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The problem of the speed of the objects inside the Schwarzschild black holeis considered. The general result is that the value of the relative speed ofthe objects following their non-zero angular momentum trajectories, both ofgeodesic and non-geodesic character, when approaching the ultimate singularity,tends to the value of speed of light. There is only one exception when bothobjects move in the same plane and have parallel angular momenta. This outcomeappears to have a deeper sense: it reflects the anisotropic character of thedynamics of interior of this particular black hole. The result in questionmeans that near the singularity, collisions of two particles lead to anindefinitely large energy in the center of mass frame. Aforementionedproperties have their counterpart in the phenomenon of an indefinitely largeblueshift near the singularity. Thus the angular momentum of a particle turnsout to be an important feature that affects the final behavior of particle nearthe singularity. Motivated by this fact, we generalize the Lema\^{\i}tre frameunder the horizon in such a way that reference particles themselves havenonzero angular momentum. Our results apply not only to the Schwarzschildsingularity but also to other space-like ones for which the scale factor$g\rightarrow \infty $. We also analyze another type of singulairites for whichthe circumference radius vanishes but $g$ remains finite.

On particle dynamics near the singularity inside the Schwarzschild black hole and T-spheres