The extremal Kerr entropy in higher-derivative gravities

We investigate higher derivative corrections to the extremal Kerr black hole in the context of heterotic string theory with alpha ' corrections and of a cubic-curvature extension of general relativity. By analyzing the near-horizon extremal geometry of these black holes, we are able to compute the Iyer-Wald entropy as well as the angular momentum via generalized Komar integrals. In the case of the stringy corrections, we obtain the physically relevant relation S(J) at order alpha '(2). On the other hand, the cubic theories, which are chosen as Einsteinian cubic gravity plus a new odd-parity density with analogous features, possess special integrability properties that enable us to obtain exact results in the higher-derivative couplings. This allows us to find the relation S(J) at arbitrary orders in the couplings and even to study it in a non-perturbative way. We also extend our analysis to the case of the extremal Kerr-(A)dS black hole.