Effectiveness of Weyl gravity in probing quantum corrections to AdS black holes

Computing leading higher curvature contributions to thermodynamic quantities of AdS black hole is drastically simplified once the higher curvature terms are expressed in terms of powers of Weyl tensor by applying proper field redefinitions, avoiding the usual complications caused by higher derivative Gibbons-Hawking-York term or surface counterterms. We establish the method by computing the Euclidean action of general rotating anti–de Sitter (AdS) black holes in five-dimensional quadratic curvature theories with or without supersymmetry and verifying the results numerically. Our result is the state of the art for charged rotating AdS black holes in five-dimensional minimal gauged supergravity including corrections from all three supersymmetric curvature squared terms. Our approach facilitates precision tests in the AdS/CFT correspondence and should be applicable in diverse dimensions.