Images and flares of geodesic hotspots around a Kerr black hole

In this study, we develop a numerical method to generate images on an observer's screen, formed by radiation from hotspots 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 hotspots 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 lightcurve. Notably, we observe flare phenomena across all orbit types and classify these flares into three categories based on the Doppler and gravitational redshift effects.