Measuring the spin parameter of kerr black holes and naked singularities

The possibility that the existence of black holes as compact objects at the cores of galaxies has become high. The black hole is said to cast an apparent shape (or a shadow) as an optical appearance because of the strong gravitational field in the black hole itself. The apparent shape is of varied forms mainly depending on the spin parameter and the inclination angle of the object. In this paper, we investigate whether it is possible to determine the spin parameter and the inclination angle by observing the apparent shape, on the assumption that the intended compact object is the Kerr space-time. In particular, we define observables which definitely characterize the apparent shape. We find that one can estimate the spin parameter and the inclination angle of the Kerr black hole even when it is naked singularity, by measuring the observables. As a prerequisite, one needs only information of the mass of the object to say so. The result will become a realistic method which come a step closer to probe the Galactic centre using future advanced interferometers.