A Lovelock black hole bestiary

We revisit the study of (A)dS black holes in Lovelock theories. We present a new tool that allows to attack this problem in full generality. In analyzing maximally symmetric Lovelock black holes with non-planar horizon topologies many distinctive and interesting features are observed. Among them, the existence of maximally symmetric vacua do not supporting black holes in vast regions of the space of gravitational couplings, multi-horizon black holes, and branches of solutions that suggest the existence of a rich diagram of phase transitions. The appearance of naked singularities seems unavoidable in some cases, raising the question about the fate of the cosmic censorship conjecture in these theories. There is a preferred branch of solutions for planar black holes, as well as non-planar black holes with high enough mass or temperature. Our study clarifies the role of all branches of solutions, including asymptotically dS black holes, and whether they should be considered when studying these theories in the context of AdS/CFT.