Generalized entropy in higher curvature gravity

Chandrasekaran, Penington and Witten (CPW) used the crossed product construction in modular theory to associate an entropy with the algebra of observables in the Schwarzschild black hole exterior. This entropy was shown to equal the generalized entropy modulo a constant. They also proved a version of the generalized second law (GSL) in Einstein gravity. We summarize these developments and our generalization of these results to static black holes in an arbitrary diffeomorphism invariant theory of gravity [1] — this article is a summary of that work and is based on a talk at the QGatRRI conference in Sep.2023. The algebra entropy again equals the generalized entropy modulo a constant where the generalized entropy now contains the Wald entropy. A version of the GSL follows by employing the arguments of CPW to this case.