Probing the quantum speed limit and entanglement in flavor oscillations of neutrino-antineutrino system in curved spacetime

We consider a spinning primordial black hole (PBH) described by the Kerr metric in Kerr-Schild polar coordinates. We derive an analytical expression for the four-vector gravitational potential in the underlying Hermitian Dirac Hamiltonian using these coordinates. This gravitational potential introduces an axial vector term in the Dirac equation in curved spacetime. We find that the magnitudes of the temporal and spatial components of the four-vector gravitational potential are significantly affected by the angle of the position vector of the spinor with respect to the spin axis of the PBH, its radial distance from the PBH, and the strength of the specific angular momentum of the PBH. These potentials modify the effective mass matrix of the neutrino-antineutrino system and significantly affect the transition probabilities during the flavor oscillation of the neutrino-antineutrino system. We then use the transition probability to investigate the quantum speed limit time bound ratio for the two-flavor oscillation of the neutrino-antineutrino system in curved spacetime. This helps us estimate how quickly the initial neutrino flavor state evolves over time under the influence of the gravitational field. Finally, we discuss quantum correlations such as entanglement entropy during the two-flavor oscillation of the neutrino-antineutrino system near a spinning PBH.