Can a Dehnen-type dark matter halo affect the neutrino flavor oscillations?

The gravitational weak lensing of neutrinos in the presence of a Schwarzschild black hole surrounded by a Dehnen-type dark matter halo is investigated. The event horizon structure is explored, and the existence of the BH is studied in two different slices of the parameter space. Additionally, we derive analytic expressions for the oscillation phase and transition probabilities for both radial and non-radial neutrino propagation. Finally, we use a two-flavor toy model, and numerically analyze how the dark matter halo parameters as density and scale radius, affect oscillation probabilities and examine the role of decoherence. The results show that the presence of a dark matter halo modifies the oscillation phase and damping factor, leading to measurable deviations from the standard Schwarzschild BH case. These findings suggest that neutrino oscillations could, in principle, serve as a probe for dark matter distributions around compact astrophysical objects.