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We analyze BPS black hole attractors in 4d gauged supergravity in thepresence of higher derivative supersymmetric terms, including aWeyl-squared-type action, and determine the resulting corrections to theBekenstein-Hawking entropy. The near-horizon geometry AdS$_2 \times$S$^2$ (orother Riemann surface) preserves half of the supercharges in $N=2$ supergravitywith Fayet-Iliopoulos gauging. We derive a relation between the entropy and theblack hole charges that suggests via AdS/CFT how subleading correctionscontribute to the supersymmetric index in the dual microscopic picture.  Depending on the model, the attractors are part of full black hole solutionswith different asymptotics, such as Minkowski, AdS$_4$, and hvLif$_4$. We giveexplicit examples for each of the asymptotic cases and comment on theimplications. Among other results, we find that the Weyl-squared terms spoilthe exact two-derivative relation to non-BPS asymptotically flat black holes inungauged supergravity.

Higher derivative corrections to BPS black hole attractors in 4d gauged supergravity