Event Horizon Wrinklification

The possible existence of stable black holes with entropies larger than the corresponding Schwarzschild black hole has been discussed extensively. The recently proposed "rough" black holes provide a concrete example of this. The fear is that, in accordance with the Second Law of thermodynamics, the familiar smooth-skinned black holes might spontaneously "wrinklify" into such an object. We show that this fear is to some extent justified, in the sense that AdS black holes with more entropy than the AdS-Schwarzschild black hole of the same mass do exist.