Second law violations in Lovelock gravity for black hole mergers

We study the classical second law of black hole thermodynamics, for Lovelock theories (other than general relativity), in arbitrary dimensions. Using the standard formula for black hole entropy, we construct scenarios involving the merger of two black holes in which the entropy instantaneously decreases. Our construction involves a Kaluza-Klein compactification down to a dimension in which one of the Lovelock terms is topological. We discuss some open issues in the definition of the second law which might be used to remove this entropy decrease.

Figure 1

The head-on collision of two black holes, pictured on time slices before, at, and after the moment of joinder. While the horizons may be smooth after the collision, before the collision each of the two black holes must have a nonsmooth point.