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arxiv: 2604.02214 · v2 · submitted 2026-04-02 · 🌀 gr-qc

Recognition: 2 theorem links

· Lean Theorem

Quadratic gravity corrections to scalar QNMs of rapidly rotating black holes

Stef J. B. Husken , Tom van der Steen , Simon Maenaut , Kelvin Ka-Ho Lam , Maxim D. Jockwer , Adrian Ka-Wai Chung , Thomas Hertog , Tjonnie G. F. Li
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Nicol\'as Yunes
Authors on Pith no claims yet

Pith reviewed 2026-05-13 20:31 UTC · model grok-4.3

classification 🌀 gr-qc
keywords quasinormal modesrotating black holesquadratic gravityscalar Gauss-BonnetChern-Simons gravityeffective field theoryblack hole perturbations
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0 comments X

The pith

Scalar quasinormal mode corrections in quadratic gravity grow sharply for high-spin 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 the leading-order deviations from general relativity in the scalar quasinormal mode spectrum of rotating black holes in scalar Gauss-Bonnet and dynamical Chern-Simons gravity. It relies on recently constructed numerical black-hole background solutions that remain valid at large spins rather than on perturbative expansions in the spin parameter. The perturbation equations are solved with pseudo-spectral collocation methods, yielding corrections for dimensionless spins up to a/M = 0.99 with stated accuracies. For spins a/M > 0.9 the corrections to certain modes increase by orders of magnitude. This matters because the ringdown phase of gravitational-wave signals from black-hole mergers is governed by these modes and could therefore reveal the presence of quadratic curvature terms.

Core claim

In an effective-field-theory framework for gravity, black-hole quasinormal mode spectra acquire corrections in quadratic-curvature, scalar-tensor extensions of general relativity. Using recently constructed numerical black-hole solutions valid for large spin, the leading-order deviations from general relativity in the scalar quasinormal mode spectrum of rotating black holes in scalar Gauss-Bonnet and dynamical Chern-Simons gravity are computed. The perturbation equations are solved with pseudo-spectral collocation methods, allowing determination of the quasinormal-mode corrections for dimensionless spins up to a/M=0.99, with accuracy better than 10^{-3} for the l=m=0 mode and 10^{-6} for the

What carries the argument

Numerical black-hole background solutions in scalar Gauss-Bonnet and dynamical Chern-Simons gravity, combined with pseudo-spectral collocation solution of the scalar perturbation equations

If this is right

  • The method extends previous spin-expansion calculations to near-extremal regimes where corrections become much larger.
  • Certain scalar modes exhibit significantly enhanced sensitivity to the quadratic curvature couplings at high spins.
  • Accurate spectra with quantified numerical errors are now available for comparison with gravitational-wave ringdown signals.

Where Pith is reading between the lines

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

  • Gravitational-wave observations of high-spin mergers could therefore place stronger bounds on the effective coupling constants.
  • Spin-dependent enhancements imply that slowly rotating approximations miss important beyond-GR signatures.
  • The same numerical approach could be used to study other perturbation sectors or different quadratic gravity models.

Load-bearing premise

The recently constructed numerical black-hole background solutions remain accurate and stable up to a/M = 0.99.

What would settle it

An independent recalculation of the scalar quasinormal mode corrections at a/M = 0.95 that fails to reproduce the reported order-of-magnitude increase would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.02214 by Adrian Ka-Wai Chung, Kelvin Ka-Ho Lam, Maxim D. Jockwer, Nicol\'as Yunes, Simon Maenaut, Stef J. B. Husken, Thomas Hertog, Tjonnie G. F. Li, Tom van der Steen.

Figure 1
Figure 1. Figure 1: Lowest order corrections ω (1) to l = m = 0 scalar QNMs, visualized in the complex plane. Results that were obtained using the spin-expanded background (lines), shown up until a = 0.8, are compared to results for the spectral background (circles). The circles have a colour-scale to indicate their corresponding spin, going from a = 0 until a = 0.99. m values show signs of a divergence as we start to ap￾proa… view at source ↗
Figure 2
Figure 2. Figure 2: Lowest order corrections to l = 2 scalar QNMs in sGB for different m, visualized in the complex plane. A comparison is made between results (up until a = 0.8) using spin expansion as background spacetime and results for spins up to a = 0.99, using the spectral background. The lines show spin expansion results. A dotted line represents m = −2, a long dashed line m = −1, a full line m = 0, a short dashed lin… view at source ↗
Figure 3
Figure 3. Figure 3: Lowest order corrections to l = 2 scalar QNMs in dCS for different m, visualized in the complex plane. A comparison is made between results (up until a = 0.8) using spin expansion as background spacetime and results for spins up to a = 0.99, using the spectral background. The lines show spin expansion results. A dotted line represents m = −2, a long dashed line m = −1, a full line m = 0, a short dashed lin… view at source ↗
Figure 4
Figure 4. Figure 4: Convergence of lowest order correction to [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Phase space diagram to illustrate which modes [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

In an effective-field-theory framework for gravity, black-hole quasinormal mode spectra acquire corrections in quadratic-curvature, scalar-tensor extensions of general relativity. Previous calculations of such corrections were limited to moderate spins, since the corresponding background solutions relied on expansions in the spin parameter. Using recently constructed numerical black-hole solutions valid for large spin, we compute the leading-order deviations from general relativity in the scalar quasinormal mode spectrum of rotating black holes in scalar Gauss-Bonnet and dynamical Chern-Simons gravity. We solve the resulting perturbation equations with pseudo-spectral collocation methods, allowing us to determine the quasinormal-mode corrections for dimensionless spins up to $a/M=0.99$, with accuracy better than $\lesssim 10^{-3}$ for the $l=m=0$ mode and $\lesssim 10^{-6}$ for higher multipoles. For spins $a/M>0.9$, the corrections to certain modes can increase by orders of magnitude.

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 / 0 minor

Summary. The paper computes leading-order corrections to the scalar quasinormal-mode spectrum of rapidly rotating black holes in scalar Gauss-Bonnet and dynamical Chern-Simons gravity. It employs recently constructed numerical background solutions valid at high spin, solves the linearized perturbation equations with pseudo-spectral collocation, and reports results up to a/M = 0.99 with stated accuracies ≲10^{-3} (l=m=0) and ≲10^{-6} (higher multipoles). The central finding is that, for a/M > 0.9, corrections to certain modes grow by orders of magnitude.

Significance. If the imported numerical backgrounds are accurate at a/M = 0.99, the work meaningfully extends prior perturbative-spin calculations into the near-extremal regime and demonstrates that quadratic-gravity corrections can become observationally relevant for high-spin black holes. The adoption of pseudo-spectral collocation on independently constructed backgrounds is a technical strength that supports the reported precision.

major comments (1)
  1. [Numerical background construction] The quantitative claim that corrections increase by orders of magnitude for a/M > 0.9 rests on the accuracy of the numerical black-hole backgrounds at a/M = 0.99. The manuscript provides no explicit convergence tests, residual norms, or comparisons against analytic limits for these backgrounds within the present work, even though the abstract asserts the stated accuracies for the QNM corrections themselves.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for highlighting the importance of the background accuracy. We address the single major comment below and agree that additional clarification will strengthen the presentation.

read point-by-point responses

  1. Referee: [Numerical background construction] The quantitative claim that corrections increase by orders of magnitude for a/M > 0.9 rests on the accuracy of the numerical black-hole backgrounds at a/M = 0.99. The manuscript provides no explicit convergence tests, residual norms, or comparisons against analytic limits for these backgrounds within the present work, even though the abstract asserts the stated accuracies for the QNM corrections themselves.

    Authors: We agree that the accuracy of the imported numerical backgrounds is central to our claims. These backgrounds were constructed and validated in our companion paper (cited as Ref. [X] in the manuscript), which contains the requested convergence tests, residual norms, and comparisons to analytic limits up to a/M = 0.99. The present work focuses on the perturbation sector and therefore cites rather than repeats that material. To address the referee's concern directly, we will add a brief dedicated paragraph in Section II summarizing the key validation metrics from Ref. [X] (including maximum residual norms and convergence orders at a/M = 0.99). This addition will make the manuscript self-contained without altering any results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on independent numerical backgrounds and standard perturbation solving

full rationale

The paper computes leading-order QNM corrections by linearizing scalar perturbation equations on numerical rotating black-hole backgrounds (imported from prior literature) and solving the resulting system with pseudo-spectral collocation. No step reduces a claimed prediction to a fitted parameter, self-definition, or unverified self-citation chain. The backgrounds are treated as external inputs whose accuracy is asserted via the cited construction; the present work adds only the perturbation analysis. This is a standard, non-circular numerical pipeline.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on the validity of the effective-field-theory truncation at quadratic order and on the accuracy of pre-existing numerical black-hole solutions; no new free parameters are introduced beyond the theory couplings whose leading-order effects are computed.

axioms (2)
  • domain assumption Validity of the effective-field-theory framework for quadratic-curvature scalar-tensor gravity at leading order
    Invoked to justify computing only linear corrections in the coupling constants.
  • domain assumption Accuracy of the recently constructed numerical black-hole solutions for spins up to a/M = 0.99
    Central numerical input whose error budget is not quantified in the abstract.

pith-pipeline@v0.9.0 · 5512 in / 1241 out tokens · 41259 ms · 2026-05-13T20:31:43.719779+00:00 · methodology

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Forward citations

Cited by 2 Pith papers

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

  1. Beyond Three Terms: Continued Fractions for Rotating Black Holes in Modified Gravity

    gr-qc 2026-04 unverdicted novelty 7.0

    A reduction scheme transforms arbitrary N-term scalar and matrix recurrence relations from black hole perturbations in modified gravity into three-term relations solvable by continued fractions.

  2. Ringing of rapidly rotating black holes in effective field theory

    gr-qc 2026-04 unverdicted novelty 6.0

    Leading-order cubic-curvature corrections to scalar quasinormal modes of black holes with spins up to 0.99M are computed numerically for modes up to l=5 with relative errors below 10^{-4}.

Reference graph

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