Black rings in (Anti)-de Sitter space

Abstract

We construct solutions for thin black rings in Anti-deSitter and deSitter spacetimes using approximate methods. Black rings in AdS exist with arbitrarily large radius and satisfy a bound |J| ≤ LM , which they saturate as their radius becomes infinitely large. For angular momentum near the maximum, they have larger area than rotating AdS black holes. Thin black rings also exist in deSitter space, with rotation velocities varying between zero and a maximum, and with a radius that is always strictly below the Hubble radius. Our general analysis allows us to include black Saturns as well, which we discuss briefly. We present a simple physical argument why supersymmetric AdS black rings must not be expected: they do not possess the necessary pressure to balance the AdS potential. We discuss the possible existence or absence of 'large AdS black rings' and their implications for a dual hydrodynamic description. An analysis of the physical properties of rotating AdS black holes is also included.

Blackfolds, plane waves and minimal surfaces

“…Therefore one obtains the requirement 28) which justifies the arguments used in [11,27]. If we focus on minimal surfaces, which by definition satisfy condition (2.4) then of the six invariants involved in (2.26) only five are non-trivial.…”

“…It would be interesting to study this for more non-trivial embeddings of the black ring as in appendix D.1 using the methods of [27,41] and to use numerical methods as in [14][15][16][17] in order to construct the full solution.…”

A general black string and its microscopics

“…It was speculated that supersymmetry is presumably incompatible with this pressure, and so, in AdS we should not expect supersymmetric black rings. However, the three parameter supersymmetric black string of [22] invalidates the argument made in [49]. The supersymmetric black string of [22] can have non-zero pressure (see (4.15)), so one can indeed balance it in AdS by curving it into a contractible circle.…”

“…The analysis of [47,48] shows that there is no smooth near-horizon geometry that describes a supersymmetric black ring in AdS -the near horizon geometry of a supersymmetric black ring in AdS necessarily possesses a conical singularity. In [49] a more physical argument was presented for the absence of supersymmetric black rings in AdS. It was based on the observation that the AdS potential requires pressure along the one-brane in order to achieve mechanical equilibrium when the onebrane is curved into a contractible circle in AdS.…”

“…The extremal strings of [22] and more generally our general string provide requisite candidate strings that might correspond to the infinite radius limit of some (non-)extremal black rings in AdS. A detailed perturbative study following [46,49] is left for the future.…”