Unveiling the unconventional optical signatures of regular black holes within accretion disk

The optical characteristics of three types of black holes (BHs) surrounded by a thin accretion disk are discussed, namely the Schwarzschild BH, Bardeen BH, and Hayward BH. We calculate the deflection angle of light as it traverses the vicinity of each BH using numerical integration and semi-analytical methods, revealing that both approaches can effectively elucidate the deflection of light around the BH. We investigate the optical appearance of the accretion disk and its corresponding observational images at various viewing angles, discovering that the luminosity in the region near the BH on the inner side of the accretion disk is higher than that on the outer side owing to higher material density in closer proximity to the BH. We observe a significant accumulation of brightness on the left side of the accretion disk, attributed to the motion of matter and geometric effects. Our findings emphasize the significant influence of the observation inclination angle on the observed outcomes. An increase in the observation inclination angle results in the separation of higher-order images. With the improvement in EHT observation accuracy, we believe that the feature of a minimal distance between the innermost region of the direct image of the Hayward BH and the outermost region of the secondary image can be used as an indicator for identifying Hayward BHs.