  Under the explicit violation of the general covariance to the unimodular one,
the effect of the emerging scalar graviton on the static spherically symmetric
metrics is studied. The main results are three-fold. First, there appears the
two-parametric family of such metrics, instead of the one-parametric black-hole
family in General Relativity (GR). Second, there may exist the one-parametric
subfamily describing a pure gravitational object, the ``graviball'', missing in
GR. Third, in a simplifying assumption, all the metrics possess the correct
Newton's limit as in GR.
