Probing rotating Hayward black holes: magnetic-charge-induced distortions, dynamic shadows, and polarization patterns*

Abstract This study investigates the imaging properties, photon-ring structure, and polarization signatures of rotating Hayward black holes, endowed with magnetic charges. We first derive the null geodesic and polarization parallel-transport equations in the rotating Hayward spacetime and cast them into a unified system of first-order differential equations suitable for numerical ray tracing. Using a fisheye camera model, together with an angular normalization scheme, we generate black hole images illuminated by both a spherical emission source and prograde/retrograde optically thin accretion disks to analyze the resulting redshift distribution and strong gravitational lensing features. By incorporating a set of representative magnetic-field configurations—including radial, polar, toroidal, and helical geometries—we compute the corresponding polarization maps and reveal how magnetic-field structure, black-hole spin, and magnetic charge shape the electric-vector position angle and polarization intensity. Our results show that magnetic charge induces a pronounced “D-shaped” distortion of the black hole shadow and enhances the polarization structure of the photon ring. We further observe that rotating Hayward black holes exhibit observable differences from Kerr black holes in their shadow morphology, photon-ring profiles, and polarization patterns. These findings offer theoretical predictions for future ground- and space-based interferometric observations and provide potential observational diagnostics for distinguishing between conventional Kerr and regular black hole models.