Brito, Richard, Cardoso, Vitor and Pani, Paolo (2012), "Tidal effects around higher-dimensional black holes", PHYSICAL REVIEW D, 86, 2.
Abstract: 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 outward. 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.