arxiv: 2604.05084 · v1 · submitted 2026-04-06 · 🌀 gr-qc · hep-ph· hep-th

Recognition: 2 theorem links

· Lean Theorem

Parametrized quasinormal modes, greybody factors and their correspondence

Georgios Antoniou

Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:53 UTC · model grok-4.3

classification 🌀 gr-qc hep-phhep-th

keywords quasinormal modesgreybody factorsparametrized frameworkmodified gravityblack hole perturbationscorrespondence

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The pith

Small corrections to the black hole potential alter quasinormal mode frequencies and greybody factors according to their perturbative order and polynomial power.

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

The paper examines how quasinormal modes and greybody factors respond when general relativity is altered through small additions to the effective potential inside the parametrized quasinormal mode framework. It derives the explicit scaling of both quantities with the order of the modification and the power of the polynomial term that is added. A sympathetic reader would care because this supplies a controlled, model-independent route to forecast changes in gravitational-wave ringdown signals and to locate the breakdown of a proposed link between the modes and the factors.

Core claim

In the parametrized quasinormal mode framework, modifications to general relativity appear as small corrections to the effective potential; the resulting quasinormal mode frequencies and greybody factors then depend systematically on the perturbative order of the correction and on the power of the polynomial term. The paper also tests the recently proposed correspondence between quasinormal modes and greybody factors inside this framework and identifies the regime in which the correspondence ceases to hold.

What carries the argument

The parametrized quasinormal mode framework, which encodes modifications to general relativity as small corrections to the potential and thereby tracks their effect on quasinormal modes, greybody factors, and their mutual correspondence.

Load-bearing premise

Modifications to general relativity can be introduced as small corrections in the potential within the parametrized quasinormal mode framework, and the framework remains valid for the orders and powers considered.

What would settle it

A measured black-hole ringdown spectrum whose frequency shifts fail to follow the predicted dependence on the order of a potential correction would show that the framework does not apply to that system.

Figures

Figures reproduced from arXiv: 2604.05084 by Georgios Antoniou.

**Figure 2.** Figure 2: FIG. 2. We show the real and imaginary parts of the axial fundamental ( [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Greybody factors for angular numbers [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Relative differences between the GBFs derived using a DI approach and the QNM-GBF correspon [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Scalar effective potential under deformations. In the first row, we fix the bookkeeping parameter [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗

read the original abstract

We present a detailed study of quasinormal modes and greybody factors in the context of the parametrized quasinormal mode framework, in which modifications to general relativity are introduced as small corrections in the potential. We deduce the QNMs' and GBFs' dependence on the order of the modifications and their polynomial power. We also test the validity of the recently proposed QNM-GBF correspondence in the pQNM framework by inspecting the regime at which it breaks down.

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

This extends the parametrized QNM setup to greybody factors, gives explicit dependence on modification order and polynomial power, and maps the breakdown of the QNM-GBF correspondence under controlled perturbative corrections.

read the letter

This paper shows how small corrections to the black hole potential in the parametrized quasinormal mode framework lead to explicit shifts in both the quasinormal modes and the greybody factors, depending on the order of the correction and the polynomial power used. It also locates the point where the recently suggested QNM-greybody correspondence breaks down. The work does a good job laying out the perturbative expansions and then verifying them against numerical solutions as the correction strength increases. Using WKB or continued-fraction methods for the modes keeps things standard and reproducible. The breakdown test is useful because it gives a practical limit rather than just claiming the correspondence always holds. The main limitation is that the whole setup assumes the modifications remain small enough for perturbation theory to apply, which is stated up front but means the results do not cover strong deviations. The specific powers chosen for the polynomials could use more physical motivation from actual modified gravity theories, though that is a minor point. Researchers focused on gravitational wave ringdown signals and black hole perturbation theory in beyond-GR scenarios will find this directly relevant. It is a solid incremental step rather than a broad new method. I think it deserves peer review. The calculations are transparent and the numerical checks are there to back them up.

Referee Report

0 major / 2 minor

Summary. The manuscript investigates quasinormal modes (QNMs) and greybody factors (GBFs) within the parametrized quasinormal mode (pQNM) framework, modeling modifications to general relativity as small corrections to the effective potential. It derives the explicit dependence of QNMs and GBFs on the order of these modifications and the polynomial power of the corrections, and tests the recently proposed QNM-GBF correspondence by determining the regime in which it breaks down through comparison of perturbative results with direct numerical integration.

Significance. If the central results hold, the work supplies a controlled perturbative toolkit for mapping how deviations from GR propagate into observable black-hole ringdown and scattering quantities. The systematic expansion of the wave equation combined with WKB/continued-fraction methods and explicit numerical cross-checks of the breakdown threshold constitute a reproducible and falsifiable contribution that could inform template construction for future gravitational-wave tests of gravity.

minor comments (2)

The abstract states that the dependence on 'order of the modifications and their polynomial power' is deduced, but does not specify the precise functional forms (e.g., the powers or the range of orders) considered in the potential corrections; this should be stated explicitly for reproducibility.
In the description of the breakdown regime, the criterion used to declare that the perturbative QNM formula 'deviates' from numerical integration should be quantified (e.g., a relative error threshold or a specific figure of merit) rather than left qualitative.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of our manuscript and the recommendation for minor revision. The referee accurately captures our investigation of how QNMs and GBFs depend on the order of modifications and the polynomial power of corrections within the pQNM framework, as well as our numerical tests of the QNM-GBF correspondence breakdown. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; derivations rely on independent perturbative expansions

full rationale

The paper applies standard perturbative expansions to the wave equation in the pQNM framework using WKB and continued-fraction methods to derive QNM/GBF dependence on modification order and power. The QNM-GBF correspondence test compares against an externally proposed relation and checks breakdown via direct numerical integration against the perturbative formula. No load-bearing step reduces to self-definition, fitted inputs renamed as predictions, or self-citation chains; the framework remains self-contained within stated perturbative assumptions without internal fitting loops.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; the parametrized framework likely introduces free parameters for the amplitude and power of potential corrections, but no explicit list or values are given.

pith-pipeline@v0.9.0 · 5365 in / 1192 out tokens · 52603 ms · 2026-05-10T18:53:16.405055+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

modifications to general relativity are introduced as small corrections in the potential... δṼ = 1/r² Σ α(i) (r_h/r)^i ... α(i) ≪ α_max^(i) = (1 + 1/i)^i (i+1)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

ω = ω_GR + Σ α(i) e(i) ... WKB formula to arbitrary order... correspondence formula (20) truncated at O(ℓ^{-2})

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Novel ringdown tests of general relativity with black hole greybody factors
gr-qc 2026-04 unverdicted novelty 7.0

GreyRing model based on greybody factors reproduces numerical relativity ringdown signals with mismatches of order 10^{-6} and enables a new post-merger consistency test of general relativity applied to GW250114.

Reference graph

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