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Gravitational spin-orbit coupling through third-subleading post-Newtonian order: from first-order self-force to arbitrary mass ratios

Andrea Antonelli, Chris Kavanagh, Mohammed Khalil, Jan Steinhoff, Justin Vines

TL;DR

This work determines the complete spin-orbit sector at $N^3LO$ ($4.5\mathrm{PN}$) for arbitrary mass ratios by leveraging gauge-invariant scattering-angle constraints and first-order self-force results, extending the weak-field/self-force link to spinning binaries. It constructs an aligned-spin EOB Hamiltonian with gyro-gravitomagnetic ratios $g_S$ and $g_{S^*}$ fixed by self-force observables, yielding the $N^3LO$ spin-orbit contributions to the scattering angle and the circular-orbit binding energy, $E_b^{SO}$. The authors demonstrate that these corrections substantially improve agreement with NR data in the strong-field regime, roughly halving the NR gap for equal masses, and provide enhanced inputs for SEOBNR/TEOBResumS waveform models. This advances accurate GW predictions for spinning binaries, with implications for parameter estimation and GR tests, and outlines future extensions to higher spins, multipoles, and generic spin orientations.

Abstract

Exploiting simple yet remarkable properties of relativistic gravitational scattering, we use first-order self-force (linear-in-mass-ratio) results to obtain arbitrary-mass-ratio results for the complete third-subleading post-Newtonian (4.5PN) corrections to the spin-orbit sector of spinning-binary conservative dynamics, for generic (bound or unbound) orbits and spin orientations. We thereby improve important ingredients of models of gravitational waves from spinning binaries, and we demonstrate the improvement in accuracy by comparing against aligned-spin numerical simulations of binary black holes.

Gravitational spin-orbit coupling through third-subleading post-Newtonian order: from first-order self-force to arbitrary mass ratios

TL;DR

This work determines the complete spin-orbit sector at () for arbitrary mass ratios by leveraging gauge-invariant scattering-angle constraints and first-order self-force results, extending the weak-field/self-force link to spinning binaries. It constructs an aligned-spin EOB Hamiltonian with gyro-gravitomagnetic ratios and fixed by self-force observables, yielding the spin-orbit contributions to the scattering angle and the circular-orbit binding energy, . The authors demonstrate that these corrections substantially improve agreement with NR data in the strong-field regime, roughly halving the NR gap for equal masses, and provide enhanced inputs for SEOBNR/TEOBResumS waveform models. This advances accurate GW predictions for spinning binaries, with implications for parameter estimation and GR tests, and outlines future extensions to higher spins, multipoles, and generic spin orientations.

Abstract

Exploiting simple yet remarkable properties of relativistic gravitational scattering, we use first-order self-force (linear-in-mass-ratio) results to obtain arbitrary-mass-ratio results for the complete third-subleading post-Newtonian (4.5PN) corrections to the spin-orbit sector of spinning-binary conservative dynamics, for generic (bound or unbound) orbits and spin orientations. We thereby improve important ingredients of models of gravitational waves from spinning binaries, and we demonstrate the improvement in accuracy by comparing against aligned-spin numerical simulations of binary black holes.

Paper Structure

This paper contains 6 sections, 9 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The mass dependence of the scattering angle
  3. Scattering angle, Hamiltonian, and binding energy
  4. Comparison to NR
  5. Conclusions
  6. Acknowledgments

Figures (2)

  • Figure 1: Illustration of aligned-spin scattering BHs.
  • Figure 2: Comparison of the gauge-invariant relation between the circular-orbit aligned-spin spin-orbit binding energy $E_b$ and $v_\omega$. The figure shows results obtained numerically from the (PN-resummed) EOB Hamiltonian \ref{['HEOB']} and NR results from Refs. Ossokine:2017dgeSXS. The linear-in-spin contribution is isolated using Eq. \ref{['EbSO']} with spin magnitudes $\hat{a} = 0.6$ and for mass ratios $q=1$ and $1/3$.