The Entropy Function for the extremal Kerr-(anti-)de Sitter Black Holes

TL;DR

This paper applies the entropy function formalism to extremal Kerr-(anti-)de Sitter black holes, deriving their entropy exactly and extending the analysis to include higher derivative corrections like the Gauss-Bonnet term.

Contribution

It provides an exact solution for the entropy of extremal Kerr-(anti-)de Sitter black holes and incorporates higher derivative corrections, advancing the understanding of black hole entropy in modified gravity.

Findings

Exact agreement with Bekenstein-Hawking entropy

Extension to include Gauss-Bonnet higher derivative corrections

Analytical solutions to differential equations from extremizing the entropy function

Abstract

Based on the entropy function formalism, we consider the extremal Kerr-(anti-)de Sitter black holes in 4-dimensions. Solving differential equations exactly, which are obtained by extremizing the entropy function, we find agreement of the result with Bekenstein-Hawking entropy. Concerning the higher derivative corrections, we extend the computation to the case with Gauss-Bonnet term.