Nonlinear Magnetohydrodynamics from Gravity
Abstract
Description
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.
20 pages. v3: Added section 2.3 on comparison to other approaches and definition of viscosity
20 pages. v3: Added section 2.3 on comparison to other approaches and definition of viscosity