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

TL;DR

This paper develops a gauge-invariant framework for comparing spinning compact binary dynamics in different regimes, bridging the gap between test particle and comparable mass systems using action variables and perturbative Hamiltonians.

Contribution

It introduces novel closed-form gauge-invariant formulas for spinning particles in Kerr spacetime and matches these with post-Newtonian Hamiltonians to interpolate between limits.

Findings

Derived gauge-invariant actions and frequencies for spinning particles near Kerr black holes.

Matched the Hamiltonian perturbations at 3PN with 1.5PN actions, enabling interpolation.

Provided a new gauge-invariant dictionary connecting different binary regimes.

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.