Magnetohydrodynamics from gravity

TL;DR

This paper derives magnetohydrodynamic equations from Einstein's gravity with electromagnetic fields by imposing boundary conditions near black hole horizons, extending the fluid/gravity correspondence to charged black holes.

Contribution

It introduces a general framework for deriving hydrodynamics from gravity with matter fields and obtains magnetohydrodynamic equations for charged black holes.

Findings

Derivation of incompressible Navier-Stokes equations for charged black holes.

Standard magnetohydrodynamic equations emerge in the magnetic charge case.

Framework applicable to spacetime with electromagnetic matter fields.

Abstract

Imposing the Petrov-like boundary condition on the hypersurface at finite cutoff, we derive the hydrodynamic equation on the hypersurface from the bulk Einstein equation with electromagnetic field in the near horizon limit. We first get the general framework for spacetime with matter field, and then derive the incompressible Navier-Stokes equations for black holes with electric charge and magnetic charge respectively. Especially, in the magnetic case, the standard magnetohydrodynamic equations will arise due to the existence of the background electromagnetic field on the hypersurface.