Images and flares of geodesic hot spots around a Kerr black hole
Jiewei Huang, Zhenyu Zhang, Minyong Guo, Bin Chen
Abstract
In this study, we develop a numerical method to generate images on an observer's screen, formed by radiation from hot spots on any timelike orbits outside a black hole. This method uses the calculation of fractional numbers, enabling us not only to produce the overall image but also to distinguish between primary, secondary, and higher-order images. Building upon this, we compute the images of hot spots from eight potential types of geodesic timelike orbits outside a Kerr black hole, summarizing the properties of both the overall and individual order images. Furthermore, we calculate the centroid motion and light curve. Notably, we observe flare phenomena across all orbit types and classify these flares into three categories based on the Doppler and gravitational redshift effects.