Universality of the superpotential for d=4d=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=2N=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 t3t3 model. As an application, we explicitly provide W   and the solutions to the related gradient flows for the st2st2 and stu   models. The procedure is shown to hold also for the full N=8N=8 theory. The role of flat directions in moduli space is clarified.