Black ringoids: spinning balanced black objects in $d\geq 5$ dimensions -- the codimension-two case

TL;DR

This paper introduces a unified framework for studying asymptotically flat black objects with multiple angular momenta in higher dimensions, revealing new solutions called black ringoids and analyzing their phase diagram.

Contribution

It develops a codimension-two approach to describe black objects with various horizon topologies, including new black ringoid solutions, and provides a comprehensive phase diagram based on numerical results.

Findings

Black ringoids generalize black rings to higher dimensions.

The phase diagram shows distinct patterns for different horizon topologies.

Numerical results support the proposed classification and properties of solutions.

Abstract

We propose a general framework for the study of asymptotically flat black objects with $k+1$ equal magnitude angular momenta in $d\geq 5$ spacetime dimensions (with $0\leq k\leq \big[\frac{d-5}{2} \big]$). 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 $S^{n+1} \times S^{2k+1}$ 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.