On the collapse of a gravitating ball

Exact solution of the Tolmen problem in the standard (Scharzschild) coordinate system is obtained. It follows from the solution, that during collapse inside the sphere endless density areas appear, when its radius R reaches critical value of Rs≥rg. The equality sign is realized in particular case of homogeneous density (with R0≥rg), while singularity is formed with R=rg. In particular, for falling density (with R0>rg) the cold gravitating sphere collapse is limited by singularity appearance in the center, which is formed with radius Rs>rg value, by close analogy with equilibrium spherical configurations case