Gravitomagnetism in Quantum Mechanics

TL;DR

This paper systematically analyzes the quantum mechanics of a spin-zero particle in combined electromagnetic and weak gravitational fields, focusing on gravitomagnetic effects and the interaction of orbital angular momentum with the gravitomagnetic field.

Contribution

It provides a covariant Klein-Gordon framework and derives a Schrödinger equation form to study gravitomagnetic phenomena in quantum mechanics.

Findings

Orbital angular momentum interacts with gravitomagnetic fields.

Derived observable effects related to gravitomagnetism.

Non-relativistic limit of Klein-Gordon in gravitational and electromagnetic fields.

Abstract

We give a systematic treatment of the quantum mechanics of a spin zero particle in a combined electromagnetic field and a weak gravitational field, which is produced by a slow moving matter source. The analysis is based on the Klein-Gordon equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The Klein-Gordon equation is recast into Schroedinger equation form (SEF), which we then analyze in the non-relativistic limit. We include a discussion of some rather general observable physical effects implied by the SEF, concentrating on gravitomagnetism. Of particular interest is the interaction of the orbital angular momentum of the particle with the gravitomagnetic field.