Abstract
Abstract
This study investigates how dark matter in the background of the phantom field (DMPF) near a black hole influences neutrino flavor oscillations using a two-flavor model. It is found that gravitational effects are cancelled for radially moving neutrinos, causing the oscillation phase to increase with distance and mass-splitting, similar to flat spacetime. However, deflected neutrinos experience additional phase shifts due to dark matter, which slightly alters the mass-difference term and the total phase. Numerical analysis supports these findings and reveals a degeneracy between lens mass and dark matter parameters, affecting the transition probability curves based on source angle changes. Neutrinos modeled as Gaussian wave packets show that decoherence in a gravitational field is minimally influenced by dark matter, with the absolute neutrino mass determining the oscillation duration. Our findings imply that curved spacetime and dark matter significantly impact neutrino oscillations, offering potential insights into dark matter through neutrino astronomy in extreme environments.