  Conditions for smooth cosmological models are set out and applied to
inhomogeneous spherically symmetric models constructed by matching together
different Lemaitre-Tolman-Bondi solutions to the
  Einstein field equations. As an illustration the methods are applied to a
collapsing dust sphere in a curved background. This describes a region which
expands and then collapses to form a black hole in an
  Einstein de Sitter background. We show that in all such models if there is no
vacuum region then the singularity must go on accreting matter for an infinite
LTB time.
