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Assuming that the near horizon geometry of the black hole solution of thegravity dual to the ABJM model, in the presence of a coupling between the Weyltensor and the field strength, is $AdS_{2}\times S^{2}$, we compute Sen'sentropy function for this theory. By extremizing the entropy function we writea formula for the entropy of the black hole, and then we compute the sameentropy using Wald's formula and show that the results are the same. In thisway we generalize the calculation of black hole entropy to cases of curvaturecoupling to the field strength, including at first order, and we also show howto calculate the black hole entropy when the black hole solution is unknown,from just a few simple assumptions about the horizon.

Massive ABJM and black hole entropy in the presence of field strength coupling to curvature