Method for distinguishing very compact stellar objects from black holes

We propose a way to distinguish a compact stellar object, whose size is very close to its Schwarzschild radius, from the collapsing stars. Namely, we show that massive fields in the vicinity of a very compact stellar object have discrete energy levels. (These levels are different from the standard nonrelativistic ones present in Coulomb-type 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.