Four-dimensional black holes with unusual horizons

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