The Entropy Function for the extremal Kerr-(anti-)de Sitter Black Holes
  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. 
Jin-Ho Cho, Yumi Ko, Soonkeon Nam