Black ringoids: spinning balanced black objects in d ≥ 5 dimensions — the codimension-two case

We propose a general framework for the study of asymptotically flat black objects with k + 1 equal magnitude angular momenta in d ≥ 5 spacetime dimensions (with 0 ≤ k ≤ d − 5 2 $$ 0\le k\le \left[\frac{d-5}{2}\right] $$ ). In this approach, the dependence on all angular coordinates but one is factorized, which leads to a codimension-two problem. This framework can describe black holes with spherical horizon topology, the simplest solutions corresponding to a class of Myers-Perry black holes. A different set of solutions describes balanced black objects with S n +1 × S 2 k +1 horizon topology. The simplest members of this family are the black rings ( k = 0). The solutions with k > 0 are dubbed black ringoids . Based on the nonperturbative numerical results found for several values of ( n, k ), we propose a general picture for the properties and the phase diagram of these solutions and the associated black holes with spherical horizon topology: n = 1 black ringoids repeat the k = 0 pattern of black rings and Myers-Perry black holes in 5 dimensions, whereas n > 1 black ringoids follow the pattern of higher dimensional black rings associated with ‘pinched’ black holes and Myers-Perry black holes