Compactness Criterion for the Formation of Averaged Trapped Surfaces in Gravitational Collapse

An average trapped surface is defined as a closed two-surface with the property that the area of the wave fronts formed by light rays emitted in the orthogonal inward and outward directions are both decreasing. A sufficient criterion is given for the formation of average trapped surfaces in a general gravitational collapse. The criterion has the qualitative form that if a given amount of matter is compacted into a sufficiently small region, then an average trapped surface must be formed. In the case of nearly spherically symmetric gravitational collapse, it is shown that average trapped surfaces always form to second order in the perturbations of spherical symmetry.