Boundary to bound dictionary for generic Kerr orbits

Abstract

We establish a new relation between classical observables for scattering and bound orbits of a massive probe particle in a Kerr background. We find an exact representation of the Hamilton-Jacobi action in terms of the conserved charges which admits an analytic continuation, both for the radial and polar contribution, for a general class of geodesics beyond the equatorial case. Remarkably, this allows to extend the boundary to bound dictionary and it provides an efficient method to compute the deflection angles and the time delay for scattering orbits, as well as frequency ratios for bound orbits, in the probe limit but at all orders in the perturbative expansion.

arXiv comment6 pages, 2 figures; v2: minor improvements, references added; v3: published version

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• Relativistic aerodynamics of spinning black holes
• Massive twistor worldline in electromagnetic fields
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• The first law of binary black hole scattering
• Resummed energy loss in extreme-mass-ratio scattering using critical orbits
• Constants of motion in gravitational self-force theory
• Mass and spin coevolution of black holes inspiralling through dark matter
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