  We use the membrane paradigm to analyze the horizon dynamics of a uniformly
boosted black brane in a (d+2)-dimensional asymptotically Anti-de-Sitter
space-time and a Rindler acceleration horizon in (d+2)-dimensional Minkowski
space-time. We show that in these cases the horizon dynamics is governed by the
relativistic CFT hydrodynamics equations. The fluid velocity and temperature
correspond to the normal to the horizon and to the surface gravity,
respectively. The second law of thermodynamics for the fluid is mapped into the
area increase theorem of General Relativity. The analysis is applicable, in
general, to perturbations around a stationary horizon, when the scale of
variations of the macroscopic fields is much larger than the inverse of the
temperature. We show that the non-relativistic limit of our analysis yields the
incompressible Navier-Stokes equations.
