Holographic Fluids with Vorticity and Analogue Gravity

TL;DR

This paper explores holographic three-dimensional fluids with vorticity, analyzing their frames, applying to specific geometries, and deriving rotational Hall viscosity, with implications for analogue gravity and vortex flows.

Contribution

It introduces a novel holographic framework for fluids with vorticity, connecting fluid dynamics, geometry, and analogue gravity, and derives a new formula for rotational Hall viscosity.

Findings

Fluid description via Papapetrou-Randers and Zermelo frames.

Application to Kerr-AdS_4 and Taub-NUT-AdS_4 geometries.

Derived rotational Hall viscosity formula resembling plasma results.

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.