Observable signatures of RN black holes with dark matter halos via strong gravitational lensing and constraints from EHT observations

We explore the influence of dark matter halos on gravitational lensing produced by electrically charged, spherically symmetric black holes in the strong-field regime. This study delves into the strong gravitational lensing effects within the context of two significant dark matter models: the Universal Rotation Curve Model and the cold dark matter model. Initially, we derive the coefficients for the strong deflection limit and numerically analyze the substantial variations of the deflection angle. Additionally, we present graphical representations of these results. We find that the strong deflection angle, denoted as αD, increases with the rising charge parameter magnitude Q in presence of a dark matter halo. Furthermore, we examine the various astrophysical consequences of the compact objects M87∗ and SgrA∗, as charged black holes, and compare results with those for other astrophysical black holes such as standard Reissner–Nordström (RN) and Schwarzschild black holes, via strong gravitational lensing observations. From our study, the observations point out that it may be possible to quantitatively differentiate and characterize charged black holes with dark matter halos from astrophysical black holes, such as the standard Reissner–Nordström and Schwarzschild black holes. Finally, We constrain the charge parameter Q with the observational data by the Event Horizon Telescope Collaboration for the supermassive black holes M87∗ and SgrA∗. We constrain the charge parameter Q of the charged black holes with universal rotation curve dark matter halo as 0≤|Q|≤0.366M for M87∗, 0≤|Q|≤0.586M for SgrA∗. The charged black hole with cold dark matter halo can be constrained with 0≤|Q|≤0.364M for M87∗, and 0≤|Q|≤0.584M for SgrA∗. It suggests that such charged black holes with dark matter halo satisfy the Event Horizon Telescope constraints. These results suggest, in principle, that it could be possible to identify charged black holes with dark matter halo in the future fine observational campaigns.