Holographic Fluids with Vorticity and Analogue Gravity

TL;DR

The paper develops a holographic framework for 3D conformal fluids with vorticity by using the Fefferman–Graham expansion to identify a comoving Papapetrou–Randers frame and, via a local Lorentz transformation, a non-inertial Zermelo frame suitable for analogue gravity interpretations. It applies the construction to Kerr–AdS$_4$ and Taub–NUT–AdS$_4$ boundaries, yielding cyclonic and vortex holographic fluids and revealing how Misner strings and closed timelike curves relate to analogue optical horizons; it also derives a simple, classical rotational Hall viscosity ζ_H = (ε + p)/Ω for neutral rotating fluids. The work clarifies how observer choice affects holographic hydrodynamics, enabling moving-media perspectives and setting the stage for holographic transport studies and experimental analogues in rotating quantum systems. These results bridge holographic fluid dynamics, analogue gravity, and topological transport, with potential implications for rotating Bose gases and horizon phenomenology in strongly coupled systems.

Abstract

We study holographic three-dimensional fluids with vorticity in local equilibrium and discuss their relevance to analogue gravity systems. The Fefferman-Graham expansion leads to the fluid's description in terms of a comoving and rotating Papapetrou-Randers frame. A suitable Lorentz transformation brings the fluid to the non-inertial Zermelo frame, which clarifies its interpretation as moving media for light/sound propagation. We apply our general results to the Lorentzian Kerr-AdS_4 and Taub-NUT-AdS_4 geometries that describe fluids in cyclonic and vortex flows respectively. In the latter case we associate the appearance of closed timelike curves to analogue optical horizons. In addition, we derive the classical rotational Hall viscosity of three-dimensional fluids with vorticity. Our formula remarkably resembles the corresponding result in magnetized plasmas.