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Analytic solutions for parallel transport along generic bound geodesics in Kerr spacetime
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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.
Forward citations
Cited by 5 Pith papers
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Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order
Closed-form action and frequency formulas for spinning particles in Kerr spacetime are matched to the 1.5 post-Newtonian Hamiltonian of spinning binaries, yielding a gauge-invariant action dictionary.
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Quadrupolar tidal effects destroy the integrability of black hole geodesics: analytic proof and numerical evidence of chaos
Leading-order tidally induced quadrupoles destroy Kerr geodesic integrability: no polynomial deformation of the Carter constant is conserved for generic Love couplings and Kerr spin.
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Analytic Solution for the Motion of Spinning Particles in Kerr Space-Time
A small worldline shift, built from the hidden symmetry of Kerr spacetime, separates the linear-in-spin equations of motion and yields a closed-form analytic trajectory.
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Tidal perturbations of an extreme mass ratio inspiral around a Kerr black hole
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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Observable signature of magnetic tidal coupling in hierarchical triple systems
Magnetic tidal fields from a supermassive black hole trigger new orbital resonances in a companion compact binary, boosting eccentricity and altering its gravitational-wave signal.
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