Higher derivative corrections to Kerr-AdS black hole thermodynamics

Instead of the much more involved covariant counterterm method, we apply the well-justified background subtraction method to calculate the first-order corrections to Kerr-AdS black hole thermodynamics induced by the higher derivative terms up to the cubic of Riemann tensor, where the computation is further simplified by the decomposition trick for the bulk action. The validity of our results is further substantiated by examining the corrections induced by the Gauss-Bonnet term. Moreover, by comparing our results with those obtained via the Arnowitt-Deser-Misner and Wald formulas in Lorentzian signature, we can extract some generic information about the first-order corrected black hole solution induced by each higher derivative term.