Determination of the spin parameter and the inclination angle from the primary and secondary images caused by gravitational lensing

We study the primary images(PIs)and secondary images(SIs)caused by strong gravitational lensing around a Kerr black hole shadow,which carry some essential signatures related to the black hole space-time.We define a new celestial coordinate,whose origin is the center of the black hole shadow,to locate the PIs and SIs of luminous celestial objects.Based on the dragging effect caused by the rotating black hole and the inclination angle of the observer,the relative positions between the PIs and SIs are different for different values of the Kerr spin parameter a and the observer's inclination angle i;hence,it can be used to determine the values of a and i.We propose a specific approach to measure a and i using the PIs and SIs.The time delays between the PIs and SIs are different for different values of a and i.The time delays,in conjunction with the relative positions between the PIs and SIs,can enable us to measure a and i more precisely.These PIs and SIs around the black hole shadow act as unique fingerprints for the black hole space-time,using which we can further determine other parameters of different types of compact objects and verify various theories of gravity.Our results provide a new method to implement parameter estimation in the study of black hole physics and astrophysics.