Quadratic Curvature Correction and Its Breakdown to Thermodynamics of Rotating Black Holes

We adopt the Reall-Santos method to obtain the quadratic curvature corrections to the thermodynamics of Myers-Perry rotating black holes in diverse dimensions. We consider the corrections in canonical and grand canonical ensembles, and also for fixed mass and angular momenta. We find that there exist inevitable divergences for generic rotation parameters so that the perturbative approach breaks down. We present a simple and universal formula to determine where these divergences could arise, and argue, using an explicit example, that these divergences are artefact of perturbation and may not exist in the full nonlinear theory.
Comment: LaTeX, 34 pages, some typos were corrected and a new subsection on the sign of \Delta S was added