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BPS black holes in a non-homogeneous deformation of the stu model of $N=2$, $D=4$ gauged supergravity

We consider a deformation of the well-known stu model of $N=2$, $D=4$ supergravity, characterized by a non-homogeneous special Kähler manifold, and by the smallest electric-magnetic duality Lie algebra consistent with its upliftability to five dimensions. We explicitly solve the BPS attractor equations and construct static supersymmetric black holes with radial symmetry, in the context of $\text{U}(1)$ dyonic Fayet-Iliopoulos gauging, focussing on axion-free solutions. Due to non-homogeneity of the scalar manifold, the model evades the analysis recently given in the literature. The relevant physical properties of the resulting black hole solution are discussed.