  New exact vacuum solutions with various singularities in the plane-symmetric
spacetime are shown, and they are applied to the analysis of inhomogeneous
cosmological models and colliding gravitational waves. One of the singularities
can be true null singularities, whose existence was locally clarified by Ori.
These solutions may be interesting from the viewpoint of the variety of
cosmological singularities and the instability problem of Cauchy horizons
inside black holes.
