Abstract
We investigate higher derivative corrections to the extremal Kerr black hole in the context of heterotic string theory with α′ 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 α′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.
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Acknowledgments
We thank Nikolay Bobev, Evan McDonough, Rishi Mouland, David Pereñiguez, Thomas Van Riet and Nicolas Yunes for useful discussions. The work of PAC is supported by a postdoctoral fellowship from the Research Foundation - Flanders (FWO grant 12ZH121N). MD is supported by KU Leuven C1 grant ZKD1118 C16/16/005, and by the Research Programme of The Research Foundation — Flanders (FWO) grant G0F9516N.
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Cano, P.A., David, M. The extremal Kerr entropy in higher-derivative gravities. J. High Energ. Phys. 2023, 219 (2023). https://doi.org/10.1007/JHEP05(2023)219
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DOI: https://doi.org/10.1007/JHEP05(2023)219