From Petrov-Einstein-Dilaton-Axion to Navier-Stokes equation in anisotropic model

TL;DR

This paper extends previous work to show that the near-horizon dynamics of an Einstein-Dilaton-Axion system can be described by the incompressible Navier-Stokes equation, with shear viscosity saturating the KSS bound.

Contribution

It generalizes the fluid/gravity correspondence to anisotropic models with dilaton and axion fields, demonstrating the universality of shear viscosity in this context.

Findings

The Navier-Stokes equation governs the near-horizon dynamics.

Shear viscosity saturates the KSS bound.

Viscosity is independent of dilaton and axion fields.

Abstract

In this paper we generalize the previous works to the case that the near-horizon dynamics of the Einstein-Dilaton-Axion theory can be governed by the incompressible Navier-Stokes equation via imposing the Petrov-like boundary condition on hypersurfaces in the non-relativistic and near-horizon limit. The dynamical shear viscosity $\eta$ of such dual horizon fluid in our scenario, which isotropically saturates the Kovtun-Son-Starinet (KSS) bound, is independent of both the dilaton field and axion field in that limit.