  We investigate the geometry of a twisting non-shearing congruence of null
geodesics on a conformal manifold of even dimension greater than four and
Lorentzian signature. We give a necessary and sufficient condition on the Weyl
tensor for the twist to induce an almost Robinson structure, that is, the
screen bundle of the congruence is equipped with a bundle complex structure. In
this case, the (local) leaf space of the congruence acquires a partially
integrable contact almost CR structure of positive definite signature. We give
further curvature conditions for the integrability of the almost Robinson
structure and the almost CR structure, and for the flatness of the latter.
  We show that under a mild natural assumption on the Weyl tensor, any metric
in the conformal class that is a solution to the Einstein field equations
determines an almost CR-Einstein structure on the leaf space of the congruence.
These metrics depend on three parameters, and include the Fefferman-Einstein
metric and Taub-NUT-(A)dS metric in the integrable case. In the non-integrable
case, we obtain new solutions to the Einstein field equations, which, we show,
can be constructed from strictly almost Kaehler-Einstein manifolds.
