Matching of spatially homogeneous nonstationary space-times to vacuum in cylindrical symmetry

We study the matching of locally rotationally symmetric spatially homogeneous collapsing dust space-times with nonstationary vacuum exteriors in cylindrical symmetry. Given an interior with diagonal metric we prove existence and uniqueness results for the exterior. The matched solutions contain trapped surfaces and singularities and are determined up to a limit surface H in the exterior. The solutions cannot be asymptotically flat and we present evidence that they are singular on the limit surface