  Einstein equations are addressed with the energy-momentum tensor that appears
if the equations under discussion are required to possess conformal invariance.
It is proved that thus derived equations (equations of conformally invariant
geometrodynamics) can have not only smooth solutions, but also solutions with
discontinuities on space-like hypersurfaces. The solutions obtained are similar
to the well-known discontinuous Einstein equation solutions like shock-wave
solutions, extended-source solutions, etc.
  For the centrally symmetric stationary solution discussed in the paper, the
discontinuity surface removes the singularity. The degree of generality of this
solution regularization mechanism is discussed. The issue of the mechanism that
forces any smooth solution in the conformally invariant geometrodynamics to be
rearranged into the discontinuous one when certain conditions are met is also
discussed. The conditions can be: (1) sound speed becoming to be higher than
light speed; (2) the solution becoming intolerant to smaller and smaller-scale
perturbation modes.
