  By decomposing the Riemann curvature into electric and magnetic parts, we
define the gravoelectric duality transformation by interchange of active and
passive electric parts which amounts to interchange of the Ricci and Einstein
tensors. It turns out that the vacuum equation is duality-invariant. We obtain
solutions dual to the Kerr solution by writing an effective vacuum equation in
such a way that it still admits the Kerr solution but is not duality invariant.
The dual equation is then solved to obtain the dual-Kerr solution which can be
interpreted as the Kerr black hole sitting in a string dust universe.
