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This paper explores gravitational phenomena associated with a non-commutativeblack hole. Geodesic equations are derived, and a thin accretion disk isanalyzed to model the black hole shadow image, considering an optically thin,radiating, and infalling gas. Retrolensing effects are examined to trace photonemission configurations, while gravitational lensing is investigated throughweak and strong deflection limits, with lensing equations and observablesapplied to Sagittarius A*. The study also includes calculations of time delay,energy deposition rate from neutrino annihilation, phase and probability ofneutrino oscillation, and neutrino gravitational lensing.

Geodesics, accretion disk, gravitational lensing, time delay, and effects on neutrinos induced by a non-commutative black hole