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

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