Small black hole explosions

A bstract Small black holes are a powerful tool to explore infinite distances in moduli spaces. However, we show that 4d theories with scalar potential growing fast enough at infinity, it is energetically too costly for scalars diverge the core, and small hole puffs up into regular hole, or follows runaway behaviour. We derive critical exponent characterizing occurrence not of such explosions, both from perspective, 2d theory after an S 2 truncation. The latter setup allows unified discussion fluxes, domain walls holes, solving apparent puzzle expression their potentials $$ \mathcal{N} N = gauged supergravity context. discuss realization these ideas supergravities. Along way many solutions literature context incomplete, due Freed-Witten anomalies (or duals thereof), require emission strings by hole. From correspond dynamical cobordisms, core describing end world brane. explosions represent obstructions completing cobordism. study implications Cobordism Distance Conjecture, which states any there should exist cobordisms accessing all possible distance limits field space. this principle using leads non-trivial constraints on consistent theory; context, they allow recover purely bottom-up several properties vector spaces near infinity familiar CY 3 compactifications.