  We derive a general form of first-order flow equations for extremal and
non-extremal, static, spherically symmetric black holes in theories with
massless scalars and vectors coupled to gravity. By rewriting the action as a
sum of squares a la Bogomol'nyi, we identify the function governing the
first-order gradient flow, the `generalised superpotential', which reduces to
the `fake superpotential' for non-supersymmetric extremal black holes and to
the central charge for supersymmetric black holes. For theories whose scalar
manifold is a symmetric space after a timelike dimensional reduction, we
present the condition for the existence of a generalised superpotential. We
provide examples to illustrate the formalism in four and five spacetime
dimensions.
