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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 $$Q_\text {m}$$ Q m and the screening factor $$\gamma $$ γ . 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 $$Q_\text {m}$$ Q m and $$\gamma $$ γ . 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.

In this paper, we investigated the effect of dark matter on the weak deflection angle by black holes at the galactic center. We consider three known dark matter density profiles such as the Cold Dark Matter, Scalar Field Dark Matter, and the Universal Rotation Curve from the Burkert profile. To achieve this goal, we used how the positional angles are measured by the Ishihara et al. method based on the Gauss–Bonnet theorem on the optical metric. With the help of the non-asymptotic form of the Gauss-Bonnet theorem, the longitudinal angle difference is also calculated. First, we find the emergence of apparent divergent terms on the said profiles, which indicates that the spacetime describing the black hole-dark matter combination is non-asymptotic. We showed that these apparent divergent terms vanish when the distance of the source and receiver are astronomically distant from the black hole. Using the current observational data in the Milky Way and M87 galaxies, we find interesting behaviors of how the weak deflection angle varies with the impact parameter, which gives us some hint on how dark matter interacts with the null particles for each dark matter density profile. We conclude that since these deviations are evident near the dark matter core radius, the weak deflection angle offers a better alternative for dark matter detection than using the deviation from the black hole shadow. With the dark matter profiles explored in this study, we find that the variation of the values for weak deflection angle strongly depends on the dark matter mass on a particular profile.

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