Gup-corrected black holes: thermodynamic properties, evaporation time and shadow constraint from EHT observations of M87 and Sgr A

In this manuscript, we implement the generalized uncertainty principle (GUP) with linear and quadratic moment for Schwarzschild black hole metric in order to study the influence of quantum effect on the thermodynamics and evaporation of black hole. To this end, we first derive the GUP-modified Hawking temperature of a black hole in the semi-classical framework. Due to the existence of the GUP effect, there is a maximum Hawking temperature. We determine the entropy, heat capacity and Helmholtz free energy with heuristic analysis that investigates the particle absorbed by black hole. Furthermore, we also verify that these quantities are modified by the GUP, the influence of quantum effect on the black hole phase transition is discussed in detail. Then, we analyze the black hole evaporation process in the mentioned framework and examine the obtained results by graphical methods and compare them with each other. We likewise explore the behavior of the event horizon radius, photon sphere radius, and shadow silhouette when influenced by the GUP-corrected Schwarzschild black hole (GCSBH) parameters. We intend to establish restrictions for α by utilizing the event horizon telescope (EHT) data for M87* and Sagittarius A* (Sgr A*). Our findings show that Sgr A* provides more robust constraints. As the parameter β grows, the range of constraints for α expands. For Sgr A* one, we find that the shadow radius is close to the observed value at smaller values of α .