Flat space compressible fluid as holographic dual of black hole with curved horizon

TL;DR

This paper constructs a novel holographic duality between a compressible fluid on flat space and a higher-dimensional black hole with a curved horizon, extending beyond traditional bulk/boundary frameworks.

Contribution

It introduces the first example of holographic duality involving a flat space fluid and a black hole with a conformally flat horizon, beyond standard bulk/boundary models.

Findings

Fluid dual exhibits compressibility, viscosity, and stationarity.

Holographic duality connects flat space fluid dynamics with black hole horizon geometry.

First example of holography beyond bulk/boundary correspondence.

Abstract

We consider the fluid dual of $(d+2)$-dimensional vacuum Einstein equation either with or without a cosmological constant. The background solutions admit black hole event horizons and the spatial sections of the horizons are conformally flat. Therefore, a $d$-dimensional flat Euclidean space $\mathbb{E}^d$ is contained in the conformal class of the spatial section of the black hole horizon. A compressible, forced, stationary and viscous fluid system can be constructed on the product (Newtonian) spacetime $\mathbb{R}\times\mathbb{E}^d$ as the lowest order fluctuation modes around such black hole background. This construction provides the first example of holographic duality which is beyond the class of bulk/boundary correspondence.