Non-Supersymmetric Attractors and Entropy Function

TL;DR

The paper develops a non-supersymmetric extension of the entropy-function formalism to extremal black holes exhibiting attractor behavior, showing how near-horizon data fixes entropy through a horizon function $f$ and its extremization. It then analyzes higher-order (Lovelock) corrections, deriving explicit entropy corrections in 4D and 5D and highlighting the need to extremize the full entropy function, not just the effective potential. An exact solvable model with a multi-charge potential demonstrates when the entropy takes simple forms, and connections to the 5D Strominger–Vafa framework are discussed via dualities and careful rescalings. Finally, the work links the near-horizon analysis to a CFT interpretation through a 2D effective action and a horizon C-function, illustrating the broader implications for entropy corrections and attractor dynamics in non-supersymmetric settings.

Abstract

We study the entropy of non-supersymmetric extremal black holes which exhibit attractor mechanism by making use of the entropy function. This method, being simple, can be used to calculate corrections to the entropy due to higher order corrections to the action. In particular we apply this method for five dimensional non-supersymmetric extremal black hole which carries two magnetic charges and find the R^2 corrections to the entropy. Using the behavior of the action evaluated for the extremal black hole near the horizon, we also present a simple expression for C-function corrected by higher order corrections.