Auto- and cross-correlations for multiple images of corotating hotspots in accretion disks

Because of the short gravitational timescale of Sgr A*, variable emissions near the galactic center are expected in the very-long-baseline interferometry observations. Phenomenologically, the high-flux variable emissions could be interpreted as occasional events from hotspots within accretion disks. It provides a probe of black hole (BH) geometry and accretion matter in the strong-field regime of gravity. In this study, we find that light curve profile alone is not proper for distinguishing BH geometries, as our results show that the profiles, even including those from higher-order images, are dependent on hotspot shapes, which are known in practice as amorphous. To alleviate this situation, we examine the spatial-temporal correlations between multiple images of the corotating hotspots. Our results find that the correlations, particularly those from higher-order images, could serve as a robust observable to reflect the inclination angles and BH geometries, because (i) the correlated band structure is independent of the hotspot shapes and (ii) the correlations from higher-order images could encode BH geometries and exhibit no overlap with observational signatures from the lower-order ones. We present a comprehensive study on correlations from primary the eighth-order images with various orbital configurations and inclination angles and show its observational signatures. It is expected that BH geometries can be inferred via the spatial-temporal correlation analysis.