Holographic turbulence

TL;DR

This paper constructs and analyzes turbulent black holes in AdS_4 spacetime, revealing inverse cascade behavior and fractal horizon structures, thus advancing the understanding of holographic turbulence and its geometric properties.

Contribution

It introduces a numerical construction of turbulent black holes in AdS_4 and demonstrates their fractal horizon structure linked to turbulent flow properties.

Findings

Evidence of inverse cascade in dual holographic fluid and bulk geometry.

Bulk geometry approximated by fluid/gravity gradient expansion.

Horizons exhibit fractal dimensions related to turbulence.

Abstract

We construct turbulent black holes in asymptotically AdS_4 spacetime by numerically solving Einstein equations. Both the dual holographic fluid and bulk geometry display signatures of an inverse cascade with the bulk geometry being well approximated by the fluid/gravity gradient expansion. We argue that statistically steady-state black holes dual to d dimensional turbulent flows have horizons which are approximately fractal with fractal dimension D=d+4/3.