Determining parameters of Kerr-Newman black holes by shadow observation from finite distance and spatial infinity

Abstract

We present a method for determining the physical parameters of a Kerr-Newman black hole through shadow observation. In a system comprising a Kerr-Newman black hole, an observer, and a light source, the relevant parameters are mass $M$, specific angular momentum $a$, electric charge $Q$, inclination angle $i$, and distance $r_o$. We consider the cases where the observer is at either a finite distance or spatial infinity. Using our method, the dimensionless parameters $(a/M, Q/M, i)$ can be determined by observing the shadow contour of the Kerr-Newman black hole from spatial infinity. We analytically prove that the shadow contour of the Kerr-Newman black hole observed from spatial infinity is unique, where uniqueness is defined as the absence of two congruent shadow contours for distinct sets of dimensionless parameter values. This method is versatile and can be applied to a range of black hole solutions with charge. Additionally, we show analytically that the shadow contour of a Kerr-Newman black hole observed from a finite distance $r_o$ is not unique, meaning that the parameters of a Kerr-Newman black hole at finite distance cannot be determined from shadow observations. This result reveals a new challenge and provides a clear direction for further research on black hole shadows.