Shadow, lensing, quasinormal modes, greybody bounds and neutrino propagation by dyonic ModMax black holes

Motivated by recent work on the Modified Maxwell (ModMax) black holes [Phys Lett B 10.1016/j.physletb.2020.136011], which are invariant in duality rotations and conformal transformations founded in [Phys Rev D 10.1103/PhysRevD.102.121703], we probe its effects on the shadow cast, weak field gravitational lensing, and neutrino propagation in its vicinity. Using the EHT data for the shadow diameter of Sgr. A* and M87*, and LIGO/VIRGO experiments for the dyonic ModMax black hole perturbations, we find constraints for ModMax parameters such as Qm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q_\text {m}$$\end{document} and the screening factor gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}. We also analyze how the shadow radius behaves as perceived by a static observer and one that is comoving with the cosmic expansion. The effect of the ModMax parameters is constant for a static observer, and we found That it varies when the observer is comoving with cosmic expansion. We also analyzed its effect on the weak deflection angle by exploiting the Gauss-Bonnet theorem and its application to Einstein ring formation. We also consider the finite distance effect and massive particle deflection. Our results indicate that the far approximation of massive particle gives the largest deflection angle and amplifies the effect of Qm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q_\text {m}$$\end{document} and gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}. Then we also calculate the quasinormal modes and greybody bounds which encode unique characteristic features of the dyonic ModMax black hole. With the advent of improving space technology, we reported that it is possible to detect the deviation caused through the shadow cast, Einstein rings, quasinormal modes, and neutrino oscillations.