Effect of Non-commutativity on Accretion Disks around RGI-Schwarzschild Black Hole

Abstract: In this study, we explore the combined effects of quantum gravity induced by non-commutativity and scale-dependent gravitational coupling on the thermal properties of the thin accretion disks around a Schwarzschild black hole. We consider a $\kappa$-deformed Renormalization Group Induced (RGI) Schwarzschild black hole, where the classical Schwarzschild black hole geometry is modified by the $\kappa$-deformation of space-time and the running Newton's coupling constant $G(r)$. Using the modified metric, we derive the geodesic motion of massive particles, the effective potential, and the thermal properties such as the radiated energy flux, and the temperature profile of the accretion disk around the $\kappa$-deformed RGI-Schwarzschild black hole. Our study shows that when non-commutativity is combined with the RGI framework, the effects produce a noticeable deviation from the classical Schwarzschild case. In particular, for small values of the deformation parameter, we observe an increase in the peak energy flux and the temperature of the accretion disk. This suggests that quantum gravity corrections enhance the disk's radiative efficiency, especially in the inner regions close to the black hole.