EMR binary black holes orbiting each other radiate away their orbital energy by emission of gravitational waves. The resulting decay in the orbit could be stalled if the energy from the spins of the black holes can be converted to orbital energy at the same rate as the binary loses orbital energy via gravitational wave damping. Not more than a few lines in longer reports have been published on the possibility of such non-decaying or “floating orbits”, and the prevailing opinion is that they do not exist. To maximize the possibility of floating orbits, both black holes in the binary must be spinning. Recent work by Poisson and collaborators enables us to calculate the rate of extraction of spin energy from the smaller black hole for circular equatorial orbits. This rate turns out to be several orders of magnitude smaller than the rate of extraction from the larger black hole (as calculated by our own code that uses the Teukolsky formalism), and adding both these rates does not compensate for the orbital energy loss rate. We also give plausible arguments based on previous work that adding eccentricity and an angle of inclination will not change the rate of gain of orbital energy sufficiently to equal its loss rate. Nevertheless, this gain rate is about 10% of the loss rate near the ISCO, and therefore needs to be taken into account when generating templates of gravitational waves from EMRIs.
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