Rotating black-bounce black holes in modified gravity: Photon orbits and shadow

Testing gravity using particle dynamics and black-hole optical signatures is a frontier problem in relativistic astrophysics. We construct the rotating Simpson-Visser modified gravity theory (MOG) spacetime by applying the Newman-Janis algorithm to its static seed and verify the corresponding standard Kerr ( α → 0, b → 0) and non-rotating Simpson-Visser MOG black hole ( a → 0) limits. We derive geodesic equations using the Hamilton-Jacobi formalism, thereby enabling a separable treatment of photon motion and a precise characterization of the photon region, the horizon structure, and the innermost stable circular orbits (ISCOs). Using celestial coordinates for a distant observer, we compute the apparent shadow and extract two observables: the shadow radius R_sh and the Hioki-Maeda distortion parameter δ_sh . Parameter scans reveal distinct roles of the MOG coupling α , the regularization scale b , and the black hole spin a . The parameter α enlarges the shadow radius while mitigating shape distortion, and b reduces the shadow radius and enhances asymmetry. Moreover, due to the dragging effect, a displaces and skews the black hole shadow in the direction of the rotation axis. We further quantify the energy emission rate by combining the horizon temperature with the shadow-inferred capture cross-section, isolating how a, α , and b shift both the peak and amplitude of the spectrum. These results provide observationally accessible, parameter-sensitive signatures that can help discriminate between MOG and the Kerr paradigm in current and future black hole imaging.