  In this article, we classify the set of asymptotic mass-like invariants for
asymptotically hyperbolic metrics. It turns out that the standard mass is just
one example (but probably the most important one) among the two families of
invariants we find. These invariants are attached to finite-dimensional
representations of the group of isometries of hyperbolic space. They are then
described in terms of wave harmonic polynomials and polynomial solutions to the
linearized Einstein equations in Minkowski space.
