  In this note we discuss the application of the Hamilton-Jacobi formalism to
the first order description of four dimensional spherically symmetric and
static black holes. In particular we show that the prepotential characterizing
the flow coincides with the Hamilton principal function associated with the
one-dimensional effective Lagrangian. This implies that the prepotential can
always be defined, at least locally in the radial variable and in the moduli
space, both in the extremal and non-extremal case and allows us to conclude
that it is duality invariant. We also give, in this framework, a general
definition of the ``Weinhold metric'' in terms of which a necessary condition
for the existence of multiple attractors is given. The Hamilton-Jacobi
formalism can be applied both to the restricted phase space where the
electromagnetic potentials have been integrated out as well as in the case
where the electromagnetic potentials are dualized to scalar fields using the
so-called three-dimensional Euclidean approach. We give some examples of
application of the formalism, both for the BPS and the non-BPS black holes.
