  We propose a way to distinguish compact stellar object, whose size is very
close to its Schwarzschild radius, from the collapsing stars. Namely, we show
that {\it massive} fields in the vicinity of a very compact stellar object have
discrete energy levels. (These levels are different from the standard
non-relativistic ones present in Coulomb type of potentials and from the
quasinormal modes.) At the same time we show that there are no such discrete
levels for massive fields in the vicinity of a collapsing star.
