Spherically symmetric T-models in the general theory of relativity (Reprinted from Zhurnal Eksperimentalnoy i Teoreticheskoy Fiziki, 1969)

Spherically symmetric models constructed of dustlike matter are considered in a comoving reference frame, and a general solution of the Einstein equat ions (Delta not equal 0) is obtained which contains along with the Tolman-B ondi-Lemaitre models an additional class of T-models of a "sphere" with the metric of a synchronously-comoving T-system (R = r(tau)) which represent a n inhomogeneous generalization of the anisotropic cosmological model of a " quasiclosed" type with hypercylindrical spatial sections V-3 = (S-2 x R-1). The T-models of a "sphere" yield a method, which in principle differs from the closed Friedmann model, for realizing the total mass defect maximal in GTR equal to the total rest mass of matter, and are characterized by the f act that the gravitational binding energy for each particle of "dust" exact ly compensates its rest mass so that as a result the active mass - the equi valent of the total energy - remains constant in the case of an unrestricte d growth of the "sphere" and, in general, does not contain any material con tribution. It is of a purely field nature and coincides with the geometrody namic "massless mass" of the T-regions of the Schwarzschild-deSitter-Kortle r fields in which matter is bound gravitationally and is held by the strong est possible vacuum field inside the "event horizon" of the Schwarzschild s phere type. It is shown that the T-models of a "sphere" do not have a class ical analogue, and their existence and paradoxical properties are due to th e nonlinearity of GTR: a) a mass defect which manifests itself in a charact eristic manner through the non-Euclidian nature of the co-moving space V-3, b) the presence of T-regions in SSK fields. A detailed discussion is given of the principal properties and tile dynamics of the cosmological T-models of a "sphere" (Delta not equal 0), and they are classified in accordance w ith Robertson`s scheme for a closed Friedmann model into(19) the analogous types O-1, M-1, M-2, A(1), A(2) of transverse motion of the hypercylinder V -3. It is shown that all physically acceptable solutions with rho > 0 must have time singularities of three kinds: collapse of V-3 into a line, a poin t and a sphere, with the infinite types M-1, A(2) and M-2 becoming isotropi c in the course of unlimited expansion.