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

TL;DR

This paper investigates the solutions of the Klein-Gordon equation in the gravitational field of a massive point source in general relativity, revealing how quantum states depend on the gravitational mass defect and exhibit phenomena like level repulsion or attraction.

Contribution

It is the first study to analyze Klein-Gordon solutions in the gravitational field of a massive point source, highlighting the impact of mass defect on quantum state properties.

Findings

Quantum states depend on the gravitational mass defect.

Existence of level repulsion and attraction phenomena.

Numerical analysis of discrete spectrum states.

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.