Influence of quantum correction on black hole shadows,photon rings,and lensing rings

We calculate photon sphere begin{document}$r_{ph}$end{document} and critical curve begin{document}$b_c$end{document} for a quantum corrected Schwarzschild black hole, finding that they violate universal inequalities proved for asymptotically flat black holes that satisfy the null energy condition in the framework of Einstein gravity. This violation seems to be a common phenomenon when considering quantum modification of Einstein gravity. Furthermore, we study the shadows, lensing rings, and photon rings in the quantum corrected Schwarzschild black hole. The violation leads to a larger bright lensing ring in the observational appearance of the thin disk emission near the black hole compared with the classical Schwarzschild black hole. Our analysis may provide observational evidence for the quantum effect of general relativity.