AdS 5 black hole entropy near the BPS limit

We analyze AdS 5 black holes that are nearly supersymmetric. They depart from the BPS limit in two distinct ways: a temperature takes them above extremality and a potential maintains extremality but violates a certain constraint. We study the thermodynamics of these deformations and their interplay in detail. We discuss recent microscopic computations of BPS black hole entropy in 𝒩 = 4 SYM and generalize the arguments to the nearBPS regime by relaxing constraints imposed by supersymmetry. Our methods recover gravitational results from microscopic theory also for nearBPS black holes.