A Strongly Coupled Anisotropic Fluid From Dilaton Driven Holography

TL;DR

This paper constructs a holographic model of an anisotropic fluid using 5D gravity with a dilaton, analyzing its properties, stability, and fluid mechanics, revealing small viscosity effects and new transport coefficients.

Contribution

It introduces a new anisotropic black brane solution with linearly varying boundary conditions and derives the corresponding fluid mechanics with additional transport coefficients.

Findings

Some viscosity components become parametrically small near extremality.

No instability was found close to extremality.

Small viscosity leads to minimal friction forces in certain configurations.

Abstract

We consider a system consisting of $5$ dimensional gravity with a negative cosmological constant coupled to a massless scalar, the dilaton. We construct a black brane solution which arises when the dilaton satisfies linearly varying boundary conditions in the asymptotically $AdS_5$ region. The geometry of this black brane breaks rotational symmetry while preserving translational invariance and corresponds to an anisotropic phase of the system. Close to extremality, where the anisotropy is big compared to the temperature, some components of the viscosity tensor become parametrically small compared to the entropy density. We study the quasi normal modes in considerable detail and find no instability close to extremality. We also obtain the equations for fluid mechanics for an anisotropic driven system in general, working upto first order in the derivative expansion for the stress tensor, and identify additional transport coefficients which appear in the constitutive relation. For the fluid of interest we find that the parametrically small viscosity can result in a very small force of friction, when the fluid is enclosed between appropriately oriented parallel plates moving with a relative velocity.