On Witten's Instability and Winding Tachyons

We investigate, from a spacetime perspective, some aspects of Horowitz's recent conjecture that black strings may catalyze the decay of Kaluza-Klein spacetimes into a bubble of nothing. We identify classical configurations that interpolate between flat space and the bubble, and discuss the energetics of the transition. We investigate the effects of winding tachyons on the size and shape of the barrier and find no evidence at large compactification radius that tachyons enhance the tunneling rate. For the interesting radii, of order the string scale, the question is difficult to answer due to the failure of the $\alpha^\prime$ expansion.