Scalar graviton and the modified black holes

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 threefold. 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 peculiar object, the "graviball," missing in GR. Third, in a simplifying assumption, all the metrics possess the correct Newtonian limit as in GR.