for Kaluza-Klein bubbles.

Small bubbles can have arbitrarily negative energy.

The Kaluza-Klein vacuum is more unstable than previously believed.

Abstract

We show that the ADM energy of a Kaluza-Klein bubble of nothing is unbounded from below even if the size of the circle at infinity and the size of the minimal sphere at the bubble are fixed. We demonstrate this by presenting a family of explicit time-symmetric initial data satisfying these boundary conditions with arbitrarily negative energy. In particular, this is true for very small bubbles, which indicates that the standard Kaluza-Klein vacuum is more unstable than previously thought.