Testing the black hole no-hair theorem at the galactic center

Precessions of the orbital planes of stars orbiting the galactic centre black hole depend only on the angular momentum and quadrupole moment of the central black hole. Therefore, studying precessions of the orbital planes of several stars can provide a way to test the black hole no-hair theorem, which requires that $Q=-J^2/M$. Such a measurement would give conclusive evidence that the galactic center object is really a black hole [1]. We are studying other factors that might perturb these orbits, including gravitational interaction with a population of other stars orbiting the GCBH. Using standard orbital perturbation theory, we have calculated analytically the time averaged rates of change of all the orbit elements of the target star caused by a given perturbing star and also, the r.m.s orbital plane precessions due to a population of perturbing stars inside and outside the orbit of the target star. We compare the results with those from numerical simulations [2]. Supported in part by the NSF, PHY 06-52448 and 09-65133. \\[4pt] [1] C. M. Will, Astrophys. J. Lett. 674, L25 (2008)\\[0pt] [2] D. Merritt et al., Phys. Rev. D 81, 062002 (2010)