Bound states of spin-1 equation in Schwarzschild space-time

The radial equations of the general massive spin 1 equation in Schwarzschild space-time are studied. The study is based on the separated structure of the solutions obtained by separation of variables. Asymptotic behaviours of the radial solutions are determined. The radial equations are solved exactly in case of zero angular constants. A properly covariant scalar product between solutions is considered that is induced by the conserved current. It is shown that a class of states exists that are bound with respect to the scalar product. The Hydrogen like energy spectrum around the black hole found by other authors, results to be associated, under the same physical condition, to polynomial like radial solutions.