Neutrino dynamics in a non-commutative spacetime

We investigate neutrino dynamics in a spherically symmetric non-commutative black hole spacetime generated by a Lorentzian smeared matter distribution. We work with the leading-order Lorentzian-smeared metric, in which the non-commutative parameter $\Theta$ enters explicitly through a $\sqrt{\Theta}$ correction to the Schwarzschild geometry. Within this background, we analyze the neutrino-antineutrino annihilation process, the oscillation phase acquired by massive neutrinos along geodesics, and the flavor-transition probability in the presence of weak gravitational lensing. We show that non-commutativity monotonically suppresses the relativistic energy deposition rate relative to the Schwarzschild case, while the Newtonian behavior is recovered at large radii. In the oscillation sector, the weak-field phase receives explicit $\sqrt{\Theta}$ corrections, which modify the distance of closest approach and reduce the accumulated phase with respect to the Schwarzschild limit. For lensed trajectories, the macroscopic transition probabilities remain close to the Schwarzschild prediction; however, a high-precision residual analysis reveals a coherent, non-vanishing oscillatory correction driven by the non-commutative geometry. The dependence on the absolute neutrino mass scale enters only through multi path interference terms and remains subdominant compared with the $\Theta$-induced phase shift. The full three-flavor residual analysis confirms that the same non-commutative oscillatory pattern persists beyond the effective two-flavor approximation.