Do supersymmetric anti-de Sitter black rings exist?
Hari K. Kunduri, James Lucietti, Harvey S. Reall
TL;DR
The paper classifies supersymmetric near-horizon geometries of asymptotically AdS5 black holes in minimal gauged supergravity with two commuting rotations. Using a Gaussian null coordinate framework and symmetry reductions, the authors derive the full set of constraints and solve them, obtaining a non-static family (NHmetricA) governed by a cubic polynomial and showing that, globally, the only regular near-horizon geometry compatible with two U(1) symmetries matches Chong et al.’s topologically spherical solution. A distinct conical-singularity solution corresponds to an unbalanced AdS ring, indicating the possible existence of nonsupersymmetric AdS rings or rings that require external forces to balance in the SUSY limit. The analysis rules out regular two-parameter supersymmetric AdS black rings with two rotational symmetries and highlights the role of conical defects in stabilizing ring-like near-horizons, with implications for uplift to higher dimensions and for uniqueness or existence questions in gauged supergravity. Future work could relax symmetry assumptions or include vector multiplets to explore broader classes of AdS black holes and rings.
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.