Observable Signatures of RN Black Holes with Dark Matter Halos via Strong Gravitational Lensing and Constraints from EHT Observations

We investigate the impact of dark matter halos on the gravitational lensing produced by electrically charged, spherically symmetric black holes in the strong-field regime. The study focuses on two dark matter models: the Universal Rotation Curve Model and the cold dark matter model. We derive the coefficients for the strong deflection limit and numerically analyze the deflection angle variations. Graphical representations of the results show that the strong deflection angle, $\alpha_D$ , increases with the charge parameter $Q$ in the presence of a dark matter halo. We explore the astrophysical consequences for the supermassive black holes $M87^*$ and $SgrA^*$ , comparing the results with standard Reissner-Nordstr\"{o}m and Schwarzschild black holes via strong gravitational lensing observations. Our findings suggest that charged black holes with dark matter halos can be differentiated from standard black holes. We constrain the charge parameter $Q$ using observational data from the Event Horizon Telescope Collaboration. For $M87^*$ , we find $0 \leq |Q| \leq 0.366M$ with the Universal Rotation Curve model and $0 \leq |Q| \leq 0.364M$ with the cold dark matter model. For $SgrA^*$ , the constraints are $0 \leq |Q| \leq 0.586M$ and $0 \leq |Q| \leq 0.584M$, respectively. These results suggest that charged black holes with dark matter halos satisfy the Event Horizon Telescope constraints, offering potential for future identification in observational campaigns.