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The mass and angular momentum of reconstructed metric perturbations
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We prove a key result regarding the mass and angular momentum content of linear vacuum perturbations of the Kerr metric obtained through the formalism developed by Chrzarnowski, Cohen, and Kegeles (CCK). More precisely we prove that the Abbott-Deser mass and angular momentum integrals of any such perturbation vanish, when that perturbation was obtained from a regular Fourier mode of the Hertz potential. As a corollary we obtain a generalization of previous results on the completion of the `no string' radiation gauge metric perturbation generated by a point particle. We find that for any bound orbit around a Kerr black hole, the mass and angular momentum perturbations completing the CCK metric are simply the energy and angular momentum of the particle "outside" the orbit and vanish "inside" the orbit.
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Metric reconstruction and the Hamiltonian for eccentric, precessing binaries in the small-mass-ratio limit
First-order metric perturbations and the generalized redshift invariant are computed for eccentric, precessing orbits in Kerr spacetime using four metric reconstruction methods, with open-source code provided.
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