Boundary to bound dictionary for generic Kerr orbits
Riccardo Gonzo, Canxin Shi
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 that admits an analytic continuation, for both the radial and polar contributions, for a general class of geodesics beyond the equatorial case. Remarkably, this allows to extend the boundary to a bound dictionary and provides an efficient method to compute the deflection angles and 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.
Topics & Concepts
GeodesicPhysicsUpper and lower boundsScatteringObservableBoundary (topology)Analytic continuationLimit (mathematics)Boundary value problemBound statePolarClassical mechanicsMathematical physicsQuantum mechanicsMathematical analysisMathematicsPulsars and Gravitational Waves ResearchQuantum Chromodynamics and Particle InteractionsHigh-pressure geophysics and materials