Gravitational Phenomena of a Non–Commutative Charged Black Hole

This work presents a comprehensive investigation of the gravitational phenomena that correspond to a non–commutative charged black hole, by incorporating non–commutative geometry through a (r, θ) Moyal twist. We derive the deformed metric up to the second order of non–commutative parameter Θ, utilizing the Seiberg–Witten map for Reissner–Nordstr¨om black hole. We explore how non–commutativity modifies key thermodynamic properties, such as the Hawking temperature and heat capacity, and the existence of a remnant mass at the final stage of the evaporation. Additionally, the study of Hawking radiation for bosonic and fermionic particles is discussed. Applying a perturbative method, scalar quasinormal modes are analyzed numerically. Furthermore, null geodesics and photon sphere stability are explored via curvature and topological methods. The shadow radius and deflection angle are computed to understand observational signatures. Lensing observables are compared to Event Horizon Telescope (EHT) observations to provide probable constraints on the non-commutativity parameter. This study bridges theoretical predictions with astrophysical observations, offering insights into quantum gravity effects on black hole physics.