Quadratic Curvature Correction to the Euclidean Action of Rotating AdS Black Holes in General Dimensions

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.