Arbitrarily negative energy for small Kaluza-Klein bubbles

We show that the 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, indicating that the standard Kaluza-Klein vacuum is more unstable than previously thought.