Testing the general relativistic ``no-hair'' theorems using the galactic center black hole SgrA*

If a class of stars orbits the central black hole in our galaxy in short period ($\sim 0.1$ year), high eccentricity ($\sim 0.9$) 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 $\mu$arcseconds per year, if the black hole is rotating faster than 1/2 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 ${\bf J}$ of the black hole and its quadrupole moment $Q_2$. This could lead to a test of the general relativistic no-hair theorems, which demand that $Q_2 = - J^2/M$. Future high-precision adaptive infrared optics instruments may make such a fundamental test of the black-hole paradigm possible.