  In this paper we consider an Einstein-type equation which generalizes
important geometric equations, like static and critical point equations. We
prove that a complete Einstein-type manifold with fourth-order divergence-free
Weyl tensor and zero radial Weyl curvature is locally a warped product with
$(n-1)$-dimensional Einstein fibers, provided that the potential function is
proper. As a consequence, we prove a result about the nonexistence of multiple
black holes in static spacetimes.
