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We investigate the geometry of a twisting non-shearing congruence of nullgeodesics on a conformal manifold of even dimension greater than four andLorentzian signature. We give a necessary and sufficient condition on the Weyltensor for the twist to induce an almost Robinson structure, that is, thescreen bundle of the congruence is equipped with a bundle complex structure. Inthis case, the (local) leaf space of the congruence acquires a partiallyintegrable contact almost CR structure of positive definite signature. We givefurther curvature conditions for the integrability of the almost Robinsonstructure 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 metricin the conformal class that is a solution to the Einstein field equationsdetermines an almost CR-Einstein structure on the leaf space of the congruence.These metrics depend on three parameters, and include the Fefferman-Einsteinmetric and Taub-NUT-(A)dS metric in the integrable case. In the non-integrablecase, we obtain new solutions to the Einstein field equations, which, we show,can be constructed from strictly almost Kaehler-Einstein manifolds.

Twisting non-shearing congruences of null geodesics, almost CR structures, and Einstein metrics in even dimensions