Trapped surfaces in expanding open universes

Assume we have an open $k=0\mathrm{}$ Friedmann-Lemaître universe with spherically symmetric inhomogeneities on a spacelike slice that do not change (initially) the rate of expansion of the volume of the slice. We give a set of necessary and sufficient criteria for the formation of trapped surfaces due to those inhomogeneities on the initial surface. A bound for the size of a perturbed trapped region is found, which depends on the cosmological energy density.