Gravitational lensing of neutrinos in parametrized black hole spacetimes

We consider gravitational lensing of neutrinos in a black hole geometry that parametrizes departures from the Schwarzschild spacetime in the weak-field limit with plane-wave approximation. We use the Rezzolla-Zhidenko parametrization and apply the analysis to the effects of spatial curvature deviations from GR to a hypothetical system with a central object of mass of the order of a solar mass and a detector located at an Earth-like distance from the source. We find that the deformation parameters of the metric can have significant impact on the oscillation probabilities of the neutrinos. We also investigate the role of decoherence on flavor oscillations of the lensed neutrinos and show that the parameters of the metric do not have significant effect on the decoherence length.