Multipole moments of bumpy black holes
  General relativity predicts the existence of black holes, compact objects
whose spacetimes depend on only their mass, spin, and charge in vacuum (the "no
hair" theorem). As various observations probe deeper into the strong fields of
black hole candidates, it is becoming possible to test this prediction.
Previous work suggested that such tests can be performed by measuring whether
the multipolar structure of black hole candidates has the form that general
relativity demands, and introduced a family of "bumpy black hole" spacetimes to
be used for making these measurements. These spacetimes have generalized
multipoles, where the deviation from the Kerr metric depends on the spacetime's
"bumpiness." In this paper, we show how to compute the Geroch-Hansen moments of
a bumpy black hole, demonstrating that there is a clean mapping between the
deviations used in the bumpy black hole formalism and the Geroch-Hansen
moments. We also extend our previous results to define bumpy black holes whose
{\it current} moments, analogous to magnetic moments of electrodynamics,
deviate from the canonical Kerr value.
