Thermodynamic properties, weak gravitational lensing, and parameter estimation using S2 star data of a 4D polymerized nonrotating loop quantum gravity motivated black hole

In this paper, we delve into studying thermodynamic properties, “lifetime,” weak gravitational lensing of Loop quantum gravity (LQG) motivated polymerized black hole (BH). Our study reveals that an LQG black hole attains a nonzero remnant mass at the end of the evaporation process, signified by zero Hawking temperature and heat capacity. The remnant mass, Formula: see text, depends on the LQG parameter Formula: see text. Owing to this nonzero remnant mass, the black hole can retain some information, which is not true for a Schwarzschild black hole. The Hawking temperature peaks at Formula: see text where we have local phase transition and the heat capacity diverges. We further probe the nature of Gibbs free energy and pressure for an LQG black hole to reveal its additional thermodynamic properties. We then move on to explore the dependence of the lifetime of an LQG black hole and the weak deflection angle on the parameter Formula: see text. Finally, using the periastron precession of the S2 star in Formula: see text, we obtain the upper bound on the LQG parameter, which comes out to be Formula: see text. Our result shows that LQG BH is consistent with the observed result for Formula: see text, making LQG BH a viable candidate for supermassive BH.