  In a previous article due to one of the present authors (YFP), an extension
to General Relativity, violating general covariance to the residual unimodular
one, was proposed. As a manifestation of such a violation, there appears the
(massive) scalar graviton in addition to the massless tensor one. The former
was proposed as a candidate on the dark matter in the Universe. In a subsequent
article (Yu. F. Pirogov, MPLA 24, 3239, 2009;arXiv:0909.3311 [gr-qc]), an
application of the extension was developed. Particularly, a regular solution to
the static spherically symmetric equations in empty space was studied by means
of analytical methods. This solution was proposed as a prototype model for the
galaxy soft-core dark halos, with the coherent scalar-graviton field as dark
matter. The present report is a supplement to the aforementioned article. The
statements of the latter are verified and visualized by means of numerical
analysis and symbolic calculations. The nice validity of analytical results is
found.
