The extremal Kerr entropy in higher-derivative gravities

Abstract

We investigate higher derivative corrections to the extremal Kerr black hole in the context of heterotic string theory with ${\alpha }^{\prime }$ 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 ${\alpha }^{\prime 2}$. 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.

33 pages+appendices, one figure

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