We generalize the description of the d=4 Attractor Mechanism based on an effective black hole (BH) potential to the presence of a gauging which does not modify the derivatives of the scalars and does not involve hypermultiplets. The obtained results do not rely necessarily on supersymmetry, and they can be extended to d>4, as well. Thence, we work out the example of the stu model of N=2 supergravity in the presence of Fayet-Iliopoulos terms, for the supergravity analogues of the magnetic and D0-D6 BH charge configurations, and in three different symplectic frames: the SO(1,1)^{2}, SO(2,2) covariant and SO(8)-truncated ones. The attractive nature of the critical points, related to the semi-positive definiteness of the Hessian matrix, is also studied.
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