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arxiv: 2605.16199 · v1 · pith:PTRWYTNWnew · submitted 2026-05-15 · 🌀 gr-qc

Detectability of avoided crossings in black hole ringdowns

Hayato Imafuku , Naritaka Oshita , Hiroki Takeda This is my paper

Pith reviewed 2026-05-20 17:51 UTC · model grok-4.3

classification 🌀 gr-qc
keywords quasinormal modesavoided crossingsblack hole ringdowngravitational wavesBayesian inferencewaveform modelsinterferencedetectability
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The pith

Avoided crossings in black hole quasinormal modes produce interference that may be detectable even when the individual frequencies cannot be resolved.

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

This paper studies avoided crossings where two quasinormal mode frequencies approach each other in black hole ringdown signals. At these points the amplitudes become enhanced and nearly opposite in phase, creating a characteristic interference pattern. The authors test detectability with Bayesian inference on three different waveform models and vary the frequency separation between the modes. They find that separating the close frequencies remains difficult under even optimistic conditions. Collective signatures of the avoided crossing can still be recovered through complementary waveform descriptions when the relevant modes dominate the signal and slower-decaying modes do not contaminate it substantially.

Core claim

Quasinormal modes of black holes can exhibit avoided crossings in which specific frequencies approach each other while their amplitudes are enhanced and acquire nearly opposite phases, leading to characteristic interference. Resolving such closely spaced modes through black hole spectroscopy is observationally challenging. Using Bayesian analysis with three waveform models, the work shows that inferring the separate complex frequencies and amplitudes depends on their separation and on the choice of template. Resolving the individual frequencies is difficult even under optimistic conditions, yet collective waveform signatures associated with avoided crossings may still be identified through a

What carries the argument

Avoided crossing between two quasinormal modes, in which frequencies approach, amplitudes enhance, and phases become nearly opposite to produce interference in the ringdown waveform.

If this is right

  • Individual quasinormal mode frequencies remain difficult to resolve even under optimistic conditions.
  • Collective waveform signatures tied to avoided crossings can be recovered with complementary waveform descriptions.
  • Detection requires that avoided-crossing modes dominate the ringdown and that slower modes contribute negligibly or can be removed.
  • The choice of waveform template affects how well frequencies and amplitudes are inferred near an avoided crossing.

Where Pith is reading between the lines

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

  • Observers may need waveform templates that encode collective interference rather than isolated mode frequencies when close pairs are present.
  • Time-domain and frequency-domain analyses could be combined to isolate avoided-crossing effects in real gravitational-wave data.
  • The same interference logic might apply to other resonant pairs in black-hole perturbation spectra beyond the specific cases studied.

Load-bearing premise

The assumption that the avoided-crossing modes dominate the observed ringdown signal and that contamination from more slowly damped modes is negligible or can be removed.

What would settle it

A measured ringdown waveform in which the avoided-crossing modes are expected to dominate yet no collective interference signature appears after slower modes are subtracted.

Figures

Figures reproduced from arXiv: 2605.16199 by Hayato Imafuku, Hiroki Takeda, Naritaka Oshita.

Figure 1
Figure 1. Figure 1: FIG. 1. Posterior probability distributions for the frequencies and damping times. The left and right columns correspond [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Resolvability of the frequencies (left panel) and damping times (right panel) as functions of the fractional complex [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Fractional deviations of the inferred amplitude parameters from their injected values for each waveform model. The left [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The top panels show the posterior distributions of the frequencies (left) and damping times (right) inferred using the [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Posterior probability distributions of the amplitude parameters for the frequency-shifted injection. The left, center, [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
read the original abstract

Quasinormal modes (QNMs) of black holes can exhibit avoided crossings (ACs), in which specific QNM frequencies approach each other while their amplitudes are enhanced and acquire nearly opposite phases, leading to characteristic interference. Resolving such closely spaced modes through black hole spectroscopy is observationally challenging. In this paper, we investigate the detectability of nearly degenerate QNMs in the presence of an AC within a Bayesian framework using three waveform models. We examine how the inference of the complex frequencies and amplitudes depends on the separation between the two QNM frequencies and on the choice of template waveform. We find that resolving the individual QNM frequencies is difficult even under optimistic conditions. On the other hand, collective waveform signatures associated with ACs may still be identified through complementary waveform descriptions, provided that the AC-related modes dominate the observed ringdown signal and contamination from more slowly damped modes is negligible or can be removed.

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 examines the detectability of avoided crossings (ACs) among quasinormal modes (QNMs) in black hole ringdown signals. Using a Bayesian framework applied to three waveform models on controlled injections, it finds that resolving the individual (closely spaced) QNM frequencies remains difficult even under optimistic conditions. It concludes that collective waveform signatures associated with ACs may nevertheless be identifiable through complementary descriptions, provided the AC-related modes dominate the observed signal and contamination from more slowly damped modes is negligible or can be removed.

Significance. If the central claims hold, the work usefully distinguishes the practical limits of standard black-hole spectroscopy from the potential utility of collective AC signatures. The explicit use of multiple waveform models and forward-modeling inference is a strength that allows assessment of template dependence. The conditional positive result could guide analysis strategies for ringdown data from gravitational-wave detectors, provided the dominance/contamination premise can be validated.

major comments (2)
  1. [Abstract] Abstract (final sentence): The claim that collective AC signatures 'may still be identified ... provided that the AC-related modes dominate the observed ringdown signal and contamination from more slowly damped modes is negligible or can be removed' is load-bearing for the positive detectability conclusion. The manuscript applies the three models only to controlled injections; no explicit robustness tests against realistic contamination amplitudes, removal procedures, or varying dominance ratios are described. This leaves the practical applicability of the collective-signature route unsecured.
  2. [Bayesian framework] Bayesian framework description: The abstract and main text report qualitative findings on frequency/amplitude inference but omit specifics on prior choices, sampling algorithms, convergence diagnostics, or quantitative model-comparison metrics (e.g., Bayes factors or evidence values). These omissions prevent independent verification of the reported difficulty in resolving individual QNMs.
minor comments (2)
  1. [Figures] Figure captions and legends would benefit from explicit indication of which waveform model corresponds to each curve when comparing the three templates.
  2. [Notation] Notation for the complex QNM frequencies and amplitudes should be introduced once with a clear table or equation reference to avoid ambiguity across sections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We appreciate the recognition of the strengths of our approach using multiple waveform models. Below, we provide point-by-point responses to the major comments and outline the revisions we intend to make.

read point-by-point responses

  1. Referee: [Abstract] Abstract (final sentence): The claim that collective AC signatures 'may still be identified ... provided that the AC-related modes dominate the observed ringdown signal and contamination from more slowly damped modes is negligible or can be removed' is load-bearing for the positive detectability conclusion. The manuscript applies the three models only to controlled injections; no explicit robustness tests against realistic contamination amplitudes, removal procedures, or varying dominance ratios are described. This leaves the practical applicability of the collective-signature route unsecured.

    Authors: We agree that the positive conclusion regarding collective signatures is conditional and that our current analysis relies on controlled injections without explicit tests for contamination. To address this, we will revise the manuscript to include a more detailed discussion in the conclusions section on the implications of contamination and the assumptions required for the collective signatures to be detectable. We will also modify the abstract to better reflect the idealized conditions of our study while maintaining the conditional nature of the claim. revision: yes

  2. Referee: [Bayesian framework] Bayesian framework description: The abstract and main text report qualitative findings on frequency/amplitude inference but omit specifics on prior choices, sampling algorithms, convergence diagnostics, or quantitative model-comparison metrics (e.g., Bayes factors or evidence values). These omissions prevent independent verification of the reported difficulty in resolving individual QNMs.

    Authors: We thank the referee for pointing this out. Upon review, we realize that while some details are present in the methods section, they are not sufficiently detailed. In the revised manuscript, we will expand Section 2.2 to explicitly describe the prior distributions used for the QNM frequencies and amplitudes, the nested sampling algorithm employed (with specific settings), convergence diagnostics such as the evidence tolerance, and we will include quantitative metrics like Bayes factors in a new table or figure to support the model comparisons and the difficulty in resolving individual modes. revision: yes

Circularity Check

0 steps flagged

No circularity: analysis uses forward modeling and Bayesian inference on controlled injections

full rationale

The paper performs numerical injections of ringdown waveforms containing avoided crossings into noise, then applies Bayesian inference using three distinct waveform templates to assess parameter recovery. The reported difficulty in resolving individual QNM frequencies follows directly from the posterior widths obtained in these controlled simulations. The conditional statement that collective AC signatures may be identifiable is explicitly qualified by the dominance/contamination premise and does not reduce any derived quantity to a fitted input by construction. No self-definitional equations, fitted-input predictions, or load-bearing self-citations appear in the derivation chain; the results remain externally falsifiable against the injected signals.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so free parameters, axioms, and invented entities cannot be audited in detail. The work appears to rest on standard Bayesian inference applied to existing quasinormal-mode theory without introducing new entities or ad-hoc parameters.

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