Phases of non-extremal multi-centered bound states

We investigate the phase space of multi-centered near-extremal configurations previously studied in arXiv:1108.5821 and arXiv:1110.5641 in the probe limit. We confirm that in general the energetically favored ground state of the multi-center potential, which can be a single or multi-center configuration, has the most entropy and is thus thermodynamically stable. However, we find the surprising result that for a subset of configurations, even though a single center black hole seems to be energetically favored, it is entropically not allowed (the resulting black hole would violate cosmic censorship). This disproves classical intuition that everything would just fall into the black hole if energetically favored. Along the way we highlight a shortcoming in the literature regarding the computation of the angular momentum coming from electromagnetic interaction in the probe limit and rectify it. We also demonstrate that static supertubes can exist inside ergoregions where ordinary point particles would be frame dragged.