Quadratic Curvature Correction to the Euclidean Action of Rotating AdS Black Holes in General Dimensions
Si-Yue Lu, H. Lu
TL;DR
The paper develops a perturbative framework to compute leading quadratic-curvature corrections to the on-shell Euclidean action and thermodynamics of rotating AdS black holes in general dimensions. By combining an improved Reall-Santos method with a field redefinition to Einstein–Weyl gravity, it isolates the Weyl-squared sector (which decays rapidly in AdS) and then maps back to general quadratic invariants, yielding explicit corrections to the Gibbs free energy and related thermodynamic quantities. It provides general expressions for the corrections, and supplies concrete results for $D=4$ and $D=5$ as well as the all-equal-angular-m momentum case, verifying consistency with known limits and special cases. The approach enables efficient, solution-free computation of perturbative quantum gravity corrections to rotating AdS black holes, with potential utility as a cross-check against perturbative solutions and in guiding higher-derivative gravity phenomenology in AdS/CFT contexts.
Abstract
We adopt the improved Reall-Santos method to obtain the leading-order perturbative correction of the quadratic curvature invariants to the on-shell Euclidean action of rotating anti-de Sitter (AdS) black holes in general $D$ dimensions. The corresponding Gibbs free energy is a function of thermodynamic variables, temperature and angular velocities, which are unperturbed in this approach.