Kavli Affiliate: Scott A. Hughes
| First 5 Authors: Lisa V. Drummond, Scott A. Hughes, , ,
| Summary:
Very large mass ratio binary black hole systems are of interest both as a
clean limit of the two-body problem in general relativity, as well as for their
importance as sources of low-frequency gravitational waves. At lowest order,
the smaller body moves along a geodesic of the larger black hole’s spacetime.
Post-geodesic effects include the gravitational self force, which incorporates
the backreaction of gravitational-wave emission, and the spin-curvature force,
which arises from coupling of the small body’s spin to the black hole’s
spacetime curvature. In this paper, we describe a method for precisely
computing bound orbits of spinning bodies about black holes. Our analysis
builds off of pioneering work by Witzany which demonstrated how to describe the
motion of a spinning body to linear order in the small body’s spin. Exploiting
the fact that in the large mass-ratio limit spinning-body orbits are close to
geodesics and using closed-form results due to van de Meent describing
precession of the small body’s spin along black hole orbits, we develop a
frequency-domain formulation of the motion which can be solved very precisely.
We examine a range of orbits with this formulation, focusing in this paper on
orbits which are eccentric and nearly equatorial (i.e., the orbit’s motion is
$mathcal{O}(S)$ out of the equatorial plane), but for which the small body’s
spin is arbitrarily oriented. We discuss generic orbits with general small-body
spin orientation in a companion paper. We characterize the behavior of these
orbits and show how the small body’s spin shifts the frequencies $Omega_r$ and
$Omega_phi$ which affect orbital motion. These frequency shifts change
accumulated phases which are direct gravitational-wave observables,
illustrating the importance of precisely characterizing these quantities for
gravitational-wave observations. (Abridged)
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