Gravity-Induced Geometric Phases and Entanglement in Spinors and Neutrinos: Gravitational Zeeman Effect

TL;DR

This paper demonstrates how gravitational fields induce Zeeman-like splitting, geometric phases, and entanglement in spinors and neutrinos, revealing novel gravitational effects on quantum states.

Contribution

It introduces the gravitational Zeeman effect, analyzes geometric phases in neutrinos under gravity, and explores gravity-induced neutrino-antineutrino entanglement and oscillations.

Findings

Spinors exhibit Zeeman-like energy splitting in gravitational fields.

Neutrinos acquire geometric phases in strong gravitational backgrounds.

Gravity can induce entanglement and oscillations between neutrino and antineutrino states.

Abstract

We show Zeeman-like splitting in the energy of spinors propagating in a background gravitational field, analogous to the spinors in an electromagnetic field, otherwise termed the Gravitational Zeeman Effect. These spinors are also found to acquire a geometric phase, in a similar way as they do in the presence of magnetic fields. However, in a gravitational background, the Aharonov-Bohm type effect, in addition to Berry-like phase, arises. Based on this result, we investigate geometric phases acquired by neutrinos propagating in a strong gravitational field. We also explore entanglement of neutrino states due to gravity, which could induce neutrino-antineutrino oscillation in the first place. We show that entangled states also acquire geometric phases which are determined by the relative strength between gravitational field and neutrino masses.