Tidal effects around higher-dimensional black holes

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.