Black rings in global anti-de Sitter space

TL;DR

This paper constructs and analyzes five-dimensional black rings in global anti-de Sitter space, revealing their geometric properties, stability issues, and thermodynamic behavior, with implications for dual conformal field theories.

Contribution

The paper presents the first numerical construction of AdS black rings, exploring their geometry, stability bounds, and thermodynamics, including novel membrane-like horizon structures.

Findings

Black rings satisfy the BPS bound but violate the Hawking-Reall bound, indicating potential superradiant instability.

At high temperatures, thin rings approach the superradiant limit with large radii.

At low temperatures, new membrane-like rings emerge with non-proportional hole and outer circle sizes.

Abstract

We construct five dimensional black rings in global anti-de Sitter space using numerical methods. These rings satisfy the BPS bound $| J | < M \ell$, but the angular velocity always violates the Hawking-Reall bound $| \Omega_H \ell | \leq 1$, indicating that they should be unstable under superradiance. At high temperatures, the limit $| \Omega_H \ell | \searrow 1$ is attained by thin rings with an arbitrarily large radius. However, at sufficiently low temperatures, this limit is saturated by a new kind of rings, whose outer circle can still be arbitrarily long while the hole in the middle does not grow proportionally. This gives rise to a membrane-like horizon geometry, which does not have an asymptotically flat counterpart. We find no evidence for thin AdS black rings whose transverse $S^2$ is much larger than the radius of AdS, $\ell$, and thus these solutions never fall into the hydrodynamic regime of the dual CFT. Thermodynamically, we find that AdS black rings never dominate the grand canonical ensemble. The behaviour of our solutions in the microcanonical ensemble approaches known perturbative results in the thin-ring limit.