  Spacetime geometries dual to arbitrary fluid flows in strongly coupled N=4
super Yang Mills theory have recently been constructed perturbatively in the
long wavelength limit. We demonstrate that these geometries all have regular
event horizons, and determine the location of the horizon order by order in a
boundary derivative expansion. Intriguingly, the derivative expansion allows us
to determine the location of the event horizon in the bulk as a local function
of the fluid dynamical variables. We define a natural map from the boundary to
the horizon using ingoing null geodesics. The area-form on spatial sections of
the horizon can then be pulled back to the boundary to define a local entropy
current for the dual field theory in the hydrodynamic limit. The area theorem
of general relativity guarantees the positivity of the divergence of the
entropy current thus constructed.
