Flavour interferometry in Reissner-Nordstrom background

We derive the phase acquired by a neutral scalar particle propagating along Reissner-Nordstrom geodesics. Considering two flavours 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 characterised by two oscillation lengths which, if known, would allow the determination of both eigen masses independently.