Testing the General Relativistic "No-Hair" Theorems Using the Galactic Center Black Hole Sagittarius A*

If a class of stars orbits the central black hole in our galaxy in short-period (~0.1 yr), high-eccentricity (~0.9) orbits, they will experience precessions of their orbital planes induced by both relativistic frame dragging and the quadrupolar gravity of the hole, at levels that could be as large as 10 μas per year, if the black hole is rotating faster than half of its maximum rotation rate. Astrometric observations of the orbits of at least two such stars can in principle lead to a determination of the angular momentum vector \boldsymbol{J} of the black hole and its quadrupole moment Q₂. This could lead to a test of the general relativistic no-hair theorems, which demand that Q₂ = - J²/M. Future high-precision adaptive infrared optics instruments may make such a fundamental test of the black hole paradigm possible.