Determination of the angular momentum of the Kerr black hole from equatorial geodesic motion

Abstract

We present a method to determine the angular momentum of a black hole, based on observations of the trajectories of the bodies in the Kerr space-time. We use the Hamilton equations to describe the dynamics of a particle and present results for equatorial trajectories, obtaining an algebraic equation for the magnitude of the black hole's angular momentum. We tailor a numerical code to solve the dynamical equations and use it to generate synthetic data. We apply the method in some representative examples, obtaining the parameters of the trajectories as well as the black hole's angular momentum in good agreement with the input data.