Incompressible Navier-Stokes Equations from Einstein Gravity with Chern-Simons Term

TL;DR

This paper derives incompressible Navier-Stokes equations with Hall and curl viscosities from a holographic model involving Einstein gravity with a Chern-Simons term, revealing cutoff-dependent viscosity ratios.

Contribution

It introduces a holographic approach to non-relativistic fluids with parity-breaking viscosities, extending previous models by analyzing cutoff scale dependence.

Findings

Hall viscosity over entropy density depends on the cutoff scale

The ratio tends to zero as the cutoff surface approaches the horizon

Derived Navier-Stokes equations include Hall and curl viscosities

Abstract

In (2+1)-dimensional hydrodynamic systems with broken parity, the shear and bulk viscosity is joined by the Hall viscosity and curl viscosity. The dual holographic model has been constructed by coupling a pseudo scalar to the gravitational Chern-Simons term in (3+1)-dimensional bulk gravity. In this paper, we investigate the non-relativistic fluid with Hall viscosity and curl viscosity living on a finite radial cutoff surface in the bulk. Employing the non-relativistic hydrodynamic expansion method, we obtain the incompressible Navier-Stokes equations with Hall viscosity and curl viscosity. Unlike the shear viscosity, the ratio of the Hall viscosity over entropy density is found to be cutoff scale dependent, and it tends to zero when the cutoff surface approaches to the horizon of the background spacetime.