Gravitational Influence on the Quantum Speed Limit in Flavor Oscillations of Neutrino-Antineutrino System

TL;DR

This paper explores how the gravitational field of a spinning primordial black hole affects the quantum speed limit in neutrino-antineutrino flavor oscillations, revealing significant influence on transition probabilities and state evolution.

Contribution

It derives an analytical gravitational potential in curved spacetime and demonstrates its impact on the quantum speed limit in neutrino oscillations, a novel integration of gravity and quantum dynamics.

Findings

Gravitational field significantly alters transition probabilities.

The gravitational potential affects the quantum speed limit in neutrino oscillations.

Analysis of the Bures angle reveals gravity's role in quantum state evolution.

Abstract

We investigate the quantum speed limit (QSL) during the time evolution of neutrino-antineutrino system under the influence of the gravitational field of a spinning primordial black hole (PBH). We derive an analytical expression for the four-vector gravitational potential in the underlying Hermitian Dirac Hamiltonian using the Boyer-Lindquist (BL) coordinates. This gravitational potential leads to an axial vector term in the Dirac equation in curved spacetime, contributing to the effective mass matrix of the neutrino-antineutrino systems. Our findings indicate that the gravitational field, expressed in BL coordinates, significantly influences the transition probabilities in two-flavor oscillations of the neutrino-antineutrino system. We then apply the expression for transition probabilities between states to analyze the Bures angle, which quantifies the closeness between the initial and final states of the time-evolved flavor state. We use this concept to probe the QSL for the time evolution of the initial flavor neutrino state.