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

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.