The phase structure of higher-dimensional black rings and black holes

Abstract

We construct an approximate solution for an asymptotically flat, neutral, thin rotating black ring in any dimension D ⩾ 5 by matching the near-horizon solution for a bent boosted black string, to a linearized gravity solution away from the horizon. The rotating black ring solution has a regular horizon of topology S1 × SD−3 and incorporates the balancing condition of the ring as a zero-tension condition. For D = 5 our method reproduces the thin ring limit of the exact black ring solution. For D ⩾ 6 we show that the black ring has a higher entropy than the Myers-Perry black hole in the ultra-spinning regime. By exploiting the correspondence between ultra-spinning black holes and black membranes on a two-torus, we take steps towards qualitatively completing the phase diagram of rotating blackfolds with a single angular momentum. We are led to propose a connection between MP black holes and black rings, and between MP black holes and black Saturns, through merger transitions involving two kinds of `pinched' black holes. More generally, the analogy suggests an infinite number of pinched black holes of spherical topology leading to a complicated pattern of connections and mergers between phases.