# 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.

## Key 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.