Spin 0 and spin 1/2 particles in a spherically symmetric static gravity and a Coulomb field

TL;DR

This paper investigates the energy levels of spin 0 and spin 1/2 particles in combined Coulomb and gravitational fields, showing their relativistic and nonrelativistic behaviors are consistent.

Contribution

It provides a perturbative analysis of relativistic particles in combined Coulomb and gravitational fields, comparing spin 0 and spin 1/2 cases.

Findings

Energy levels coincide for spin 0 and spin 1/2 particles.

Results match nonrelativistic Schrödinger equation in the appropriate limit.

Gravitational effects are incorporated perturbatively.

Abstract

A relativistic particle in an attractive Coulomb field as well as a static and spherically symmetric gravitational field is studied. The gravitational field is treated perturbatively and the energy levels are obtained for both spin 0 (Klein-Gordon) and spin 1/2 (Dirac) particles. The results are shown to coincide with each other as well as the result of the nonrelativistic (Schrodinger) equation in the nonrelativistic limit.