Voids in the tolman-bondi universe

Abstract

In the paper the void is modeled as a spherical underdense region surrounded by shells changing into the Friedmannian exterior. This model is in fact a single Tolman-Bondi metric, where at the edge of the void the density need not be continuous. In principle, there may exist 72 variations. These models contain also the cases, when in the void itself there is a Minkowskian vacuum; the shell crossing is not excluded, too. Some technical results are obtained for the Tolman-Bondi metric. Using them, the questions of stability and other theoretical problems are investigated. Some observational facts concerning the voids are also used. As the key result a truncation of the possible models is obtained; only 14 models are physically reasonable. This means that the universe is either hyperbolically expanding (this possibility strengthens the proposition of Bonnor and Chamorro, (1990); (1991)), or there is a shell crossing. Thus the discovery of voids is an observational support either for the open universe or for the shell crossing scenario of galaxy formation (Mészáros, 1991), where no anisotropy of microwave background radiation is needed in a baryon dominated universe.