Novel Properties of Bound States of Klein-Gordon Equation in Gravitational Field of Massive Point

Abstract

We consider for the first time the solutions of Klein-Gordon equation in gravitational field of {\em a massive} point source in GR. We examine numerically the basic bounded quantum state and the next few states in the discrete spectrum for different values of the orbital momentum. A novel feature of the solutions under consideration is the essential dependence if their physical properties on the gravitational mass defect of the point source, even not introduced up to recently. It yields a repulsion or an attraction of the quantum levels up to their quasi-crossing.