  The old suggestive observation that black holes often resemble lumps of fluid
has recently been taken beyond the level of an analogy to a precise duality. We
investigate aspects of this duality, and in particular clarify the relation
between area minimization of the fluid vs. area maximization of the black hole
horizon, and the connection between surface tension and curvature of the fluid,
and surface gravity of the black hole. We also argue that the Rayleigh-Plateau
instability in a fluid tube is the holographic dual of the Gregory-Laflamme
instability of a black string. Associated with this fluid instability there is
a rich variety of phases of fluid solutions that we study in detail, including
in particular the effects of rotation. We compare them against the known
results for asymptotically flat black holes finding remarkable agreement.
Furthermore, we use our fluid results to discuss the unknown features of the
gravitational system. Finally, we make some observations that suggest that
asymptotically flat black holes may admit a fluid description in the limit of
large number of dimensions.
