Thermodynamic Properties and Shadow of a New, Improved Schwarzschild Black Hole in the Infrared Limit

In this work, we propose a modified Schwarzschild geometry inspired by the Asymptotic Safety approach to quantum gravity, in which the Newtonian coupling becomes a running quantity depending on the radial coordinate. We employ an infrared cutoff at the proper distance and obtain a new quantum-corrected black hole metric. We provide a thermodynamical analysis, first using standard methods and then proceeding to a geometrothermodynamical study of the phase space and to a topological analysis of phase transitions. We also calculate the grey-body factors of our solution, providing exact lower bounds in the quantum-corrected transmission coefficients. Finally, we present the shadow size and intensity profile of our solution, showing its consistency with current observational constraints.