  We show that the Einstein equations in the vacuum are invariant under an
$SO(2)$ duality symmetry which rotates the curvature 2-form into its tangent
space Hodge dual. Akin to electric-magnetic duality in gauge theory, the
duality operation maps classical solutions into each other. As an example, we
demonstrate that the Kerr solution is non-linearly mapped by duality into
Kerr-Taub-NUT.
