Black Rings in (Anti)-deSitter space

TL;DR

This work develops an approximate, yet powerful, framework to construct thin black rings in Anti-deSitter and deSitter spaces by bending boosted black strings, revealing that AdS rings can have arbitrarily large radii and obey a BPS-like bound $|J|\leq ML$ that is saturated for long rings. It systematically derives the equilibrium conditions, computes thermodynamic quantities, and compares rings to rotating AdS black holes, showing rings can outperform black holes in horizon area near maximal spin, especially in higher dimensions. The analysis extends to black Saturns, explores the existence (or absence) of large AdS rings and their potential fluid-dual descriptions, and argues against supersymmetric AdS rings due to pressure balance constraints. The results illuminate phase connections between ring and hole solutions, discuss stability via Gregory-Laflamme-type instabilities, and outline implications for holographic hydrodynamics and broader backgrounds.

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| \leq 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.

Figures (6)

• Figure 1: Plots in five dimensions of ${\textsf{A}_\textsf{H}}({\textsf{J}})$ for fixed ${\textsf{M}}$, at small ${\textsf{M}}$ (left) and large ${\textsf{M}}$ (right). Thin lines correspond to rotating AdS black holes, thick lines to black rings. The thick solid line continues to a thick dashed line when the thin-ring approximation $r_0\ll R/\sqrt{1+{\textsf{R}}^2}$ breaks down (here and in the next figures the solid-dashed divide is arbitrarily taken at $r_0=\frac{R}{5\sqrt{1+{\textsf{R}}^2}}$ and the dashed line is extended up to $r_0= \frac{R}{2\sqrt{1+{\textsf{R}}^2}}$). The spin of black rings reaches up to the BPS bound ${\textsf{J}}={\textsf{M}}$, but the spin of rotating AdS black holes is bounded by ${\textsf{J}}\leq {\textsf{J}}_{max}({\textsf{M}})<{\textsf{M}}$, eq. \ref{['jmax5d']}. For small ${\textsf{M}}$, and ${\textsf{J}}$ not too close to ${\textsf{M}}$, the curves are very similar to the asymptotically flat case.
• Figure 2: Plots in seven dimensions of ${\textsf{A}_\textsf{H}}({\textsf{J}})$ for fixed ${\textsf{M}}$, at small ${\textsf{M}}$ (left) and large ${\textsf{M}}$ (right). Thin lines correspond to rotating AdS black holes, thick lines to black rings (dashed line when the thin-ring approximation breaks down). Both rotating AdS black holes and black rings extend up to the BPS bound ${\textsf{J}}={\textsf{M}}$, but black rings have larger area near the maximum ${\textsf{J}}$. The asymptotic curves near this point are \ref{['amaxjr']} and \ref{['amaxjh']}.
• Figure 3: Proposal for the completion of phase curves at small ${\textsf{M}}$ in $d\geq 6$ (the situation in $d=5$ is a simple adaptation of the same idea). The patterns proposed in Emparan:2007wm are compressed here to the range ${\textsf{J}}\leq {\textsf{M}}$. We stress that the details of the connections ( e.g., first order vs. second order transitions) remain unknown and are arbitrarily drawn.
• Figure 4: Two alternatives for the completion of phase curves at ${\textsf{M}}\gg 1$. The gray-shaded area, which extends from ${\textsf{J}} \sim {\textsf{J}}_c$ where $({\textsf{M}}-{\textsf{J}}_c)/{\textsf{M}}\sim {\textsf{M}}^{-1/2}$, to the upper limit ${\textsf{J}}={\textsf{M}}$, corresponds to solutions that do not qualify as large AdS black holes or rings. In the left picture, no large AdS black rings exist. In the right picture, thin large AdS black rings, with $L<r_0\ll R$ exist. This second alternative requires an explanation of why these black rings do not appear in dual hydrodynamic studies.
• Figure 5: Boundaries of the phase space $({\textsf{J}}_{\phi},{\textsf{J}}_{\psi},{\textsf{M}})$ covered by doubly spinning rotating AdS black holes in five (a) and six (b) dimensions. The mass increases along the vertical axis. The surfaces correspond to extremal, zero-temperature black holes, except at the edges where they become naked singularities. The interior of the pyramids is filled by non-extremal black holes.