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arxiv: 2510.27320 · v2 · submitted 2025-10-31 · 🌀 gr-qc

The quasinormal modes of the rotating quantum corrected black holes

Jia-Ning Chen , Zong-Kuan Guo , Liang-Bi Wu This is my paper

Pith reviewed 2026-05-18 03:05 UTC · model grok-4.3

classification 🌀 gr-qc
keywords quasinormal modesrotating quantum corrected black holesgravitational wave ringdownparameter estimationhyperboloidal methodpyRingscalar perturbations
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The pith

Informative priors from inspiral-merger data tighten the posterior on the quantum correction parameter and shift the inferred spin away from the Kerr value in ringdown analyses of rotating quantum-corrected black holes.

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

The paper computes scalar quasinormal mode spectra for rotating quantum-corrected black holes by casting the perturbation equation as a two-dimensional eigenvalue problem and solving it with a pseudo-spectral method on a hyperboloidal grid. These spectra are inserted into the pyRing ringdown pipeline to perform parameter estimation on gravitational-wave signals, with priors drawn from the mass and spin distributions expected after the inspiral-merger phase. When these informative priors are used, the posterior on the quantum correction parameter becomes narrower than in runs with uninformative priors, and the recovered spin begins to differ noticeably from the Kerr case. The authors emphasize that the exercise is methodological because the waveform model inside pyRing assumes tensor perturbations while the modes supplied are scalar. A sympathetic reader would see this as a concrete first step toward using ringdown spectroscopy to look for quantum-gravity modifications once full tensor modes become available.

Core claim

The quasinormal modes of the rotating quantum corrected black hole are obtained by reducing the scalar perturbation problem to a two-dimensional eigenvalue problem via the hyperboloidal framework and solving it with the pseudo-spectral method. These scalar spectra are then fed into a pyRing-based ringdown parameter-estimation pipeline that adopts informative priors on mass and spin taken from the inspiral-merger stage. The resulting posteriors show that informative priors produce a tighter bound on the quantum correction parameter than flat priors, while the spin inferred under the rotating quantum-corrected model becomes statistically significant and deviates from the value recovered under

What carries the argument

The hyperboloidal framework that converts the scalar perturbation equation on the rotating quantum-corrected metric into a two-dimensional eigenvalue problem solved by the pseudo-spectral method, which then supplies the frequencies and damping times to the pyRing ringdown likelihood.

If this is right

  • Informative priors drawn from the inspiral-merger phase consistently narrow the posterior width on the quantum correction parameter relative to uninformative priors.
  • The spin recovered under the rotating quantum-corrected model becomes statistically significant and differs from the Kerr-model value once informative priors are supplied.
  • The pipeline demonstrates a practical route for incorporating early-phase mass and spin distributions directly into ringdown analyses of non-Kerr black holes.
  • The approach opens a path for testing quantum-gravity-induced deviations once tensor quasinormal modes are substituted into the same likelihood.

Where Pith is reading between the lines

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

  • If scalar-to-tensor substitution proves reliable, the same pipeline could be applied to other parametrically deformed black-hole metrics without recomputing full numerical waveforms.
  • Future detectors with higher ringdown signal-to-noise ratios could use this method to place quantitative upper limits on the quantum correction parameter even before complete non-Kerr waveform models exist.
  • A direct mismatch test between scalar and tensor mode sets for the same background would quantify the systematic error introduced by the current approximation.

Load-bearing premise

Scalar quasinormal modes computed for the rotating quantum-corrected metric can be inserted into a tensor-perturbation waveform model inside pyRing to extract parameter constraints, even though the two perturbation types are physically distinct.

What would settle it

A calculation of the actual tensor quasinormal modes of the same rotating quantum-corrected metric that produces posteriors on the quantum correction parameter differing by more than the reported statistical uncertainty from those obtained with the scalar modes.

Figures

Figures reproduced from arXiv: 2510.27320 by Jia-Ning Chen, Liang-Bi Wu, Zong-Kuan Guo.

Figure 1
Figure 1. Figure 1: Parameter space (α/M2 , a/M) for RQCBH. The red solid line corresponds to the extremal black holes with degenerate horizons. The sample green points which are used to obtain the QNMs spectra in the parameter space (α/M2 , a/M) corresponding to the points (q, κ) in the q − κ plane (see [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The parameter space (q, κ) for the RQCBH, where the feasible range of parameters is represented by shaded areas. Now, it is ready to solve the QNMs spectra of RQCBH within the hyperboloidal framework. The complete mapping from Boyer-Lindquist to the hyperboloidal coordinates are given by t = λ h τ − h(σ, θ) i − r⋆(r(σ)), r(σ) = λ ρ(σ) σ , φ = ϕ − k(r(σ)), (3.8) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The QNMs spectra for RQCBH with ℓ = 3, m = 2 and ℓ = 2, m = 2. The left top panel is the real part of the four “regular” modes. The right top panel is the imaginary part of the four “regular” modes. The left bottom panel is the real part of the four “mirror” modes. The right bottom is the imaginary part of the four “mirror” modes. IV. BAYESIAN ANALYSIS AND PARAMETER ESTIMATION In this section, the Bayesian… view at source ↗
Figure 4
Figure 4. Figure 4: The real (left) and imaginary (right) parts of QNMs spectra as functions of the dimensionless spin parameter [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Posterior distributions of black hole parameters inferred from ringdown signals for [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
read the original abstract

The quasinormal modes (QNMs) of a rotating quantum corrected black hole (RQCBH) are studied by employing the hyperboloidal framework for the scalar perturbation. This framework is used to cast the QNMs spectra problem into a two-dimensional eigenvalue problem, then the spectra are calculated by imposing the two-dimensional pseudo-spectral method. Based on the resulting scalar spectra, a parameter estimation pipeline for this RQCBH model with gravitational wave data is constructed by using \texttt{pyRing} in the ringdown phase. We use informative priors in our inference that incorporates the mass and spin distributions predicted by the inspiral-merger phase as the prior distributions for the ringdown analysis. Notably, since the waveform model beyond Kerr black hole in $\texttt{pyRing}$ is designed for the tensor perturbation, the inferred posterior distributions should be interpreted as a methodological investigation rather than as physical constraints from observations. The methodological results show that the use of informative priors consistently yields a tighter posterior on the quantum correction parameter compared to analyses without such priors, and the spin inferred from the RQCBH model begins to be significant and differs from that of the Kerr model. This opens a promising avenue for testing quantum-gravity-induced deviations using gravitational-wave spectroscopy.

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

1 major / 2 minor

Summary. The manuscript computes quasinormal mode spectra for scalar perturbations of rotating quantum-corrected black holes by recasting the problem as a two-dimensional eigenvalue problem within the hyperboloidal framework and solving it with a pseudo-spectral method. These scalar spectra are then inserted into the pyRing ringdown likelihood to perform Bayesian parameter estimation on gravitational-wave data, using informative priors derived from inspiral-merger mass and spin distributions. The reported methodological results indicate that informative priors produce tighter posteriors on the quantum-correction parameter and yield a statistically significant spin value that differs from the Kerr case; the authors explicitly caveat that the exercise is methodological rather than a physical constraint because pyRing’s beyond-Kerr waveform model is constructed for tensor perturbations.

Significance. If the scalar-to-tensor substitution can be justified, the work offers a transparent methodological template for testing quantum-gravity corrections via ringdown spectroscopy. The explicit interpretive caveat regarding the scalar-versus-tensor mismatch is a strength that improves the paper’s credibility. The demonstration that informative priors tighten the posterior on the correction parameter is a concrete, falsifiable outcome that could guide future analyses once tensor QNMs become available.

major comments (1)
  1. [Abstract and parameter-estimation section] Abstract and parameter-estimation section: the central methodological claim—that informative priors tighten the posterior on the quantum-correction parameter and produce a statistically significant spin shift—rests on substituting scalar-field QNM frequencies and damping times directly into pyRing’s tensor-perturbation ringdown likelihood. For the rotating quantum-corrected metric the scalar and tensor spectra are not guaranteed to respond identically to the correction term; no cross-check, rescaling, or error-budget estimate is reported that would confirm the substitution preserves the direction and magnitude of the inferred-parameter shifts.
minor comments (2)
  1. [Abstract] The abstract states that “the spin inferred from the RQCBH model begins to be significant”; a quantitative statement of the credible-interval overlap or Bayes factor relative to the Kerr case would make this claim more precise.
  2. Notation for the quantum-correction parameter should be introduced once and used consistently; the current text alternates between descriptive phrases and symbols without a clear first definition.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive feedback. We appreciate the recognition that our explicit caveat regarding the scalar-versus-tensor mismatch strengthens the paper's credibility. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract and parameter-estimation section] Abstract and parameter-estimation section: the central methodological claim—that informative priors tighten the posterior on the quantum-correction parameter and produce a statistically significant spin shift—rests on substituting scalar-field QNM frequencies and damping times directly into pyRing’s tensor-perturbation ringdown likelihood. For the rotating quantum-corrected metric the scalar and tensor spectra are not guaranteed to respond identically to the correction term; no cross-check, rescaling, or error-budget estimate is reported that would confirm the substitution preserves the direction and magnitude of the inferred-parameter shifts.

    Authors: We agree that substituting scalar QNM spectra into pyRing’s tensor-based likelihood is an approximation whose quantitative accuracy cannot be verified without tensor QNMs for the same metric. The manuscript already states explicitly (both in the abstract and in the parameter-estimation section) that the exercise is methodological rather than a physical constraint precisely because of this mismatch. While we do not claim the substitution preserves the exact magnitude of shifts, the central demonstration—that informative priors derived from the inspiral-merger phase tighten the posterior on the quantum-correction parameter—remains valid as an illustration of the pipeline. To address the referee’s concern, we will revise the parameter-estimation section to add a short paragraph discussing the expected qualitative similarities in the leading-order response of scalar and tensor modes to small quantum corrections, together with an explicit statement that a full error budget awaits the computation of tensor QNMs. This is a partial revision that improves contextualization without altering the reported methodological results. revision: partial

Circularity Check

0 steps flagged

Independent numerical QNM spectra computed from perturbation equations feed into standard Bayesian ringdown inference without definitional reduction or self-citation load-bearing

full rationale

The paper solves the scalar perturbation equation on the RQCBH metric via the hyperboloidal framework cast as a 2D eigenvalue problem and applies the pseudo-spectral method to obtain the spectra; these numerically computed frequencies and damping times are then inserted as fixed inputs into pyRing's likelihood for parameter estimation. The quantum-correction parameter enters the metric and thus the eigenvalue problem directly, so the resulting spectra are not defined in terms of the posterior or the fit itself. Informative priors are taken from the inspiral-merger phase (external to the ringdown analysis), and the authors explicitly label the exercise methodological rather than physical. No step reduces a claimed prediction to a fitted quantity by construction, no uniqueness theorem is imported from self-citation, and the central inference result follows from standard Bayesian updating on independently obtained model predictions. The derivation chain is therefore self-contained against external numerical benchmarks and data.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central results rest on the assumed form of the rotating quantum-corrected black-hole metric and on the transferability of scalar-mode spectra to a tensor-based waveform model; both are taken from prior literature without independent derivation in this work.

free parameters (1)
  • quantum correction parameter
    The free parameter that quantifies the strength of the quantum correction in the black-hole metric and is the target of the posterior inference.
axioms (2)
  • domain assumption The spacetime geometry is given by the rotating quantum-corrected black-hole metric
    Invoked throughout the perturbation calculation and inference pipeline; the metric itself is taken from earlier work on quantum corrections to general relativity.
  • domain assumption Scalar-field perturbations adequately represent the ringdown dynamics for the purpose of methodological testing
    Used to justify feeding the computed spectra into the tensor-oriented pyRing code.

pith-pipeline@v0.9.0 · 5754 in / 1575 out tokens · 52879 ms · 2026-05-18T03:05:05.361765+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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

  1. Assessing EMRI Detectability of the Rotating Quantum Oppenheimer-Snyder Black Hole

    gr-qc 2026-04 unverdicted novelty 4.0

    Quantum corrections in rotating black holes produce detectable but spin-suppressed gravitational wave phase shifts in LISA EMRIs.

Reference graph

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