  A new spherically-symmetric solution for a gravitational field is found in
the conformally-unimodular metric. It is shown, that the surface of the black
hole horizon in the standard Schwarzschild metric can be squeezed to a point by
converting coordinates to the conformally-unimodular metric. In this new
metric, there is no black hole horizon, while the naked singularity corresponds
to a point massive particle. The reason for the study of this particular gauge
(i.e., conformally-unimodular metric) is its relation to the vacuum energy
problem. That aims to relate it to other physical phenomena (including black
holes), and one could argue that they should be considered in this particular
metric. That means the violation of the gauge invariance of the general theory
of relativity. As a result, the nonsingular "eicheons" appear as the non-point
compact objects with different masses and structures. They are a final product
of the stellar collapse, with the masses exceeding the
Tolman-Oppenheimer-Volkoff limit.
