  We explore the prospects for Advanced LIGO to detect gravitational waves from
neutron stars and stellar mass black holes spiraling into intermediate-mass
($M\sim 50 M_\odot$ to $350 M_\odot$) black holes. We estimate an event rate
for such \emph{intermediate-mass-ratio inspirals} (IMRIs) of up to $\sim
10$--$30 \mathrm{yr}^{-1}$. Our numerical simulations show that if the central
body is not a black hole but its metric is stationary, axisymmetric, reflection
symmetric and asymptotically flat then the waves will likely be tri-periodic,
as for a black hole. We report generalizations of a theorem due to Ryan (1995)
which suggest that the evolutions of the waves' three fundamental frequencies
and of the complex amplitudes of their spectral components encode (in
principle) a full map of the central body's metric, full details of the energy
and angular momentum exchange between the central body and the orbit, and the
time-evolving orbital elements. We estimate that Advanced LIGO can measure or
constrain deviations of the central body from a Kerr black hole with modest but
interesting accuracy.
