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General Relativity and Quantum Cosmology, gr-qc
Abstract:
In this work we present the first calculation of the gravitational self-force
on generic bound geodesics in Kerr spacetime to first order in the mass-ratio.
That is, the local correction to equations of motion for a compact object
orbiting a larger rotating black hole due to its own impact on the
gravitational field. This includes both dissipative and conservative effects.
Our method builds on and extends earlier methods for calculating the
gravitational self-force on equatorial orbits. In particular we reconstruct the
local metric perturbation in the outgoing radiation gauge from the Weyl scalar
$\psi_4$, which in turn is obtained by solving the Teukolsky equation using
semi-analytical frequency domain methods. The gravitational self-force is
subsequently obtained using (spherical) $l$-mode regularization.
We test our implementation by comparing the large $l$-behaviour against the
analytically known regularization parameters. In addition we validate our
results be comparing the long-term average changes to the energy, angular
momentum, and Carter constant to changes to these constants of motion inferred
from the gravitational wave flux to infinity and down the horizon.
