Shell crossings and the Tolman model

Abstract

In the present consideration of shell crossings and regular maxima in Tolman (1934) models, necessary and sufficient conditions for the preclusion of shell crossings are derived. It is explicitly shown that a generally surface layer-incorporating Tolman model may contain both elliptic and hyperbolic regions without developing any shell crossings and without recollapse of the hyperbolic regions. These findings contradict the recent hypothesis of Zel'dovich and Grishchuk (1984). It is also noted that the properties distinguishing shell crossings from more serious singularities in spherical symmetry are independent of the equation of state.