T-spheres as a limit of Lemaitre-Tolman-Bondi solutions

TL;DR

This paper demonstrates that T-spheres can be derived as a limit of Lemaitre-Tolman-Bondi solutions, revealing their connection and inheritance of singularities, including shell-crossing analogs, within the Tolman model.

Contribution

It establishes a novel link showing T-spheres as a limit of LTB solutions without an origin, clarifying their singularity structure.

Findings

T-spheres are obtainable as a limit of LTB solutions.

All singularities of T-models are inherited from LTB solutions.

Disc-type singularity in T-spheres is analogous to shell-crossing.

Abstract

In the Tolman model there exist two quite different branches of solutions - generic Lemaitre-Tolman-Bondi (LTB) ones and T-spheres as a special case. We show that, nonetheless, T-spheres can be obtained as a limit of the class of LTB solutions having no origin and extending to infinity with the areal radius approaching constant. It is shown that all singularities of T-models are inherited from those of corresponding LBT solutions. In doing so, the disc type singularity of a T-sphere is the analog of shell-crossing.