Entropy function and attractors for AdS black holes

TL;DR

This work generalizes Sen's entropy function to asymptotically AdS black holes in gauged supergravities, deriving fixed near-horizon geometries and entropies for static and rotating solutions in d=4 and d=5 with U(1)^{4,3} gaugings. By extremizing the entropy function, the authors express horizon data solely in terms of the gauge coupling, electric charges, and angular momentum, including explicit results for Einstein and Gauss-Bonnet gravity. They address subtleties from Chern-Simons terms in AdS$_5$, establish relations to known zero-temperature limits, and discuss holographic implications. The analysis yields compact, parameterized forms for the horizon data and confirms the Bekenstein-Hawking entropy in the Einstein case while revealing explicit higher-derivative corrections to the entropy.

Abstract

We apply Sen's entropy formalism to the study of the near horizon geometry and the entropy of asymptotically AdS black holes in gauged supergravities. In particular, we consider non-supersymmetric electrically charged black holes with AdS_2 xS^{d-2} horizons in U(1)^4 and U(1)^3 gauged supergravities in d=4 and d=5 dimensions, respectively. We study several cases including static/rotating, BPS and non-BPS black holes in Einstein as well as in Gauss-Bonnet gravity. In all examples, the near horizon geometry and black hole entropy are derived by extremizing the entropy function and are given entirely in terms of the gauge coupling, the electric charges and the angular momentum of the black hole.