  We study the matching of LRS spatially homogeneous collapsing dust
space-times with non-stationary 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, singularities and
Cauchy horizons. The solutions cannot be asymptotically flat and we present
evidence that they are singular on the Cauchy horizons.
