  Modified gravity theories capable of genuine self-acceleration typically
invoke a galileon scalar which mediates a long range force, but is screened by
the Vainshtein mechanism on small scales. In such theories, non-relativistic
stars carry the full scalar charge (proportional to their mass), while black
holes carry none. Thus, for a galaxy free-falling in some external
gravitational field, its central massive black hole is expected to lag behind
the stars. To look for this effect, and to distinguish it from other
astrophysical effects, one can correlate the gravitational pull from the
surrounding structure with the offset between the stellar center and the black
hole. The expected offset depends on the central density of the galaxy, and
ranges up to ~0.1 kpc for small galaxies. The observed offset in M87 cannot be
explained by this effect unless the scalar force is significantly stronger than
gravity. We also discuss the systematic offset of compact objects from the
galactic plane as another possible signature.
