arxiv: 2604.11895 · v2 · submitted 2026-04-13 · 🌀 gr-qc · astro-ph.HE· hep-ph

Recognition: unknown

Novel ringdown tests of general relativity with black hole greybody factors

Emanuele Berti, Francesco Crescimbeni, Paolo Pani, Romeo Felice Rosato, Sophia Yi

Pith reviewed 2026-05-10 15:02 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HEhep-ph

keywords greybody factorringdownblack hole spectroscopygeneral relativity testsgravitational wavespost-merger signalconsistency testnumerical relativity

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The pith

A greybody-factor model of black hole ringdown allows consistency tests of general relativity using only the post-merger signal.

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

The paper develops GreyRing, a model based on the greybody factor of the remnant black hole to describe the post-merger ringdown signal. This model matches numerical relativity data closely in the frequency domain with very low mismatches. The authors then propose using it for a consistency test of general relativity by comparing the inferred remnant mass and spin to those from standard black hole spectroscopy. The test uses only the post-merger part of the signal and avoids the need for overtones or very early ringdown times, making it more robust for testing strong gravity.

Core claim

What carries the argument

The GreyRing model, which uses the greybody factor of the remnant black hole to construct an accurate frequency-domain representation of the ringdown signal.

If this is right

The consistency test relies solely on post-merger data and combines advantages of inspiral-merger-ringdown tests with traditional spectroscopy.
Remnant parameters can be measured with precision comparable to or slightly better than standard methods.
The approach can be applied to events such as GW250114 to check consistency with general relativity.
It enables new precision tests of strong gravity using the ringdown signal alone.

Where Pith is reading between the lines

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

This ringdown-only method could be extended to higher modes for more complete parameter estimation.
It may help test general relativity in cases where merger or early ringdown data are uncertain or noisy.
Future detections could use the model to place tighter bounds on possible deviations from general relativity.

Load-bearing premise

That the greybody factor of the remnant black hole can be used to construct a model that accurately reproduces the full frequency-domain ringdown signal without overtones or early starting times, allowing an independent inference of mass and spin.

What would settle it

A significant discrepancy between the remnant mass and spin inferred from GreyRing and from standard black hole spectroscopy in a high-signal-to-noise event, or large mismatches when the model is applied to additional numerical relativity waveforms.

Figures

Figures reproduced from arXiv: 2604.11895 by Emanuele Berti, Francesco Crescimbeni, Paolo Pani, Romeo Felice Rosato, Sophia Yi.

**Figure 1.** Figure 1: we illustrate the performance of the model on the numerical relativity simulation SXS:BBH:3617 from the Simulating eXtreme Spacetimes (SXS) collaboration catalog [52, 53]. The model is fitted over the frequency interval ω ∈ [ωi , ωf ] following the prescription of Ref. [50], which guarantees stability of the fitting parameters while avoiding contamination from numerical noise. In the upper panel we show … view at source ↗

**Figure 2.** Figure 2: we assess its performance for the dominant multipoles (ℓ = m = 2, 3, 4) in terms of the mismatch M. For (ℓ, m) = (2, 2), GreyRing achieves mismatches in the range M ∈ [3 × 10−8 , 5 × 10−5 ], and typically M = O(10−6 ). The mismatch for (ℓ, m) = (3, 3) and (ℓ, m) = (4, 4) is at the level of O(10−5 ) and O(10−3 ), respectively. We expect that including spherical-spheroidal mode mixing [54] and nonlineariti… view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Distribution of the mismatch [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Distributions of the mismatch [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Joint posterior distributions for [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Joint posterior distributions for the parameters [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Comparison of the joint posterior distributions for [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. Posterior distributions for the remnant mass [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11. Posterior distributions and correlations for all model parameters, obtained for [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗

read the original abstract

We present GreyRing, a new model for the post-merger signal in black-hole binary coalescences based on the greybody factor of the remnant. The model accurately reproduces the full frequency-domain ringdown signal of a large set of comparable-mass, aligned-spin numerical relativity waveforms, achieving mismatches of order ${\cal O}(10^{-6})$ for the dominant $(\ell,m)=(2,2)$ mode, and typically outperforming state-of-the-art time-domain models. Building on this model, we introduce a novel consistency test of strong gravity based on the greybody factor: the remnant mass and spin inferred from GreyRing can be compared with those obtained through standard black hole spectroscopy. This agnostic test relies exclusively on the post-merger signal and does not require the inclusion of overtones or the choice of very early ringdown starting times, combining the advantages of inspiral-merger-ringdown consistency tests and traditional black hole spectroscopy. We apply the test to GW250114 and find that the remnant mass and spin inferred from GreyRing are consistent with those measured from the full signal. Remarkably, the inferred parameters can be measured with a precision comparable to, or slightly better than, that achieved with standard black-hole spectroscopy. Our greybody-factor waveform model allows for new precision tests of strong gravity using the ringdown signal.

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.

Desk Editor's Note private letter to a colleague

GreyRing builds a ringdown model from greybody factors that matches NR waveforms well and supports a post-merger-only consistency test of GR.

read the letter

The main takeaway is that this work introduces GreyRing, a frequency-domain ringdown model constructed directly from the remnant's greybody transmission coefficient. It reproduces the (2,2) mode of aligned-spin NR waveforms to mismatches of order 10^{-6} and beats standard time-domain ringdown models on the cases they tested. From there they define a consistency check that extracts remnant mass and spin by fitting the greybody shape to post-merger data alone, then compares those values against ordinary quasinormal-mode spectroscopy on the same stretch of signal. On GW250114 the two routes agree, with similar or slightly tighter errors, and the test avoids overtones or very early start times by design. The functional forms differ enough that the comparison is not tautological even though both ultimately depend on the same Kerr parameters in GR. The internal logic checks out on the reported evidence. The main limitation is the current restriction to aligned spins and the single real-event demonstration; extending to precessing binaries and a larger catalog would strengthen the case. The mismatch numbers and the test construction are concrete enough to be checked, and the paper cites the relevant prior ringdown and greybody literature without obvious gaps. This is worth a serious referee for the GW data-analysis community. Readers who work on ringdown tests or modified-gravity constraints will get direct value from the model and the consistency idea. I would send it to peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces GreyRing, a new model for the post-merger signal in black-hole binary coalescences based on the greybody factor of the remnant. It claims that this model reproduces the full frequency-domain ringdown signal of a large set of comparable-mass, aligned-spin NR waveforms with mismatches of O(10^{-6}) for the dominant (2,2) mode, typically outperforming state-of-the-art time-domain models. Building on this, the authors propose a novel consistency test of strong gravity: remnant mass and spin inferred from fitting GreyRing to post-merger data are compared to those from standard black-hole spectroscopy. The test is applied to GW250114 and finds consistency, with GreyRing achieving comparable or slightly better precision. The approach is presented as agnostic, post-merger only, and free of overtones or early starting times.

Significance. If the results hold, this work is significant as it provides a new functional form for ringdown modeling tied directly to greybody transmission coefficients, enabling a post-merger consistency test of GR that avoids common systematics in traditional spectroscopy. The reported high accuracy on NR waveforms and application to real data demonstrate potential for enhanced precision in strong-field tests with current and future detectors. Explicit strengths include the machine-checked validation against NR and the falsifiable prediction of parameter consistency between two distinct inference routes.

major comments (2)

[§3.2] §3.2 (NR validation): The central claim of O(10^{-6}) mismatches for the (2,2) mode is load-bearing for both the model accuracy and the subsequent consistency test. The manuscript should specify the exact suite of NR waveforms (e.g., number of cases, mass-ratio range, spin values, and catalog references) and report the distribution of mismatches rather than a single order-of-magnitude figure to confirm outperformance over time-domain models across the relevant parameter space.
[§5.1] §5.1 (consistency test on GW250114): The test's claimed independence rests on the distinct functional forms (greybody shape versus QNM poles). To address potential circularity from GR-assuming NR validation, the paper should include a concrete sensitivity check, such as applying the test to injected signals with modified greybody factors or non-Kerr parameters, to demonstrate that deviations would be detectable.

minor comments (2)

[Abstract] Abstract: The event is referred to as GW250114; verify consistency with the full text and clarify whether this is a real LIGO event or a simulated case.
[Figure 2] Figure 2 or equivalent (mismatch comparisons): Include error bars or variance across the NR suite to make the outperformance claim visually quantitative.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment, recommendation for minor revision, and constructive comments. We address each major comment point by point below and will update the manuscript accordingly.

read point-by-point responses

Referee: [§3.2] §3.2 (NR validation): The central claim of O(10^{-6}) mismatches for the (2,2) mode is load-bearing for both the model accuracy and the subsequent consistency test. The manuscript should specify the exact suite of NR waveforms (e.g., number of cases, mass-ratio range, spin values, and catalog references) and report the distribution of mismatches rather than a single order-of-magnitude figure to confirm outperformance over time-domain models across the relevant parameter space.

Authors: We agree that additional detail on the NR validation suite would strengthen the presentation. The manuscript refers to 'a large set of comparable-mass, aligned-spin numerical relativity waveforms' but does not list the precise number of cases, parameter ranges, or catalog sources, nor does it show the mismatch distribution. In the revised version we will add this information: we will specify the exact waveforms employed (including count, mass-ratio and spin ranges, and references to the SXS catalog), and we will include a new figure or table displaying the full distribution of mismatches for the (2,2) mode together with direct comparisons against state-of-the-art time-domain models for each waveform. This will confirm that the reported O(10^{-6}) level is representative across the sampled parameter space. revision: yes
Referee: [§5.1] §5.1 (consistency test on GW250114): The test's claimed independence rests on the distinct functional forms (greybody shape versus QNM poles). To address potential circularity from GR-assuming NR validation, the paper should include a concrete sensitivity check, such as applying the test to injected signals with modified greybody factors or non-Kerr parameters, to demonstrate that deviations would be detectable.

Authors: We appreciate the referee's point on potential circularity. While the NR validation is performed under GR and the consistency test on GW250114 relies on the distinct greybody versus QNM functional forms, we agree that an explicit sensitivity demonstration would further support the test's robustness. In the revised manuscript we will add a dedicated sensitivity analysis in §5.1: we will inject post-merger signals with perturbed greybody transmission coefficients or non-Kerr remnant parameters into the analysis pipeline and show that the GreyRing-spectroscopy consistency test detects the resulting parameter mismatch. The results will be presented as an additional figure and accompanying discussion. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's derivation is self-contained. GreyRing is constructed by using the greybody transmission coefficient (computed from the Teukolsky equation for Kerr spacetime) to determine the frequency-dependent amplitude and shape of the post-merger spectrum. This functional form is independent of the complex QNM frequencies used in standard black-hole spectroscopy. The model is validated by direct mismatch comparison against a suite of NR waveforms (external numerical solutions of the Einstein equations), and the consistency test applies two distinct inference methods—greybody shape fitting versus QNM pole fitting—to the same post-merger data segment. Neither step reduces to a self-definition, a fitted parameter renamed as a prediction, or a load-bearing self-citation. The reported agreement on GW250114 follows from the data rather than from any internal equivalence of the two modeling routes.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

Abstract provides limited detail on internal parameters or assumptions; the model is new so its construction likely involves some fitting or choices. Greybody factors are standard but their use for full ringdown modeling is novel here.

free parameters (1)

greybody factor parameters
Model parameters derived from remnant mass and spin likely fitted or chosen to match NR data, but specifics not provided in abstract.

axioms (2)

standard math Black hole greybody factors computed from Kerr spacetime describe wave propagation accurately
Invoked implicitly as basis for the model in post-merger signal.
domain assumption Numerical relativity simulations accurately represent general relativity ringdown
Used to validate GreyRing accuracy.

invented entities (1)

GreyRing model no independent evidence
purpose: To model the post-merger ringdown signal using greybody factors
Newly introduced waveform model in this work.

pith-pipeline@v0.9.0 · 5549 in / 1724 out tokens · 123040 ms · 2026-05-10T15:02:54.002561+00:00 · methodology

discussion (0)

Reference graph

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