On certain twisting type-N solutions of Einstein equations with pure radiation energy–momentum tensor and nonvanishing shear

Abstract

An explicit form of a certain class of type-N solutions of Einstein equations with pure radiation energy–momentum tensor is studied. In particular, the general solution of a constraint equation is found and the uniqueness of an example which already exists in the literature is established. The metric depends on two nonzero real parameters and a holomorphic function h of one complex variable. The congruence of principal null geodesics possesses nonvanishing twist and shear. If h is entire and nowhere vanishing, the solution is interpreted by means of geometrically distinguished set of freely falling observers as a gravitational wave accompanied by an incoherent electromagnetic radiation in an ‘expanding’ half-space of a three-space with the curvature's singularity at the boundary of the half-space.