Includes Indexes and References

The study of black holes has advanced significantly, especially after the Event Horizon Telescope (EHT) provided direct images that revealed photon rings—key probes of the strong-field regime of general relativity (GR). While most studies focus on the Kerr solution, astrophysical black holes may carry charge and exist in an expanding universe characterized by a cosmological constant. The Kerr–Newman–de Sitter (KNdS) metric extends the Kerr geometry by including both electric charge and cosmological constant Λ, resulting in richer space-time structures with distinct observational signatures. However, the role of charge in shaping photon rings within KNdS space-time remains insufficiently explored. This work presents an analytic investigation of charge imprints on photon ring structure in KNdS black holes. Using the Hamilton–Jacobi formalism, we derive null geodesic equations and employ Mino time parametrization to decouple the motion, allowing radial and angular integrals to be expressed via Jacobi elliptic functions. These solutions enable analytic ray tracing to reconstruct direct images, lensing rings and photon rings under varying charge and cosmological constant values. We further compute observables, including time delay, Lyapunov exponent, and azimuthal angle deviation, which describe how photons orbit before escaping to a distant observer. Our results show that charge modifies photon ring radius, shape and intensity profile and influences the thickness and separation of subrings, altering the predicted self-similar structure. These findings suggest that charge introduces measurable deviations from the Kerr case, offering potential observational signatures to distinguish charged from uncharged black holes.