Holographic perfect fluidity, Cotton energy-momentum duality and transport properties

TL;DR

This paper explores holographic theories with perfect fluid behavior, revealing a duality between Cotton tensor and energy-momentum tensor, and shows how specific geometries lead to simplified transport properties and black-hole solutions.

Contribution

It introduces stationary perfect-Cotton geometries with a novel Cotton/energy-momentum duality and connects black-hole uniqueness to holographic perfect equilibrium.

Findings

Certain transport coefficients vanish in holographic fluids.

Exact black-hole solutions without naked singularities are constructed.

A duality between Cotton tensor and energy-momentum tensor constrains fluid vorticity.

Abstract

We investigate background metrics for 2+1-dimensional holographic theories where the equilibrium solution behaves as a perfect fluid, and admits thus a thermodynamic description. We introduce stationary perfect-Cotton geometries, where the Cotton--York tensor takes the form of the energy--momentum tensor of a perfect fluid, i.e. they are of Petrov type D_t. Fluids in equilibrium in such boundary geometries have non-trivial vorticity. The corresponding bulk can be exactly reconstructed to obtain 3+1-dimensional stationary black-hole solutions with no naked singularities for appropriate values of the black-hole mass. It follows that an infinite number of transport coefficients vanish for holographic fluids. Our results imply an intimate relationship between black-hole uniqueness and holographic perfect equilibrium. They also point towards a Cotton/energy--momentum tensor duality constraining the fluid vorticity, as an intriguing boundary manifestation of the bulk mass/nut duality.