Strong Gravitational Lensing and Shadows by Quantum Schwarzschild Black Hole in Homogeneous Plasma

In this paper, we investigate the strong gravitational effects of a quantum Schwarzschild black hole in the presence of homogeneous plasma, focusing on the impact of the polymerization parameter lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}. The analytical expression for the deflection angle in a strong field limit in a quantum Schwarzschild black hole surrounded by homogeneous plasma is derived. It is found that both the polymerization parameter lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document} and the presence of uniform plasma can lead to an increase in the strong field parameters a<overline>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{a}$$\end{document} and b<overline>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{b}$$\end{document} and deflection angle alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}(b). Further, we performed the numerical calculation for the lensing observables, such as the angular position of the innermost image, the angular separation between the outermost image and the remaining image, the relative magnification, and the time delay between images on opposite sides of the lens for the supermassive black hole SgrA* in strong field limit, considering the effects of homogeneous plasma. We also studied the effect of plasma on the radius of the shadow. In conclusion, the polymerization parameter lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document} and the presence of homogeneous plasma significantly affect the characteristics of shadows and strong gravitational lensing.