Flow equations for non-BPS extremal black holes

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