Type-D solutions describing the collision of plane-fronted gravitational waves

Abstract

Some exact solutions of the Einstein vacuum equations describing the collision of plane-fronted gravitational shock waves accompanied by impulsive waves which produces a type-D geometry in the region of interaction are presented. The collision results in the development of a null surface acting like an event horizon, and the metric has been analytically extended beyond it by using Kruskal coordinates properly adapted to the problem. The extension shows that all null rays emerging from the interaction region escape to infinity: no focusing is present on the horizon. The connection between focusing and creation of singularities has also been investigated by analysing the behaviour of a particular congruence of null geodesics.