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

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 η 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.