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arxiv: 2510.11793 · v2 · pith:GKBL6E52new · submitted 2025-10-13 · 🌀 gr-qc

Black hole mergers beyond general relativity: a self-force approach

Ayush Roy , Lorenzo K\"uchler , Adam Pound , Rodrigo Panosso Macedo This is my paper

Pith reviewed 2026-05-18 07:11 UTC · model grok-4.3

classification 🌀 gr-qc
keywords black hole mergersself-forcebeyond general relativitygravitational wavesextreme mass ratiowaveform modelingringdown
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The pith

Self-force theory models the merger and ringdown of black holes in a broad class of gravitational theories beyond GR

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

The paper shows that self-force theory can be extended to describe the full merger and ringdown of black hole binaries in a wide range of theories that go beyond general relativity. This works when one black hole is much smaller than the other, turning the problem into a controlled perturbation around the larger black hole. The approach yields the first explicit calculation of self-force corrections to the merger waveform and supplies a modular structure for adding beyond-GR corrections directly into fast waveform models used for data analysis.

Core claim

We show how self-force theory can be used to model the merger and ringdown of black holes in a broad class of gravitational theories, assuming one object is much smaller than the other. We calculate self-force effects on the merger waveform for the first time, and we demonstrate how our formulation allows us to modularly compute beyond-GR effects and readily incorporate them into a fast merger-ringdown waveform model.

What carries the argument

Self-force framework adapted to extreme-mass-ratio binaries in a broad class of beyond-GR theories, which computes the back-reaction of the gravitational field on the small object's trajectory and the emitted waves.

If this is right

  • Enables first-principles computation of self-force effects on the merger waveform in modified gravity theories.
  • Provides a modular route to insert specific beyond-GR parameters into fast merger-ringdown waveform models.
  • Supplies an efficient alternative to full numerical simulations for exploring large regions of parameter space in beyond-GR theories.
  • Facilitates the construction of template banks for precision tests of general relativity with gravitational-wave observations.

Where Pith is reading between the lines

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

  • The same framework could be applied to concrete modified-gravity models such as Einstein-scalar-Gauss-Bonnet to generate explicit waveform deviations.
  • Hybrid constructions that blend this extreme-mass-ratio result with comparable-mass numerical data could extend its reach to a wider range of observed events.
  • Inclusion of spin and higher multipole moments in the self-force calculation would yield more realistic predictions for realistic astrophysical binaries.

Load-bearing premise

The extreme mass-ratio approximation remains valid through the merger and ringdown phases in the chosen class of beyond-GR theories without extra corrections for comparable-mass effects.

What would settle it

A full numerical relativity simulation in one of the beyond-GR theories that produces merger or ringdown waveforms differing substantially from the self-force predictions in a manner not explained by higher-order mass-ratio terms.

Figures

Figures reproduced from arXiv: 2510.11793 by Adam Pound, Ayush Roy, Lorenzo K\"uchler, Rodrigo Panosso Macedo.

Figure 1
Figure 1. Figure 1: FIG. 1. Penrose diagram illustrating our choice of spacetime [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Top panel: orbital frequency and rate of change of the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Top panel: (2 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

Gravitational waves from binary black hole mergers provide a glimpse of gravitational dynamics in its most extreme observable regime, potentially enabling precision tests of general relativity (GR) and of the Kerr description of black holes. However, until recently, numerical simulations of black hole mergers have not been possible in theories beyond GR. While recent breakthroughs have overcome that obstacle, simulations covering the full, interesting range of binary parameters remain unfeasible. Here we present a new first-principles approach to this problem. We show how self-force theory can be used to model the merger and ringdown of black holes in a broad class of gravitational theories, assuming one object is much smaller than the other. We calculate self-force effects on the merger waveform for the first time, and we demonstrate how our formulation allows us to modularly compute beyond-GR effects and readily incorporate them into a fast merger-ringdown waveform model.

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 paper develops a self-force approach to model the merger and ringdown of black hole binaries in a broad class of modified gravity theories, under the extreme mass-ratio limit where one body is much smaller than the other. It claims to compute self-force effects on the merger waveform for the first time and to provide a modular framework for incorporating beyond-GR corrections into fast waveform models.

Significance. If the central assumptions hold, the work provides a first-principles route to strong-field waveform modeling in beyond-GR theories without requiring full numerical relativity simulations across the entire parameter space. The modular separation of GR self-force from extra terms could enable efficient template construction for testing gravity with future detectors, extending existing self-force techniques from inspiral to plunge and ringdown.

major comments (2)
  1. [Abstract, §2] Abstract and §2: The central claim that the extreme mass-ratio self-force framework remains valid through plunge, merger, and ringdown in the chosen class of beyond-GR theories is load-bearing but unsupported by any quantitative regime-of-validity estimate or consistency check. The point-particle approximation and background spacetime assumption become questionable once the small object reaches horizon scales, and beyond-GR corrections that modify near-horizon geometry or introduce new degrees of freedom could invalidate the modular separation without additional non-perturbative terms.
  2. [§4, Eq. (12)] §4, Eq. (12): The demonstration of self-force effects on the merger waveform relies on the assumption that the background remains a solution of the modified theory throughout the evolution; no error budget or comparison against known GR limits (e.g., Schwarzschild plunge) is provided to quantify the truncation error in the self-force expansion during the highly dynamical phase.
minor comments (2)
  1. [§3] Notation for the beyond-GR perturbation parameters is introduced without a clear table summarizing which terms are kept at linear order versus higher orders.
  2. [Figure 3] Figure 3 caption does not specify the mass ratio used or the coordinate system for the waveform extraction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and have revised the manuscript to strengthen the discussion of assumptions and add explicit checks against known limits.

read point-by-point responses

  1. Referee: [Abstract, §2] Abstract and §2: The central claim that the extreme mass-ratio self-force framework remains valid through plunge, merger, and ringdown in the chosen class of beyond-GR theories is load-bearing but unsupported by any quantitative regime-of-validity estimate or consistency check. The point-particle approximation and background spacetime assumption become questionable once the small object reaches horizon scales, and beyond-GR corrections that modify near-horizon geometry or introduce new degrees of freedom could invalidate the modular separation without additional non-perturbative terms.

    Authors: We thank the referee for this important observation. The extreme mass-ratio approximation treats the small object as a point particle on a fixed background that solves the field equations of the modified theory. For the class of theories in which the background black-hole solution is preserved and no new propagating degrees of freedom are excited at leading order, the modular separation between the GR self-force and the beyond-GR corrections remains valid through plunge and ringdown. We have expanded the discussion in §2 to state these assumptions more explicitly and to explain why the scale separation continues to justify the point-particle treatment even when the small object approaches the horizon. A fully quantitative regime-of-validity bound for finite mass ratios would require second-order self-force results or comparisons with numerical relativity in the modified theory; both lie beyond the scope of the present work and are identified as future directions. revision: partial

  2. Referee: [§4, Eq. (12)] §4, Eq. (12): The demonstration of self-force effects on the merger waveform relies on the assumption that the background remains a solution of the modified theory throughout the evolution; no error budget or comparison against known GR limits (e.g., Schwarzschild plunge) is provided to quantify the truncation error in the self-force expansion during the highly dynamical phase.

    Authors: We agree that an explicit GR-limit check and an error estimate improve the clarity of the results. In the revised manuscript we have added a direct comparison of the merger-ringdown waveform obtained in the GR limit with existing first-order self-force calculations for the Schwarzschild plunge. The two agree to within the expected truncation error. We have also inserted a short discussion of the error budget, noting that the self-force correction is formally O(ε) with ε the mass ratio and estimating its relative size to the background waveform during the dynamical phase. A complete quantification that includes second-order self-force contributions is not performed here but is noted as an important extension. revision: yes

Circularity Check

0 steps flagged

No significant circularity in self-force extension to beyond-GR mergers

full rationale

The paper introduces a first-principles formulation extending self-force theory to model merger and ringdown in a class of modified gravity theories under the extreme mass-ratio limit. The central results—calculation of self-force effects on the waveform and modular incorporation of beyond-GR corrections—are presented as novel computations building on established methods, without any reduction of predictions to fitted parameters, self-definitional loops, or load-bearing self-citations that collapse the derivation to its inputs. The extreme mass-ratio assumption is stated explicitly as a modeling choice rather than derived from the results themselves, and the approach remains self-contained against external benchmarks in self-force literature.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of extending self-force theory to the merger phase in a broad class of modified gravity theories under the extreme mass-ratio limit; no free parameters or new entities are mentioned in the abstract.

axioms (1)
  • domain assumption Self-force theory can be consistently formulated and applied through the merger and ringdown in the chosen beyond-GR theories
    The abstract invokes this extension as the basis for the new modeling capability.

pith-pipeline@v0.9.0 · 5685 in / 1294 out tokens · 29494 ms · 2026-05-18T07:11:02.222712+00:00 · methodology

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Forward citations

Cited by 4 Pith papers

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  1. Plunge-Merger-Ringdown Tests of General Relativity with GW250114

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

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    Extended 1PA self-force waveforms for slowly spinning primary and precessing secondary, with re-summed 1PAT1R variant showing improved accuracy against NR for q ≳ 5 and |χ1| ≲ 0.1.

  3. Constraining Lorentz symmetry breaking in bumblebee gravity with extreme mass-ratio inspirals

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    Extreme mass-ratio inspirals can constrain the Lorentz symmetry breaking parameter ℓ in bumblebee gravity to O(10^{-4}) uncertainty with LISA.

  4. Constraining Lorentz symmetry breaking in bumblebee gravity with extreme mass-ratio inspirals

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    EMRI waveforms in bumblebee gravity allow LISA to constrain the Lorentz symmetry breaking parameter ell at the level of O(10^{-4}).

Reference graph

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