On the Vaidya limit of the Tolman model.

Abstract

We show that the only Tolman models which permit a Vaidya limit are those having a dust distribution that is hollow, such as the self-similar case. Thus the naked shell-focusing singularities found in Tolman models that are dense through the origin have no Vaidya equivalent. This also casts light on the nature of the Vaidya metric. We point out a hidden assumption in Lemos' demonstration that the Vaidya metric is a null limit of the Tolman metric, and in generalizing his result, we find that a different transformation of coordinates is required.