Algebraically special solutions of the Einstein equations with pure radiation fields

Abstract

The Einstein equations Rmu v= Phi kmu kv, kmu being tangent to a twisting shear-free congruence of null geodesics, are formulated as equations in a three-dimensional Cauchy-Riemann space. If the NUT parameter M vanishes and the Cauchy-Riemann space is a hypersurface in C2 then the equations reduce to a single linear second-order equation. New gravitational solutions are found for the case of the Robinson congruence.