TRAPPED SURFACES DUE TO SPHERICAL INHOMOGENEITIES IN EXPANDING OPEN UNIVERSES

Assume we have a slice in a homogeneous open k = 0 Friedmann-Lemaitre universe, with spherically symmetric inhomogeneities. Assume that inhomogeneities do not change (initially) the rate of expansion of the volume of the slice. Then trapped surfaces have to form if perturbations are compacted in a sufficiently small volume. Assuming in addition that the gravitational momentum is not changed, we conclude that trapped surfaces can appear only if the mass of perturbation is comprised in a sufficiently small volume. The mass of inhomogeneities is bounded from above by a doubled radius of the volume. A bound for the size of a trapped region is found, which depends on the cosmological energy density.