Investigating the Connection between Generalized Uncertainty Principle and Asymptotically Safe Gravity in Black Hole Signatures through Shadow and Quasinormal Modes

The links between the deformation parameter $\beta$ of the generalized uncertainty principle (GUP) to the two free parameters $\widehat{\omega }$ and $\gamma$ of the running Newtonian coupling constant of the Asymptotic Safe gravity (ASG) program, has been conducted recently in [Phys.Rev.D 105 (2022) 12, 124054]. In this paper, we test these findings by calculating and examining the shadow and quasinormal modes of black holes and demonstrate that the approach provides a theoretical framework for exploring the interplay between quantum gravity and GUP. Our results confirm the consistency of ASG and GUP and offer new insights into the nature of black holes and their signatures. The implications of these findings for future studies in quantum gravity are also discussed.