  Multipole moments carry a lot of information about the gravitational field.
Nonetheless, knowing all the multipole moments of an object does not determine
conclusively the nature of the object itself. In particular, the multipole
moments of the Kerr spacetime are not unique. Here we construct several
physically motivated Newtonian objects with multipole moments identical to
those of Kerr. Moreover, we also provide a description of how to include
post-Newtonian corrections to these objects without changing their multipole
moments.
