Geometric phase for Dirac Hamiltonian under gravitational fields in the non-relativistic regime

TL;DR

This paper demonstrates the emergence of geometric phases in Dirac particles under gravitational fields in the non-relativistic limit, highlighting effects in Kerr and Schwarzschild spacetimes with astrophysical relevance.

Contribution

It extends the concept of geometric phase to Dirac particles in gravitational fields, analyzing effects in different black hole geometries and connecting to known quantum phenomena.

Findings

Geometric phase appears in non-relativistic Dirac particles in gravitational fields.

In Kerr spacetime, both Aharonov-Bohm and Berry phases are observed.

In Schwarzschild spacetime, only the Berry phase is present.

Abstract

We show the appearance of geometric phase in a Dirac particle traversing in non-relativistic limit in a time-independent gravitational field. This turns out to be similar to the one originally described as a geometric phase in magnetic fields. We explore the geometric phase in the Kerr and Schwarzschild geometries, which have significant astrophysical implications. Nevertheless, the work can be extended to any spacetime background including that of time-dependent. In the Kerr background, i.e. around a rotating black hole, geometric phase reveals both the Aharonov-Bohm effect and Pancharatnam-Berry phase. However, in a Schwarzschild geometry, i.e. around a nonrotating black hole, only the latter emerges. We expect that our assertions can be validated in both the strong gravity scenarios, like the spacetime around black holes, and weak gravity environment around Earth.