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Quasinormal modes of rotating black holes with ultralight scalar fields

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Leif Lui, Adrian Ka-Wai Chung

General Relativity and Quantum Cosmology · Submitted 12 Oct 2026 · 106 references

Pith's verdict: Solid first computation of QNM shifts for massive nonminimally coupled scalars on rotating black holes – careful numerics, well validated, and honestly reported limitations.

T0 · AI review

How this review was made: An AI referee (deepseek/deepseek-v4-flash) read the paper on October 14, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

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  4. T3 Formal statement The claims written out in a formal math language a computer can read.
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arXiv ID2610.16054 (version 1)
Pith IDZMCRJN3E, Pith's permanent record of this paper and its review
CitationAdrian Ka-Wai Chung, Leif Lui. "Quasinormal modes of rotating black holes with ultralight scalar fields." arXiv:2610.16054 (2026). https://pith.science/paper/ZMCRJN3E
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The paper

The paper claims

First accurate computation of the leading-order shifts in the quasinormal-mode frequencies of rapidly rotating black holes surrounded by massive scalar fields with nonminimal curvature coupling.

The reading

This paper reports the first accurate computation of how the quasinormal-mode frequencies of rapidly rotating black holes shift when they are surrounded by massive scalar fields that couple nonminimally to spacetime curvature. The calculations cover dimensionless spins up to 0.9 and scalar masses comparable to or larger than the black-hole mass scale, with typical numerical errors of $10^{{-8}}$ to $10^{{-5}}$. The frequency shifts exhibit a strong dependence on parity, breaking axial–polar isospectrality, and a distinct threshold transition where the scalar perturbation switches from outgoing to evanescent at infinity. The results open the possibility of searching for ultralight scalar particles, prime dark-matter candidates, using existing gravitational-wave ringdown signals. A Fisher forecast shows that a single GW250114-like ringdown could constrain the coupling to ≲ 0.04–0.09 at 2σ for scalar masses ≲ 2×$10^{{-12}}$ eV.

What carries the argument

The key machinery is a spectral method that constructs the linearized perturbation operator numerically at collocation points, avoiding explicit symbolic derivation of the field equations. This allows efficient computation across a wide parameter space of black-hole spin, scalar mass, and coupling structure. The method imposes a Regge–Wheeler-type gauge and treats the transition between propagating and evanescent scalar channels consistently through a branch-choice rule based on the retarded Green's function, with regularization techniques such as windowing and complex scaling for numerically challenging open-channel cases.

Extended reading notes

Core claim

The central discovery is the first accurate determination of how the quasinormal-mode frequencies of rapidly rotating black holes shift when they are surrounded by massive scalar fields that couple nonminimally to curvature. The authors compute the shifts for the (2,2,0), (2,2,1), and (3,3,0) modes in dynamical Chern-Simons and scalar Gauss-Bonnet gravity. They find that the shifts depend strongly on parity, breaking axial–polar isospectrality, and that the massless limit is recovered with different scalings: linear in the scalar mass for scalar Gauss-Bonnet and quadratic for dynamical Chern-Simons, reflecting the monopole versus dipole nature of the scalar hair. They also identify a first-order threshold transition where the scalar channel closes, causing a jump in the frequency shift that is almost entirely in the damping rate. No unstable modes are found in the parameter space explored.

Load-bearing premise

The Regge-Wheeler-type gauge for metric perturbations remains applicable when the background scalar field is nonvanishing, and the first-order eigenvalue perturbation correctly captures the frequency shift without missing higher-order mixing effects.

Editorial extensions

If this is right

  • The computed spectra enable direct searches for ultralight scalar fields in gravitational-wave ringdown signals without relying on superradiance.
  • Future Bayesian parameter estimation using these spectra could place upper limits on the coupling of curvature-coupled scalar fields, complementing superradiance bounds.
  • The numerical method reduces the computational cost of black-hole perturbation calculations across theories, making it practical to generate spectra for a large grid of parameters.
  • The results provide ingredients for modelling extreme-mass-ratio inspirals around black holes with massive scalar hair, extending sensitivity to complementary scalar-mass ranges.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the method is extended to second order in the coupling, it could reveal nonlinear instabilities or confirm the absence of instabilities at higher order.
  • The threshold transition phenomenon may produce distinctive features in gravitational-wave signals from black-hole mergers, which could be searched for in stacking analyses.
  • The different mass scalings between scalar Gauss-Bonnet and dynamical Chern-Simons gravity imply that measuring the mass dependence of the ringdown frequencies could help distinguish between these two theories.
Original abstract

We report the first accurate computation of the leading-order shifts in the quasinormal-mode frequencies of rapidly rotating black holes surrounded by massive scalar fields with nonminimal curvature coupling. For fields with reduced Compton wavelengths no shorter than the black-hole mass scale, the numerical errors in the frequency shifts are typically $10^{-8} - 10^{-5}$ for dimensionless spins between 0 and 0.9, and at most $\mathcal{O}(10^{-3})$ next to the scalar-mass threshold. Our results open up the possibility of searching for ultralight scalar particles, prime dark-matter candidates, using existing gravitational-wave signals.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-14: 1 request, 3,075 input tokens.

What the abstract itself states, as probabilities: claims first 0.94 · states limitation 0.85 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.11 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We report the first accurate computation of the leading-order shifts in the quasinormal-mode frequencies of rapidly rotating black holes surrounded by massive scalar fields with nonminimal curvature coupling. For fields with reduced Compton wavelengths no shorter than the black-hole mass scale, the numerical errors in the frequency shifts are typically $10^{-8} - 10^{-5}$ for dimensionless spins between 0 and 0.9, and at most $\mathcal{O}(10^{-3})$ next to the scalar-mass threshold. Our results open up the possibility of searching for ultralight scalar particles, prime dark-matter candidates, using existing gravitational-wave signals.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We report the first accurate computation of the leading-order shifts in the quasinormal-mode frequencies of rapidly rotating black holes surrounded by massive scalar fields with nonminimal curvature coupling. contribution 0.97 0.96 0.41 asserted 1.00
s1 For fields with reduced Compton wavelengths no shorter than the black-hole mass scale, the numerical errors in the frequency shifts are typically $10^{-8} - 10^{-5}$ for dimensionless spins between 0 and 0.9, and at most $\mathcal{O}(10^{-3})$ next to the scalar-mass threshold. result 0.92 0.94 0.10 asserted 1.00
s2 Our results open up the possibility of searching for ultralight scalar particles, prime dark-matter candidates, using existing gravitational-wave signals. interpretation 0.97 0.30 0.51 hedged possibility 1.00

What kind of paper the classifier reports this is: simulation study 0.95 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. FIG. 1. Leading-order shift
Figure 2. FIG. 2. Approach to the massless limit at
Figure 3. FIG. 3. Forecast
Figure 4. FIG. 4. Threshold transition of the
Figure 5. FIG. 5. Radial convergence of the
Figure 6. FIG. 6. Numerical uncertainty of the production values,
Figure 7. FIG. 7. Approach to the massless limit of the
Figure 9. FIG. 9. Same as Fig
Figure 10. FIG. 10. Same as Fig

Showing 9 of the paper's 10 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2610.16054 by the authors.

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