Coarse Graining Holographic Black Holes

We expand our recent work on the outer entropy, a holographic coarse-grained entropy defined by maximizing the boundary entropy while fixing the classical bulk data outside some surface. When the surface is marginally trapped and satisfies certain "minimar" conditions, we prove that the outer entropy is exactly equal to a quarter the area (while for other classes of surfaces, the area gives an upper or lower bound). We explicitly construct the entropy-maximizing interior of a minimar surface, and show that it satisfies the appropriate junction conditions. This provides a statistical explanation for the area-increase law for spacelike holographic screens foliated by minimar surfaces. Our construction also provides an interpretation of the area for a class of non-minimal extremal surfaces. On the boundary side, we define an increasing simple entropy by maximizing the entropy subject to a set of "simple experiments" performed after some time. We show (to all orders in perturbation theory around equilibrium) that the simple entropy is the boundary dual to our bulk construction.