Flow equations for non-BPS extremal black hole

We exploit some common features of black hole and domain wall solutions of ( super) gravity theories coupled to scalar fields and construct a class of stable extremal black holes that are non-BPS, but still can be described by first-order differential equations. These are driven by a superpotential, which replaces the central charge Z in the usual black hole potential. We provide a general procedure for finding this class and deriving the associated superpotential. We also identify some other cases which do not belong to this class, but show a similar behaviour.