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

european physical journal. c, particles and fields

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