Gravitationally Induced Quantum Mechanical Phases and Neutrino Oscillations in Astrophysical Environments

We report a new effect of gravitationally induced quantum mechanical phases in neutrino oscillations. In the neighborhood of a neutron star, gravitationally induced quantum mechanical phases are roughly $15 \%$ of their kinematical counterparts. When this information is coupled with the mass square differences implied by the existing neutrino--oscillation data we find that the new effect may have profound consequences for supernova explosions.