  In this article, we consistently reduce the equations of motion for the
bosonic N = 2 supergravity action, using a multi-centered black hole ansatz for
the metric. This reduction is done in a general, non-supersymmetric setup, in
which we extend concepts of BPS black hole technology. First of all we obtain a
more general form of the black hole potential, as part of an effective action
for both the scalars and the vectors in the supergravity theory. Furthermore,
we show that there are extra constraints specifying the solution, which we
calculate explicitly. In the literature, these constraints have already been
studied in the one-center case. We also show that the effective action we
obtain for non-static metrics, can be linked to the "entropy function" for the
spherically symmetric case, as defined by Sen and Cardoso et al.
