Higher derivative corrections to 5-dimensional Kerr-AdS black hole thermodynamics by background subtraction method

Abstract: We justify the applicability of the background subtraction method to both Einstein's gravity and its higher derivative corrections in 5-dimensional asymptotically AdS spacetimes, where the corresponding higher derivative corrections to the expression for the ADM 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 induced by the higher derivative terms up to the quadratic of Riemann tensor for the 5-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.