Do supersymmetric anti-de Sitter black rings exist?

TL;DR

This paper proves that regular supersymmetric anti-de Sitter black rings with two rotational symmetries do not exist in minimal supergravity, but hints at possible existence of nonsupersymmetric black rings with conical singularities.

Contribution

It classifies the near-horizon geometries of supersymmetric AdS black holes and rules out the existence of supersymmetric black rings with two rotational symmetries in minimal supergravity.

Findings

Supersymmetric AdS black rings with two rotational symmetries do not exist.

A near-horizon geometry solution with a conical singularity suggests possible nonsupersymmetric black rings.

The classification confirms the uniqueness of the known supersymmetric spherical black hole solutions.

Abstract

We determine the most general near-horizon geometry of a supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional minimal gauged supergravity that admits two rotational symmetries. The near-horizon geometry is that of the supersymmetric, topologically spherical, black hole solution of Chong et al. This proves that regular supersymmetric anti-de Sitter black rings with two rotational symmetries do not exist in minimal supergravity. However, we do find a solution corresponding to the near-horizon geometry of a supersymmetric black ring held in equilibrium by a conical singularity, which suggests that nonsupersymmetric anti-de Sitter black rings may exist but cannot be "balanced" in the supersymmetric limit.