Gravitational effects on quantum coherence in neutrino oscillation

Abstract

In this paper, we investigate the quantum coherence for two flavor neutrinos propagating in a Schwarzschild metric. In fact, this issue is explored both qualitatively via calculating the parameter ${K}_{3}$ in Leggett-Garg inequality and also quantitatively by evaluating the ${l}_{1}$-norm, $\mathcal{C}(\ensuremath{\rho})$. Using the weak field approximations, we show that the gravitational effects decrease the maximum value of ${K}_{3}$ for some intervals of energy in such a way that there is no violation, while it leaves the maximum amount of the quantum coherence, $\mathcal{C}(\ensuremath{\rho})$, unchanged.