  Quite recently, some new mathematical approaches to black holes have appeared
in the literature. They do not rely on the classical concept of event horizon
-- which is very global, but on the local concept of hypersurfaces foliated by
trapped surfaces. After a brief introduction to these new horizons, we focus on
a viscous fluid analogy that can be developed to describe their dynamics, in a
fashion similar to the membrane paradigm introduced for event horizons in the
seventies, but with a significant change of sign of the bulk viscosity.
