TRAPPED SURFACES IN SPHERICAL EXPANDING OPEN UNIVERSES

Consider spherically symmetric initial data for a cosmology which, in the large part, approximates an open k = - 1, LAMBDA = 0 Friedmann-Lem eitre universe. further assume that the data are chosen so that the tr ace of the extrinsic curvature is a constant and that the matter field is at rest at this instant of time. One expects that no trapped surfa ces appear in the data if no significant clump of excess matter is to be found. This Brief Report confirms this belief by displaying a neces sary condition for the existence of trapped surfaces. This necessary c ondition, simply stated, says that a relatively large amount of excess -matter must be concentrated in a small volume for trapped surfaces to appear.