Vorticity in holographic fluids

TL;DR

This paper explores how vorticity in conformal fluids can be modeled holographically using four-dimensional bulk geometries with angular momentum or nut charge, revealing a rich set of Einstein solutions linked to Bianchi spaces.

Contribution

It reviews the holographic modeling of vorticity in fluids via AdS/CFT, connecting boundary vorticity to bulk geometries with specific properties and expanding the understanding of holographic fluid dynamics.

Findings

Identification of bulk geometries with angular momentum or nut charge corresponding to boundary vorticity.

Connection between Einstein solutions and three-dimensional Bianchi spaces.

Use of Fefferman--Graham expansion to reconstruct bulk geometries from boundary data.

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.