Comments on Sen's Classical Entropy Function for Static and Rotating AdS$_4$ Black Holes

TL;DR

This paper evaluates Sen's classical entropy function formalism for AdS$_4$ black holes, demonstrating its effectiveness in capturing higher derivative corrections to entropy without requiring full solutions, especially for static and rotating cases.

Contribution

It shows that Sen's entropy function formalism accurately reproduces higher derivative entropy corrections for AdS$_4$ black holes, including rotating solutions, with a simplified near-horizon approach.

Findings

Agreement with full solution results for static black holes.

Successful application to rotating black holes matching known limits.

Efficient method for higher derivative entropy calculations.

Abstract

We consider various aspects of Sen's classical entropy function formalism for asymptotically AdS$_4$ 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 AdS$_4$ 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 AdS$_4$ 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 AdS$_4$ black holes albeit naturally missing certain relations arising from global aspects of the full black hole solution.