Photon Dynamics and Frequency Shift in a Regular Magnetic Black Hole

In this study, we investigate the geometrical and optical properties of a regularized black-hole spacetime and examine how the model parameter Q modifies its strong-field structure. We first analyze the radial behavior of the metric function and determine the corresponding event horizon from the condition f(rₑₕ) = 0. The results show that increasing Q/M shifts the event horizon toward smaller radii, indicating a systematic modification of the near-horizon geometry. The curvature structure is further examined using the Kretschmann scalar, which demonstrates that the influence of Q is most pronounced in the inner region of the spacetime and becomes weaker at larger distances. We then study null geodesics through the photon effective potential and determine the radius of the circular photon orbit. In the Schwarzschild limit, the photon sphere approaches rₚₕ = 3M, while increasing Q/M causes it to move inward. The frequency shift of photons emitted by particles on circular geodesics is also analyzed. The obtained profiles show that the magnitude of the frequency shift decreases with increasing radial distance and with increasing Q/M, with the strongest variations occurring in the strong-field region. Taken together, these results indicate that the parameter Q affects the horizon structure, spacetime curvature, photon-sphere location, and frequency shift in a consistent manner, providing a unified picture of how the modified geometry influences photon dynamics.

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