Universality of the superpotential for d=4 extremal black holes

We provide a general strategy to obtain the superpotential W for both BPS and non-BPS extremal black holes in N = 2 four-dimensional supergravities based on symmetric spaces. This extends the construction of W in terms of U-duality invariants that was presented in previous work on the t(3) model. As an application, we explicitly provide W and the solutions to the related gradient flows for the st(2) and stu models. The procedure is shown to hold also for the full N = 8 theory. The role of flat directions in moduli space is clarified. (C) 2010 Elsevier B.V. All rights reserved.