Vorticity in holographic fluids

TL;DR

The paper addresses how vorticity in holographic, 2+1D conformal fluids arises from 4D bulk geometries with angular momentum or nut charge, leading to boundary Papapetrou--Randers geometries and stationary, non-dissipative kinematics. It develops a framework based on the Fefferman--Graham expansion to extract and interpret holographic data, and demonstrates exact bulk reconstructions from boundary data, including Kerr--AdS$_4$, Taub--NUT--AdS$_4$, and hyperbolic NUT--AdS$_4$ cases. It further elucidates the dual descriptions via the Zermelo frame and analogue gravity, and shows how vorticity spectra relate to Bianchi-type boundary geometries and their global hyperbolicity properties. The work provides a concrete, geometric pathway to study rotating holographic fluids, their transport coefficients (e.g., rotational Hall viscosity) and potential connections to analogue gravity and condensed-matter applications.

Abstract

In view of the recent interest in reproducing holographically various properties of conformal fluids, we review the issue of vorticity in the context of AdS/CFT. Three-dimensional fluids with vorticity require four-dimensional bulk geometries with either angular momentum or nut charge, whose boundary geometries fall into the Papapetrou--Randers class. The boundary fluids emerge in stationary non-dissipative kinematic configurations, which can be cyclonic or vortex flows, evolving in compact or non-compact supports. A rich network of Einstein's solutions arises, naturally connected with three-dimensional Bianchi spaces. We use Fefferman--Graham expansion to handle holographic data from the bulk and discuss the alternative for reversing the process and reconstruct the exact bulk geometries.