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.

24 pages

References in corpus (14)

• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• First Sagittarius A* Event Horizon Telescope Results. V. Testing Astrophysical Models of the Galactic Center Black Hole
• Measurement of the Kerr Spin Parameter by Observation of a Compact Object's Shadow
• The mass distribution in the Galactic Centre from interferometric astrometry of multiple stellar orbits
• Testing the general relativistic ''no-hair'' theorems using the galactic center black hole SgrA*
• The Kerr Metric
• Analytic solutions of the geodesic equation in higher dimensional static spherically symmetric space-times
• An upper limit on the spin of SgrA${}^{\ast }$ based on stellar orbits in its vicinity
• S62 on a 9.9 yr Orbit around SgrA*
• The Astrophysics of Resonant Orbits in the Kerr Metric
• Detection of faint stars near SgrA* with GRAVITY
• Complete calculations of the perihelion precession of Mercury and the deflection of light by the Sun in General Relativity
• Relativistic orbits of S2 star in the presence of scalar field