Influence of Quantum Correction on the Black Hole Shadows, Photon Rings and Lensing Rings

We calculate the photon sphere $r_{ph}$ and critical curve $b_c$ for the quantum corrected Schwarzschild black hole, finding that they violate an universal inequalities proved for asymptotically flat black holes which satisfy null energy condition in the framework of Einstein gravity. This violation seem 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 thin disk emission near the black hole compared with the classical Schwarzschild black hole. Our analysis may provide a observational evidence for quantum effect of general relativity.
Comment: LaTex, 13 pages, 3 figures, 1 table