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General Relativity and Quantum Cosmology, gr-qc
Abstract:
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.
