  We construct semi-global $(1+3)$-dimensional Lorentzian spacetimes satisfying
the Einstein vacuum equations that contain curvature singularities that are
propagated all the way up to future null infinity. Special cases of our
constructions are semi-global spacetimes containing the interaction of two
impulsive gravitational waves. The spacetimes that we construct can be
considered as the semi-global analogues of the local spacetimes containing weak
null singularities constructed by Luk, and of the local spacetimes containing
the interaction of impulsive gravitational waves constructed by Luk and
Rodnianski.
