  This article gives necessary and sufficient conditions for the formation of
trapped surfaces in spherically symmetric initial data defined on a closed
manifold. Such trapped surfaces surround a region in which there occurs an
enhancement of matter over the average. The conditions are posed directly in
terms of physical variables and show that what one needs is a relatively large
amount of excess matter confined to a small volume. The expansion of the
universe and an outward flow of matter oppose the formation of trapped
surfaces; an inward flow of matter helps. The model can be regarded as a
Friedmann-Lema\^\i tre-Walker cosmology with localized spherical
inhomogeneities. We show that the total excess mass cannot be too large.
