On Constraining the Kerr Metric of the Massive Black Hole in the Galactic Center through the Relativistic Orbital Motion of the Closest Star: Full General Relativistic Treatment

The S-stars discovered in the vicinity of the massive black hole in the Galactic center are anticipated to be able to provide unique dynamical constraint on the MBH spin and metric. In this work we develop a full general relativistic method to simultaneously constrain the MBH mass, spin and spin direction using the Markov Chain Monte Carlo fitting technique. We illustrate that the spin of the GC MBH is likely to be well constrained by using the motion of S0-2/S2 over a period of ~30-45 yr if the astrometric and spectroscopic accuracies are 10 uas, 1km/s, respectively, which may be realized by the future instruments and telescopes. In the mean time, the distance from the sun to the GC and the MBH mass can also be constrained to a unprecedented accuracy (0.01%-0.1%). Our results suggest that long term monitoring of the motions of stars in the vicinity of the GC MBH by the next generation instruments and telescopes is likely to provide an ultimate dynamical test for the first time to the no-hair theorem and the general relativity.