Optical Images of the Braneworld Black Hole Surrounded by an Optically Thin Accretion Disk

Abstract

This work examines the observational signatures of rotating black holes with tidal charge in the Randall--Sundrum braneworld scenario. Combining an elliptic-integral-based analytical treatment with numerical ray tracing, we characterize photon motion around braneworld black holes in detail. For small observer inclinations, secondary images remain embedded inside the primary emission rings. As the inclination becomes larger, the primary and secondary images gradually separate and produce a strongly asymmetric image morphology. We show that the image asymmetry and the deformation of the inner shadow are jointly controlled by the black hole spin, the tidal charge, and the observer inclination. To analyze the frequency shifts across the accretion disk, we extend the emitting region from the ISCO down to the event horizon by including the plunging flow. The results indicate that the observer inclination is the dominant factor governing the frequency-shift distribution. In addition, we reconstruct braneworld black hole images using a fisheye-lens ray-tracing model. The optical morphology and brightness distribution show a clear dependence on the observing frequency, especially when comparing 230~GHz with 86~GHz. We also contrast the brightness distributions of prograde and retrograde disks, finding that both the total intensity and the peak intensity at 86~GHz are higher than those at 230~GHz. For negative values of the tidal charge, we further investigate the corresponding frequency-shift behavior and 230~GHz intensity profiles, which may provide useful theoretical guidance for future studies of extra-dimensional gravity models.