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.