  We consider the dynamics of a d+1 space-time dimensional membrane defined by
the event horizon of a black brane in (d+2)-dimensional asymptotically
Anti-de-Sitter space-time and show that it is described by the d-dimensional
incompressible Navier-Stokes equations of non-relativistic fluids. The fluid
velocity corresponds to the normal to the horizon while the rate of change in
the fluid energy is equal to minus the rate of change in the horizon
cross-sectional area. The analysis is performed in the Membrane Paradigm
approach to black holes and it holds for a general non-singular null
hypersurface, provided a large scale hydrodynamic limit exists. Thus we find,
for instance, that the dynamics of the Rindler acceleration horizon is also
described by the incompressible Navier-Stokes equations. The result resembles
the relation between the Burgers and KPZ equations and we discuss its
implications.
