Seminarium Teorii Względności i Grawitacji

The locus of zero expansion for bundles of light rays emitted at noncentralpoints is investigated for Lemaitre - Tolman (LT) models. The three loci thatcoincide for a central emission point: (1) maxima of R along the rays, (2)expansion = 0, (3) R = 2M are all different for a noncentral emitter. Theintersection of (1) with the equatorial hypersurface (EHS) is numericallydetermined for an exemplary toy model (ETM), for two typical emitter locations.The equation of (2) is derived for a general LT model, and its intersection withthe EHS in the ETM is numerically determined for the same two emitter locations.Typically, the expansion scalar has no zeros or two zeros along a ray, andbecomes +\infty at the Big Crunch (BC) (the +\infty signifies an infinitedivergence of the ray bundle at the BC). The only rays on which \theta becomes-\infty (i.e. the rays converge) at the BC are the radial ones. For noncentralemitters in a collapsing LT model, R = 2M is still the ultimate barrier behindwhich events become invisible from outside; loci (1) and (2) are not suchbarriers. The limiting trasition from an LT model to the correspondingFriedmann model is discontinuous.