Non-supersymmetric attractor with the cosmological constant

As a test for the non-supersymmetric attractor mechanism, we consider extremal Reissner-Nordström-(anti-)de Sitter black holes. Based on the simple observation that the near-horizon geometry of a generic extremal black hole contains two-dimensional anti-de Sitter factor even in the presence of the positive cosmological constant, we apply Ashoke Sen's entropy function method to compute the entropy of these black holes. We find the results which exactly agree with the Bekenstein-Hawking entropy. We also obtain the constant higher-order correction to the entropy due to the Gauss-Bonnet term.