Nonlinear Magnetohydrodynamics from Gravity

TL;DR

This paper derives the equations of nonlinear magnetohydrodynamics for a charged fluid in a magnetic field from gravity duals, providing explicit solutions and transport coefficients up to second and third order in derivatives.

Contribution

It extends the fluid/gravity correspondence to include nonlinear magnetohydrodynamics in the presence of magnetic fields for a 2+1 dimensional charged fluid.

Findings

Derived fluid dynamical equations from gravity duals.

Constructed gravity solutions up to second order in derivatives.

Calculated transport coefficients for the charged fluid.

Abstract

We apply the recently established connection between nonlinear fluid dynamics and AdS gravity to the case of the dyonic black brane in AdS_4. This yields the equations of fluid dynamics for a 2+1 dimensional charged fluid in a background magnetic field. We construct the gravity solution to second order in the derivative expansion. From this we find the fluid dynamical stress tensor and charge current to second and third order in derivatives respectively, along with values for the associated transport coefficients.