Comments on Sen's classical entropy function for static and rotating AdS4 black holes

Abstract

We consider various aspects of Sen's classical entropy function formalism for asymptotically AdS4 black holes with emphasis on its efficacy to capture higher derivative corrections to the Bekenstein-Hawking entropy. The formalism has the important advantage of being based on near-horizon symmetries and does not require knowledge of the full interpolating supergravity solution, nor of its AdS4 asymptotics. For the static case, we focus on applying the entropy function formalism in the presence of various higher derivative terms motivated in conformal supergravities; we find agreement with recently reported results utilizing the full black hole solutions and Wald's entropy formula. For the rotating case, we demonstrate that a modified version of the formalism generates a background that coincides precisely with the Bardeen-Horowitz limit of known rotating, electrically charged AdS4 black holes and provides a swift approach to the black hole entropy, including higher derivatives corrections. We conclude that Sen's classical entropy function formalism is a viable and highly efficient approach to capturing higher-derivative corrections to the entropy of asymptotically AdS4 black holes albeit naturally missing certain relations arising from global aspects of the full black hole solution.