Qualitative analysis of the formation of T-domains under the condition of the existence of a single R-reference system

Abstract

We examine the origination of a T-domain in a spherically symmetric configuration. The following assertion is proved: If a single R-reference system can be introduced in the whole connected R-domain, where each remote observer can determine an arbitrarily large interval of coordinate R-time, then the boundary between the R-and T-domains (the R-T boundary) is formed by isotropic world lines. Certain characteristic features of the solution describing the origination of a T-domain can hence be mentioned, namely: There are throats in the T-domain; in the R-neighborhood of a definite part of the R-T boundary the reference system applicable in the whole space-time domain under consideration is broadened; the R-T boundary is a surface on which the time R-coordinate takes on an infinitely large value in the limit.