New family of exact solutions for colliding plane gravitational waves

We construct an infinite-parameter family of exact solutions to the vacuum Einstein field equations describing colliding gravitational plane waves with parallel polarizations. The interaction regions of the solutions in this family are locally isometric to the interiors of those static axisymmetric (Weyl) black-hole solutions which admit both a nonsingular horizon, and an analytic extension of the exterior metric to the interior of the horizon. As a member of this family of solutions we also obtain, for the first time, a colliding plane-wave solution where both of the two incoming plane waves are purely anastigmatic, i.e., where both incoming waves have equal focal lengths.