E\"otv\"os Experiments with Supermassive Black Holes
  By examining the locations of central black holes in two elliptical galaxies,
M\,32 and M\,87, we derive constraints on the violation of the strong
equivalence principle for purely gravitational objects, i.e. black holes, of
less than about two-thirds, $\eta_N<0.68$ from the gravitational interaction of
M\,87 with its neighbours in the Virgo cluster. Although M\,32 appears to be a
good candidate for this technique, the high concentration of stars near its
centre substantially weakens the constraints. On the other hand, if a central
black hole is found in NGC 205 or one of the other satellite ellipticals of
M\,31, substantially better constraints could be obtained. In all cases the
constraints could improve dramatically with better astrometry.
