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Analytic solutions for parallel transport along generic bound geodesics in Kerr spacetime

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arxiv 1906.05090 v1 pith:H56VMZYT submitted 2019-06-12 gr-qc

Analytic solutions for parallel transport along generic bound geodesics in Kerr spacetime

Maarten van de Meent This is my paper
classification gr-qc
keywords alongsolutionstimeanalyticalboundgeodesickerrmino
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We provide analytical closed form solutions for the parallel transport along a bound geodesic in Kerr spacetime. This can be considered the lowest order approximation for the motion a spinning black hole in an extreme mass-ratio inspiral. As an illustration of the usefulness of our new found expressions we scope out the locations of spin-spin resonances in quasi-circular EMRIs. All solutions are given as functions of Mino time, which facilitates the decoupling of the equations of motion. To help physical interpretation, we also provide an analytical expression for the proper time along a geodesic as a function of Mino time.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    gr-qc 2026-05 unverdicted novelty 6.0

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    gr-qc 2026-01 conditional novelty 6.0

    A closed-form Kerr metric under slow quadrupolar tides yields spin-dependent tidal shifts of the ISCO and light ring, with larger shifts for retrograde orbits around fast-spinning holes.

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    gr-qc 2026-05 unverdicted novelty 5.0

    Binaries around SMBHs exhibit four scattering regimes in unbound orbits and scattering-type eccentric vZLK oscillations in bound orbits, yielding a unified periapsis-driven tidal dynamics picture in galactic nuclei.