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

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