\begin{abstract}

The spin and quadrupole moment of the supermassive black hole = at

the Galactic center can in principle be measured via = astrometric monitoring

of stars orbiting at milliparsec (mpc) = distances, allowing tests of

general relativistic = ``no-hair''theorems \cite{Will-08}.

One complicating factor is = the presence of perturbations from other

stars, which may = induce orbital precession of

the same order of magnitude as = that due to general relativistic effects.

The expected number = of stars in this region is small enough that full=A0

$N$-body = simulations can be carried out.

We present the results of a = comprehensive set of such simulations,

which include a = post-Newtonian treatment of spin-orbit effects.

A number of = possible models for the distribution of stars and

stellar = remnants are considered.

We find that stellar perturbations = are likely to obscure the

signal due to frame-dragging for = stars beyond $\sim 0.5$ mpc

from the black = hole,

while measurement of the quadrupole moment is likely to = require

observation of stars inside $\sim 0.2$ = mpc.

A high fraction of stellar remnants, e.g. $10\msun$ black = =A0holes,

in this region would make tests of GR problematic at = all radii.

We discuss the possibility of separating the = effects of stellar

perturbations from those due to = GR.

\end{abstract}

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%arXiv:0911.4718