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Gyroscopes orbiting black holes: A frequency-domain approach to precession and spin-curvature coupling for spinning bodies on generic Kerr orbits | | Uchupol Ruangsri
; Sarah J. Vigeland
; Scott A. Hughes
; | | Date: |
1 Dec 2015 | | Abstract: | A small body orbiting a black hole follows a trajectory that, at leading
order, is a geodesic of the black hole spacetime. Much effort has gone into
computing "self force" corrections to this motion, arising from the small
body’s own contributions to the system’s spacetime. Another correction to the
motion arises from coupling of the small body’s spin to the black hole’s
spacetime curvature. Spin-curvature coupling drives a precession of the small
body, and introduces a "force" (relative to the geodesic) which shifts the
small body’s worldline. These effects scale with the small body’s spin at
leading order. If the smaller body is itself a black hole, this means
spin-curvature effects scale as the small body’s mass squared, the same mass
scaling as the self force. In this paper, we show that the equations which
govern spin-curvature coupling can be analyzed with a frequency-domain
decomposition, at least to leading order in the small body’s spin. We show how
to compute the frequency of precession along generic orbits, and how to
describe the small body’s precession and motion in the frequency domain. We
illustrate this approach with a number of examples. This approach is likely to
be useful for understanding spin coupling effects in the extreme mass ratio
limit, and may provide insight into modeling spin effects in the strong field
for non-extreme mass ratios. | | Source: | arXiv, 1512.0376 | | Services: | Forum | Review | PDF | Favorites | |
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