  In four-dimensional spacetime, moons around black holes generate
low-amplitude tides, and the energy extracted from the hole's rotation is
always smaller than the gravitational radiation lost to infinity. Thus, moons
orbiting a black hole inspiral and eventually merge. However, it has been
conjectured that in higher-dimensional spacetimes orbiting bodies generate much
stronger tides, which backreact by tidally accelerating the body outwards. This
effect, analogous to the tidal acceleration experienced by the Earth-Moon
system, would determine the evolution of the binary. Here, we put this
conjecture to the test, by studying matter coupled to a massless scalar field
in orbit around a singly-spinning rotating black hole in higher dimensions. We
show that in dimensions larger than five the energy extracted from the black
hole through superradiance is larger than the energy carried out to infinity.
Our numerical results are in excellent agreement with analytic approximations
and lend strong support to the conjecture that tidal acceleration is the rule,
rather than the exception, in higher dimensions. Superradiance dominates the
energy budget and moons "outspiral"; for some particular orbital frequency, the
energy extracted at the horizon equals the energy emitted to infinity and
"floating orbits" generically occur. We give an interpretation of this
phenomenon in terms of the membrane paradigm and of tidal acceleration due to
energy dissipation across the horizon.
