Tolman-Bondi-Lemaitre cell model for the universe and gravitational collapse - art. no. 084018

A piecewise Tolman-Bondi-Lemaitre (TBL) cell model for the universe incorpo rating local collapsing and expanding inhomogeneities is presented here. Th e cell model is made up of TBL underdense and overdense spherical regions s urrounded by an intermediate region of TBL shells embedded in an expanding universe. The cell model generalizes the Friedmann as well as Einstein-Stra us Swiss-cheese models and presents a number of advantages over other model s. In particular, the time evolution of the cosmological inhomogeneities is now incorporated within the scheme. The important problem of gravitational collapse of a massive dust cloud, such as a cluster of galaxies or even a massive star, in such a cosmological background is examined. It is shown th at the collapsing local inhomogeneities in an expanding universe could resu lt in either a black hole, or a naked singularity, depending on the nature of the initial data which consist of the matter distribution and the veloci ties of the collapsing shells in the cloud at the initial epoch from which the collapse commences.