Abstract
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 $$ 0\le k\le \left[\frac{d-5}{2}\right] $$ ). 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 2k+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.
Highlights
The physics of the black hole event horizon has proven a fruitful field of research in gravitational physics
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
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
Summary
The physics of the black hole event horizon has proven a fruitful field of research in gravitational physics. The main purpose of this paper is to present a general nonperturbative framework capable to describe a class of balanced black object with Sn+1 × S2k+1 horizon topology, in d ≥ 5 spacetime dimensions, d = 2k + n + 4, with n ≥ 1 In this case, the rotation provides a centrifugal repulsion that allows regular solutions to exist. Numerical results are reported for the simplest case d = 7, k = 1 Apart from these black objects with a non-spherical horizon topology, the proposed framework can describe a class of MP black holes, whose properties we review in this work..
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