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

Article

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

Witzany, V.; Skoupý, V.; Stein, L. C.; Tanay, S.

Phys. Rev. D 111(4), 044032 (2025)

Abstract

The motion of compact binaries is influenced by the spin of their components starting at the 1.5 postNewtonian (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 selfforce. 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 actionangle 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.

Institute authors

Supported by

PRIMUS/23/SCI/017 — Supratekutá dynamika v nanofluidických dvojrozměrných systémech

BibTeX

@article{UTF1075,
  author        = {Witzany, V. and Skoupý, V. and Stein, L. C. and Tanay, S.},
  title         = {{Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order}},
  journal       = {Phys. Rev. D},
  volume        = {111},
  number        = {4},
  pages         = {044032},
  year          = {2025},
  doi           = {10.1103/PhysRevD.111.044032},
  eprint        = {2411.09742},
  archivePrefix = {arXiv},
  url           = {https://doi.org/10.1103/PhysRevD.111.044032},
}