Regular charged black hole: Implications for weak field gravitational lensing

We investigate gravitational lensing within the framework of general relativity, focusing particularly on the deflection angle calculations in the weak field limit around a regular charged black hole. The presence of an inherited-centered singularity highlights the complex nature of black holes following gravitational collapse. However, non-linear electrodynamics (NLED) proposes the intriguing concept of a non-singularity, introducing new perspectives to this discussion. Our methodology explicitly incorporates NLED's role in determining the effective geometry of photons, advancing beyond standard metric analyses. The exact solution identifies a new correction term in the deflection angle that is specifically comparable to that of Reissner-Nordstrom (R.N.) model. These distinctive terms in the lensing effects significantly alter the sequence of shifts in the third angular images of a regular charged black hole. This analysis deepens our understanding of the complex interactions between a regular charged black hole and gravitational lensing. Future astronomical observations will be integral to corroborating these theoretically posited models, providing observational validation and potentially elucidating our theoretical framework.