Lorentzian manifolds with shearfree congruences and Kähler-Sasaki geometry

We study Lorentzian manifolds ( M , g ) of dimension n ≥ 4 equipped with a maximally twisting shearfree null vector field p, for which the leaf space S = / { exp ⁡ t p } is smooth manifold. If 2 k quotient naturally subconformal structure contact type and, in most interesting cases, it regular Sasaki manifold projecting onto quantisable Kähler real − . Going backwards through this line ideas, any associated we give local description all metrics on total spaces A -bundles π : → 1 R such that generator group action -null p. also prove there exists non-trivial generalised electromagnetic plane wave having as propagating direction field, result can be considered generalisation classical 4-dimensional Robinson Theorem. finally construct 2-parametric family Einstein trivial bundle × prescribed value constant. dim Ricci flat obtained way are well-known Taub-NUT metrics.