Flavor interferometry in Reissner-Nordström background

We derive the phase acquired by a neutral scalar particle propagating along Reissner-Nordström geodesics. Considering two flavors propagating on different trajectories which intersect, we plot the interference pattern induced by gravitational lensing from the charged compact object. Although the effect of the charge is subdominant in the metric, it proves to be significant in the phase, and shifts the interference pattern, compared to the Schwarzschild case. This pattern is characterized by two oscillation lengths which, if known, would allow the determination of both eigenmasses independently.