Quadratic curvature corrections to five-dimensional Kerr-AdS black hole thermodynamics by the background subtraction method

We justify the applicability of the background subtraction method to both Einstein’s gravity and its higher derivative corrections in five-dimensional asymptotically anti–de Sitter (AdS) spacetimes, where the corresponding higher derivative corrections to the expression for the Arnowitt-Deser-Misner mass and angular momentum are also worked out. Then we further apply the background subtraction method to calculate the first-order corrected Gibbs free energy by the quadratic curvature terms for the five-dimensional Kerr-AdS black hole, which is in exact agreement with the previous result obtained by the holographic renormalization method. Such an agreement in turn substantiates the applicability of the background subtraction method.