Generalized Entropy in Higher Curvature Gravity And Entropy of Algebra of Observables

Recently, Chandrasekaran, Penington and Witten (CPW) have shown that the generalized entropy of the Schwarzschild black hole at the bifurcation surface equals the entropy of an extended von Neumann algebra of quantum observables in the black hole exterior, in semiclassical Einstein gravity. They also derive a version of the Generalized Second law. We generalize these results to a static black hole in an arbitrary diffeomorphism invariant theory of gravity. Thus, a version of the Generalized second law for an arbitrary diffeomorphism invariant theory of gravity follows.