  This paper examines the possibility of floating or non-decaying orbits for
extreme mass ratio binary black holes. In the adiabatic approximation, valid in
the extreme mass ratio case, if the orbital flux lost due to gravitational
radiation reaction is compensated for by the orbital flux gained from the spins
of the black holes via superradiant scattering (or, equivalently, tidal
acceleration) the orbital decay would be stalled, causing the binary to
"float". We show that this flux balance is not, in practice, possible for
extreme mass ratio binary black holes with circular equatorial orbits;
furthermore, adding eccentricity and inclination to the orbits will not
significantly change this null result, thus ruling out the possibility of
floating orbits for extreme mass ratio binary black holes. We also argue that
binaries consisting of material bodies dense and massive enough to generate
gravitational waves detectable by any kind of gravitational wave detector are
also unlikely to float. Using a multipolar analysis, we show that a non-Kerr
spacetime which could produce a floating orbit (given the same amount of tidal
acceleration as in the case of a Kerr black hole) would need to be rapidly
rotating prolate spheroid, which would be an exotic object indeed.
