Neutrino interferometry in curved spacetime

Gravitational lensing introduces the possibility of multiple (macroscopic) paths from an astrophysical neutrino source to a detector. Such a multiplicity of paths can allow for quantum mechanical interference to take place that is qualitatively different from neutrino oscillations in flat space. After an illustrative example clarifying some underappreciated subtleties of the phase calculation, we derive the form of the quantum mechanical phase for a neutrino mass eigenstate propagating nonradially through a Schwarzschild metric. We subsequently determine the form of the interference pattern seen at a detector. We show that the neutrino signal from a supernova could exhibit the interference effects we discuss were it lensed by an object in a suitable mass range. We finally conclude, however, that—given current neutrino detector technology—the probability of such lensing occurring for a (neutrino-detectable) supernova is tiny in the immediate future.