Extremal black hole flows and duality invariants

Extremal black holes in Maxwell-Einstein supergravities with scalar fields can be obtained as solutions of first order flow equations even when they are not supersymmetric, provided one identifies a suitable superpotential W entering the effective potential, and driving the evolution of the scalar fields. We briefly review the main ideas for the construction of W in terms of duality invariants of N=2 special geometry and we comment on its properties in wider contexts. (Abstract Copyright [2010], Wiley Periodicals, Inc.)