Non-supersymmetric Attractor with the Cosmological Constant

TL;DR

This paper tests the non-supersymmetric attractor mechanism using extremal Reissner-Nordström-(anti-)de Sitter black holes, confirming the entropy calculation matches Bekenstein-Hawking entropy and including higher-order corrections.

Contribution

It extends the attractor mechanism to black holes with a cosmological constant, demonstrating the entropy function method's applicability in this context.

Findings

Entropy matches Bekenstein-Hawking formula

Higher-order Gauss-Bonnet corrections computed

Near-horizon geometry contains AdS2 factor

Abstract

As a test for the non-supersymmetric attractor mechanism, we consider extremal Reissner-Nordstr\"{o}m-(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.