  We show that in presence of a cosmological constant or, more generally, of a
scalar potential, there can exist actually more possibilities for the horizon
geometry of a four-dimensional black hole than the hitherto known spherical,
hyperbolic or flat cases. In particular, there are black holes whose event
horizons are noncompact manifolds with finite volume, which are topologically
spheres with two punctures. We give concrete examples of such black holes in
Einstein-Maxwell-AdS gravity and discuss their thermodynamics. These exotic
solutions, that seem to have been overlooked in the existing literature, may
provide interesting testgrounds to address questions related to black hole
physics or holography.
