Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order

Abstract

The motion of compact binaries is influenced by the spin of their components starting at the 1.5 post-Newtonian (PN) order. On the other hand, in the large mass ratio limit, the spin of the lighter object appears in the equations of motion at first order in the mass ratio, coinciding with the leading gravitational self-force. Frame and gauge choices make it challenging to compare between the two limits, especially for generic spin configurations. We derive novel closed formulas for the gauge-invariant actions and frequencies for the motion of spinning test particles near Kerr black holes. We use this to express the Hamiltonian perturbatively in terms of action variables up to 3PN and compare it with the 1.5 PN action-angle Hamiltonian at finite mass ratios. This allows us to match the actions across both systems, providing a new gauge-invariant dictionary for interpolation between the two limits.

Supplemental notebook with actions and frequencies for the spinning particle and the 3PN expansions in "Ancillary files"

References in corpus (13)

• Kilonovae
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Towards models of gravitational waveforms from generic binaries: A simple approximate mapping between precessing and non-precessing inspiral signals
• Binary-black-hole initial data with nearly-extremal spins
• Gravitational waveforms for compact binaries from second-order self-force theory
• Gravitational-wave energy flux for compact binaries through second order in the mass ratio
• Canonical Formulation of Spin in General Relativity
• Scattering and bound observables for spinning particles in Kerr spacetime with generic spin orientations
• Integrability of eccentric, spinning black hole binaries up to second post-Newtonian order
• Particle motion under the conservative piece of the self-force is Hamiltonian
• Motion of a spinning particle under the conservative piece of the self-force is Hamiltonian to first order in mass and spin
• Action-angle variables of a binary black hole with arbitrary eccentricity, spins, and masses at 1.5 post-Newtonian order
• Closed-form solutions of spinning, eccentric binary black holes at 1.5 post-Newtonian order

Cited by in corpus (9)

• Analytic Solution for the Motion of Spinning Particles in Kerr Space-Time
• Flux-balance laws for spinning bodies under the gravitational self-force
• Post-adiabatic waveform-generation framework for asymmetric precessing binaries
• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
• Spherical inspirals of spinning bodies into Kerr black holes
• Post-Newtonian expansion of fluxes from a scalar charge on an inclined-spherical orbit about a Kerr black hole
• Constants of motion in gravitational self-force theory
• Unexpected Symmetries of Kerr Black Hole Scattering
• Particles with precessing spin in Kerr spacetime: analytic solutions for eccentric orbits and homoclinic motion near the equatorial plane