Holographic charged fluid dual to third order Lovelock gravity

TL;DR

This paper investigates the dual fluid dynamics in third order Lovelock gravity, demonstrating that the viscosity to entropy ratio remains unaffected by the Lovelock terms while the kinematic viscosity is corrected, and confirms the fluid-gravity correspondence in this context.

Contribution

It extends the fluid-gravity duality to third order Lovelock gravity, showing the invariance of the viscosity ratio and the correction to kinematic viscosity, and relates these findings through Wilson RG flow.

Findings

Viscosity to entropy density ratio is unaffected by Lovelock corrections.

Kinematic viscosity receives correction from third order Lovelock gravity.

The fluid-gravity correspondence and isentropic flow equivalence hold in third order Lovelock gravity.

Abstract

We study the dual fluid on a finite cutoff surface outside the black brane horizon in the third order Lovelock gravity. Using nonrelativistic long-wavelength expansion, we obtain the incompressible Navier-Stokes equations of dual fluid with external force density on the finite cutoff surface. The viscosity to entropy density ratio $\eta/s$ is independent of cutoff surface and does not get modification from the third order Lovelock gravity influence. The obtained ratio agrees with the results obtained by using other methods, such as the Kubo formula at the AdS boundary and the membrane paradigm at the horizon in the third order Lovelock gravity. These results can be related by Wilson renormalization group flow. However the kinematic viscosity receives correction from the third order Lovelock term. We show that the equivalence between the isentropic flow of the fluid and the radial component of the gravitational equation observed in the Einstein and Gauss-Bonnet gravities also holds in the third order Lovelock gravity. This generalization brings more understandings of relating the gravity theory to the dual fluid.