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

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