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

d=4 Black Hole Attractors in N=2 Supergravity with Fayet-Iliopoulos Terms