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arxiv: 2510.16113 · v2 · submitted 2025-10-17 · 🌀 gr-qc · astro-ph.HE

Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary

Josh Mathews , Barry Wardell , Adam Pound , Niels Warburton This is my paper

Pith reviewed 2026-05-18 05:48 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords gravitational wavesself-forceblack hole binarieswaveform modelingpost-adiabatic approximationnumerical relativity
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0 comments X

The pith

Post-adiabatic self-force waveforms now include a slowly spinning primary and a precessing secondary for small misalignments.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors extend an existing first post-adiabatic waveform model, originally for nonspinning quasicircular binaries, to include slow spin on the primary black hole together with arbitrary precessing spin on the secondary. The extension keeps the misalignment between primary spin and orbital angular momentum small. They report close agreement with fully nonlinear numerical relativity simulations across mass ratios of five and higher, primary spins up to about 0.1, and any secondary spin up to nearly 1. A re-summed version called 1PAT1R noticeably improves accuracy over the base model when masses become comparable and primary spin increases. The resulting models are released in the WaSABI package.

Core claim

We extend the 1PA waveform model to a slowly spinning primary and generic precessing secondary under small misalignment, and obtain excellent agreement with numerical relativity for mass ratios q greater than or equal to 5, primary spins absolute value less than or equal to 0.1, and arbitrary secondary spin.

What carries the argument

The re-summed 1PAT1R waveform model that incorporates post-adiabatic corrections for slow primary spin and precessing secondary spin.

If this is right

  • Waveform generation for binaries with slow primary spin and precessing secondary becomes feasible within the post-adiabatic self-force framework.
  • The re-summed 1PAT1R version supplies higher accuracy than the original 1PAT1 model near mass ratio 5 and modest primary spin.
  • Public release in the WaSABI package allows immediate use of these extended waveforms.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could be combined with other modeling techniques to cover a broader range of mass ratios and spins.
  • Relaxing the small-misalignment restriction would open the model to more generic precessing configurations.
  • Consistency checks against effective-one-body waveforms at the same parameters would test whether different approximation schemes converge.

Load-bearing premise

The post-adiabatic approximation continues to hold and the misalignment between the primary spin and orbital angular momentum remains small throughout the quoted ranges of mass ratio and spin.

What would settle it

A direct comparison of the new waveforms against numerical relativity simulations performed at primary spins above 0.1 or with larger misalignments would reveal whether the reported agreement persists or breaks down.

Figures

Figures reproduced from arXiv: 2510.16113 by Adam Pound, Barry Wardell, Josh Mathews, Niels Warburton.

Figure 1
Figure 1. Figure 1: FIG. 1. (Top) Comparison of the flux computed from the [PITH_FULL_IMAGE:figures/full_fig_p018_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The amplitude terms in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p020_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p023_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Waveform comparison for the same equal-mass, nonspinning binary configuration shown in the top panel of Figure 1 in [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Waveform comparisons for a binary configuration with a rapid anti-aligned spin on the secondary. [PITH_FULL_IMAGE:figures/full_fig_p024_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Waveform comparisons for a binary with anti-aligned spins and a small spin on the primary. [PITH_FULL_IMAGE:figures/full_fig_p024_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Waveform comparisons for a binary with aligned spins and a small spin on the primary. [PITH_FULL_IMAGE:figures/full_fig_p025_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Higher [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Waveform comparison for a binary with large, precessing rapid spin on the secondary. In black is an NR simu [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. An illustration of the frame difference between the self-force and NR precessing waveforms. [PITH_FULL_IMAGE:figures/full_fig_p027_11.png] view at source ↗
read the original abstract

Recent progress in gravitational self-force theory has led to the development of a first post-adiabatic (1PA) waveform model for nonspinning, quasicircular compact binaries [Phys. Rev. Lett. 130, 241402 (2023)]. In this paper, we extend that model to allow for a slowly spinning primary black hole and a generic, precessing spin on the secondary object, restricting to the case of small misalignment between the primary spin and the orbital angular momentum. We demonstrate excellent agreement between our waveforms and fully nonlinear numerical relativity simulations for mass ratios $q\gtrsim 5$ and primary spins $|\chi_1|\lesssim 0.1$ and arbitrary secondary spin $\chi_2 \lesssim 1$. In particular we present the re-summed 1PAT1R waveform model, which significantly improves the accuracy of the original 1PAT1 waveforms for comparable masses and increasing primary spin. Our models are publicly available in the WaSABI package.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript extends the first post-adiabatic (1PA) self-force waveform model, previously developed for nonspinning quasicircular binaries, to the case of a slowly spinning primary black hole with small misalignment between its spin and the orbital angular momentum, together with a precessing secondary black hole of arbitrary spin. The authors introduce a re-summed 1PAT1R waveform model and report excellent agreement with fully nonlinear numerical relativity simulations for mass ratios q ≳ 5, primary spins |χ1| ≲ 0.1, and arbitrary secondary spin χ2 ≲ 1. The models are made publicly available in the WaSABI package.

Significance. If the accuracy claims hold, this work advances self-force techniques toward more astrophysically realistic spinning and precessing binaries, particularly in the intermediate-mass-ratio regime. The public release of the models constitutes a clear strength for reproducibility and community use. The extension builds directly on prior self-force calculations and supplies falsifiable comparisons to independent NR simulations.

major comments (2)
  1. [§5] §5 (Results and comparisons): The manuscript states excellent agreement with NR for q ≳ 5 and |χ1| ≲ 0.1, yet separately claims that the re-summed 1PAT1R model 'significantly improves the accuracy of the original 1PAT1 waveforms for comparable masses and increasing primary spin.' Comparable-mass systems (q ~ 1–5) lie outside the quoted NR validation range, so the improvement claim for this regime rests on the post-adiabatic expansion and re-summation procedure remaining accurate when mass ratio decreases; direct NR comparisons or quantitative error metrics in this regime would be required to support the claim.
  2. [§3.2] §3.2 (Post-adiabatic framework and assumptions): The model restricts to small misalignment between primary spin and orbital angular momentum while allowing arbitrary precessing secondary spin χ2 ≲ 1. The time-varying torques from the precessing secondary could challenge the slow-variation assumption underlying the 1PA framework more strongly at lower q; the manuscript should quantify the range of validity of this assumption with explicit error estimates or breakdown diagnostics.
minor comments (2)
  1. [Abstract] Abstract and §1: The phrase 'excellent agreement' is used without accompanying quantitative error metrics, data-exclusion criteria, or specific waveform comparisons; adding these details would improve clarity even if they appear later in the text.
  2. [Notation] Notation throughout: Ensure consistent definition and use of the mass-ratio symbol q and the spin vectors χ1, χ2 when transitioning between the nonspinning 1PA baseline and the new spinning extensions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript, their positive assessment of the work's significance, and the constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: [§5] §5 (Results and comparisons): The manuscript states excellent agreement with NR for q ≳ 5 and |χ1| ≲ 0.1, yet separately claims that the re-summed 1PAT1R model 'significantly improves the accuracy of the original 1PAT1 waveforms for comparable masses and increasing primary spin.' Comparable-mass systems (q ~ 1–5) lie outside the quoted NR validation range, so the improvement claim for this regime rests on the post-adiabatic expansion and re-summation procedure remaining accurate when mass ratio decreases; direct NR comparisons or quantitative error metrics in this regime would be required to support the claim.

    Authors: We acknowledge the referee's point that direct NR validation is limited to q ≳ 5. The improvement claim for the 1PAT1R model at comparable masses is based on the re-summation procedure's ability to capture higher-order post-adiabatic effects, as demonstrated through internal consistency checks and comparisons to the original 1PAT1 model using self-force data. In the revised manuscript we have added quantitative error metrics (e.g., phase differences between 1PAT1 and 1PAT1R) for q ~ 3–5 in §5, together with an explicit caveat that these improvements are inferred from the model's construction rather than direct NR comparisons in that regime. We have also updated the abstract and conclusions to reflect this distinction. revision: partial

  2. Referee: [§3.2] §3.2 (Post-adiabatic framework and assumptions): The model restricts to small misalignment between primary spin and orbital angular momentum while allowing arbitrary precessing secondary spin χ2 ≲ 1. The time-varying torques from the precessing secondary could challenge the slow-variation assumption underlying the 1PA framework more strongly at lower q; the manuscript should quantify the range of validity of this assumption with explicit error estimates or breakdown diagnostics.

    Authors: We agree that explicit quantification strengthens the presentation. The revised manuscript expands §3.2 with a new paragraph providing order-of-magnitude estimates of the torque-induced variations from the precessing secondary and their effect on the slow-variation assumption. We include a diagnostic based on the fractional change in orbital frequency over one orbital period and show that, for the reported range q ≳ 5 and |χ1| ≲ 0.1, the assumption remains valid to within the waveform accuracy achieved. We also note the expected degradation at lower q as a limitation of the current framework. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation rests on independent self-force theory and external NR benchmarks

full rationale

The paper extends an existing 1PA model from prior literature using post-adiabatic approximations and a re-summation procedure for improved accuracy at lower mass ratios. It explicitly compares results to fully nonlinear numerical relativity simulations for the quoted parameter ranges (q≳5, |χ1|≲0.1), which serve as independent validation rather than inputs to the derivation. No load-bearing step reduces by definition or self-citation chain to the target result; the small-misalignment restriction and precessing secondary are acknowledged limitations but do not create circularity in the presented chain. The model is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are described. The post-adiabatic approximation and small-misalignment restriction are implicit modeling choices whose justification would appear in the full text.

pith-pipeline@v0.9.0 · 5711 in / 1178 out tokens · 41331 ms · 2026-05-18T05:48:48.424354+00:00 · methodology

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Reference graph

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