The Membrane Paradigm and holographic hydrodynamics

Christopher Eling, Yasha Neiman, Yaron Oz

I will discuss recent work showing that in certain cases the equations governing the non-equilibrium dynamics of black hole horizons can be recast as the Navier-Stokes equations of viscous hydrodynamics. The analysis is applicable to long wavelength, long time perturbations about stationary, equilibrium black hole solutions. While a long wavelength expansion does not exist for a Schwarzschild black hole, it does exist for black branes in asymptotically AdS spacetimes, which are holographically dual to gauge theory thermal states. I will show how the membrane paradigm can reproduce the "fluid-gravity correspondence". Since the analysis is local, near the horizon, one can derive the viscous transport coefficients of several interesting gauge theories in a simpler way. Finally, our results imply a mapping between fluid variables and horizon geometric variables and therefore may provide a geometric structure for understanding turbulent flows.