Do floating orbits in extreme mass ratio binary black holes exist?

TL;DR

This paper investigates whether floating orbits can exist in extreme mass ratio binary black holes and concludes that such orbits are not feasible due to flux imbalance, even with added orbital complexities.

Contribution

It provides a detailed analysis showing that flux balance necessary for floating orbits is not achievable in realistic extreme mass ratio black hole binaries.

Findings

Floating orbits are not possible in extreme mass ratio binaries.

Adding eccentricity or inclination does not enable floating orbits.

Exotic non-Kerr objects would be required to produce floating orbits.

Abstract

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.