Large rotating AdS black holes from fluid mechanics

TL;DR

This work establishes and tests a fluid-gravity duality for large rotating black holes in global AdS spaces: such black holes are dual to stationary conformal fluids on spheres $S^{d-1}$, with the fluid equation of state extracted from static AdS black holes. By solving the conformal Navier–Stokes equations in these curved backgrounds, the authors derive the thermodynamics, boundary stress tensors, and charge currents of the dual black holes, showing precise agreement in the large-horizon limit across AdS$_D$, AdS$_5 imes S^5$, AdS$_4 imes S^7$, and AdS$_7 imes S^4$ cases. They demonstrate that large non-extremal and a broad class of extremal black holes have fluid descriptions with mean free path $l_{mfp}$ controlled by the horizon scale, and they discuss when and why the fluid approximation fails (notably for supersymmetric cases). The results yield universal predictions for the thermodynamics of large AdS black holes in varied gravity theories, while also exposing intriguing subleading deviations that point to deeper bulk–boundary connections and potential extensions to higher-order hydrodynamics.

Abstract

We use the AdS/CFT correspondence to argue that large rotating black holes in global AdS(D) spaces are dual to stationary solutions of the relativistic Navier-Stokes equations on S**(D-2). Reading off the equation of state of this fluid from the thermodynamics of non-rotating black holes, we proceed to construct the nonlinear spinning solutions of fluid mechanics that are dual to rotating black holes. In all known examples, the thermodynamics and the local stress tensor of our solutions are in precise agreement with the thermodynamics and boundary stress tensor of the spinning black holes. Our fluid dynamical description applies to large non-extremal black holes as well as a class of large non-supersymmetric extremal black holes, but is never valid for supersymmetric black holes. Our results yield predictions for the thermodynamics of all large black holes in all theories of gravity on AdS spaces, for example, string theory on AdS(5) x S**5 and M theory on AdS(4) x S**7 and AdS(7) x S**4.

Figures (1)

• Figure 1: The space of allowed $\kappa_i$'s. The axes correspond to $X=\frac{1}{1+\kappa_1}$, $Y=\frac{1}{1+\kappa_2}$ and $Z=\frac{1}{1+\kappa_3}$. The $X_i$'s can lie anywhere in the cube outside the "extremal" plane $X+Y+Z = 1$.