Pith. sign in

REVIEW 4 major objections 5 minor 6 cited by

Gravitational Quasinormal Modes and Grey-Body Factors of Bonanno-Reuter Regular Black Holes

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Gravitational quasinormal frequencies of the Bonanno–Reuter black hole converge to Schwarzschild for large mass or gamma, while small quantum-corrected black holes ring longer and emit less.

desk verdict The large-M Schwarzschild recovery in this Bonanno-Reuter QNM scan is plausible, but the paper's matching claim about large gamma is contradicted by its own metric and tables, and the borrowed gravitational potential needs more justification. read the letter →

arxiv 2507.07196 v1 pith:KYMAALGJ submitted 2025-07-09 gr-qc hep-th

S. V. Bolokhov , Milena Skvortsova This is my paper
classification gr-qchep-th MSC 83C5783C45 PACS 04.70.-s04.30.-w04.60.-m
keywords quasinormalmodesgrey-bodyfactorsBonanno–ReuterblackholeregularholesasymptoticsafetyaxialgravitationalperturbationsWKBmethodringdown
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper computes the gravitational quasinormal-mode frequencies and grey-body factors of the Bonanno–Reuter regular black hole, a quantum-corrected Schwarzschild-like spacetime arising in the asymptotic-safety scenario. It claims that as the black hole mass $M$ or the interpolation parameter $\gamma$ grows, both the real and imaginary parts of the fundamental quasinormal frequencies smoothly approach their classical Schwarzschild values, while significant deviations appear for small masses. The central physical result is that a quantum-corrected black hole of the same mass as a Schwarzschild one oscillates slightly more slowly and decays more slowly, and emits radiation with smaller grey-body factors. A sympathetic reader would care because these are concrete, in-principle observable signatures of quantum gravity in ringdown and Hawking radiation.

What carries the argument

The load-bearing object is the effective axial-gravitational potential of Eq. (11), obtained by modeling the quantum-corrected background as an effective anisotropic fluid so that standard Regge–Wheeler gauge perturbation theory can be applied even though the Bonanno–Reuter metric is not an exact Einstein solution. Around that potential, the paper builds a tortoise-coordinate wave equation and extracts frequencies with the sixth-order WKB formula with Padé approximants, cross-checks with characteristic time-domain integration, and computes grey-body factors both by WKB transmission and by the eikonal correspondence between grey-body factors and the fundamental quasinormal frequency. The height and width of the potential barrier transfer the geometry's quantum corrections into the ringdown frequencies and the transmission probabilities.

What would settle it

Derive axial gravitational perturbations of the Bonanno–Reuter metric directly from the linearized field equations with the full effective stress-energy tensor, or from the RG-improved action without the anisotropic-fluid analogy, and compare the fundamental $\ell=2$ frequency at $M=1.66$, $\gamma=0.1$ with the paper's Table 1 value $\omega\approx 0.263295-0.042414i$; a mismatch larger than the roughly $0.01\%$ WKB error would refute the quantitative claim.

Watch

Extended reading notes

Core claim

In the paper's own terms: gravitational axial perturbations of the Bonanno–Reuter metric obey a Regge–Wheeler-like wave equation with the effective potential $V(r)=f(r)[2g(r)/r^2 - (f(r)g(r))'/(2r f(r)) + (\ell+2)(\ell-1)/r^2]$, and solving that equation with sixth-order WKB plus Padé approximants, confirmed by time-domain integration, yields quasinormal frequencies and grey-body factors that interpolate between quantum-corrected and classical behavior. The Schwarzschild limit is recovered for large $M$ or large $\gamma$; for fixed mass, larger $\gamma$ suppresses the deviation. For equal masses, the quantum-corrected black hole has longer-lived quasinormal modes (smaller $|\operatorname{Im}\omega|$) and smaller grey-body factors than Schwarzschild. The deviations are one to two orders of magnitude larger than the WKB error estimate, so the paper treats them as genuine physical effects rather than numerical artifacts.

Load-bearing premise

The Bonanno–Reuter metric is not an exact solution of Einstein's equations, so the paper replaces the true gravitational perturbations with perturbations of an effective fluid model; if that replacement is wrong, every computed quasinormal frequency and grey-body factor is wrong.

Editorial extensions

If this is right

  • For small masses near the critical horizon limit (for example $M=1.66$ at $\gamma=0.1$), the quasinormal frequencies deviate from Schwarzschild by far more than the WKB error, so ringdown of quantum relics would carry a measurable quantum signature.
  • For large masses, or $\gamma\gtrsim 5$ with $M\gtrsim 5$, the predicted frequencies are indistinguishable from Schwarzschild within numerical error, so classical gravitational-wave tests in the astrophysical mass range are unaffected.
  • Smaller grey-body factors for equal-mass quantum-corrected black holes mean Hawking radiation is suppressed relative to Schwarzschild, which would slow evaporation and lengthen the lifetime of the remnant.
  • The agreement between WKB and quasinormal-mode-correspondence grey-body factors, within about $1\%$ even for $\ell=2$, supports using the eikonal correspondence at moderately low multipoles in this class of spacetimes.
  • Since the WKB error is one to two orders of magnitude smaller than the quantum-induced shift, the tabulated frequencies provide a concrete benchmark for future full time-domain or nonlinear evolutions.

Reading between the lines

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

  • If the anisotropic-fluid effective potential does not reproduce the true axial gravitational perturbations of the RG-improved geometry, the specific numbers in the tables would shift; the qualitative direction, longer-lived modes and suppressed transmission, is likely to survive because it follows from the barrier being lower and wider in the quantum regime.
  • A direct derivation of the axial master equation from the full effective action of the quantum-gravity scenario, without the anisotropic-fluid workaround, would settle whether the quantitative spectrum is correct.
  • The same machinery could be applied to electromagnetic and scalar perturbations and to higher overtones, which are typically more sensitive to near-horizon geometry and could show a stronger quantum imprint than the fundamental mode.
  • Translating these results into an observational test would require an estimate of whether the small-mass quantum regime is ever populated and whether its modified ringdown or suppressed emission is within reach of future gravitational-wave or primordial-black-hole searches; the paper does not make that estimate.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This paper computes the axial gravitational quasinormal-mode (QNM) frequencies and grey-body factors of the Bonanno–Reuter (BR) renormalization-group-improved black hole, with the RG parameter ω̃ fixed and the interpolation parameter γ treated as free. The QNMs are obtained with the sixth- and seventh-order WKB method with Padé approximants, checked by one time-domain integration, while the grey-body factors are computed with the sixth-order WKB transmission formula and with the recently proposed QNM–grey-body correspondence. The results are tabulated and plotted as functions of the mass M and γ, and the paper's central claim is that the Schwarzschild limit is recovered for large M or large γ, while at fixed mass the quantum-corrected black hole has longer-lived QNMs and smaller grey-body factors.

Significance. If the results held as stated, the paper would provide a useful reference for how asymptotic-safety-inspired corrections to Schwarzschild modify ringdown frequencies and Hawking-radiation transmission spectra, with deviations confined to the small-mass regime. The authors deserve credit for several concrete internal consistency checks: the WKB6/WKB7 order comparison (Tables 1–4, typically δ ≲ 0.01%), the time-domain/Prony cross-check for one parameter set (Fig. 6, agreement better than 0.005%), and the comparison of two grey-body factor prescriptions (Figs. 7–8). However, the physical input is an effective potential borrowed from an anisotropic-fluid construction whose validity for the BR metric is not established, and, more seriously, the claimed large-γ Schwarzschild limit is contradicted by the paper's own equations and tables, while the γ=9/2 tables coincide with the γ=1 tables at every overlapping entry. The niche is well populated (refs. 10–13, 32, 35–37), so the incremental contribution, once corrected, is modest but suitable for a specialist venue.

major comments (4)
  1. [§2, Eq. (3); §4.4; §6] The claim that quasinormal frequencies converge to Schwarzschild 'for large masses or large values of γ' is not supported and is contradicted by the paper's own input. In Eq. (3), at fixed M, γ→∞ gives G(r)→0 and f(r)→1, i.e., flat space, not Schwarzschild; moreover, for γ above a critical value the spacetime has no horizon (as the paper itself notes in §2 and Fig. 1), so the large-γ limit exists only outside the black-hole parameter range. Within the allowed range, the tables show the opposite trend: at M=5, ℓ=2, γ=0.1 gives ω=0.075714−0.017632i and γ=1 gives ω=0.076034−0.017481i, both moving away from the Schwarzschild value (Mω≈0.37367−0.08896i, i.e., ω≈0.07473−0.01779i at M=5). The §4.4 sentence 'increasing γ tends to suppress the deviation from the classical limit' and the statement that γ≳5 leads to frequencies indistinguishable from Schwarzschild for M≳5 are likewise inconsistent with Tables 1–3: at M=5, γ=9/2 still differs from Schwarzschild by about 1.7% in Re ω, two orders of magnitude above the WKB-order uncertainty δ≈0.007%. The abstract and Conclusions should be revised to state the correct limit structure: Schwarzschild is recovered for large M at fixed γ, while increasing γ at fixed M enhances the deviation and eventually removes the horizon.
  2. [Tables 2 and 3; §4.4] The γ=9/2 entries in Table 3 coincide exactly with the γ=1 entries in Table 2 at every overlapping mass (ℓ=2 and ℓ=3; M=3.5, 4, 4.5, 5, 10), and Table 3 adds only the intermediate masses M=3.6–3.9. This cannot be a physical saturation effect: at the barrier peak r≈3M the lapse functions differ by several percent for these parameters (e.g., at M=4, f≈0.348 for γ=1 versus f≈0.361 for γ=9/2), so the QNM frequencies should differ at the 10⁻³–10⁻² level, well above the digits displayed. The authors should recompute and present the actual γ=9/2 results, and clarify the provenance of the γ=10 curves in Figs. 4–5, since this data is the only support for the claimed γ-dependence of the spectrum.
  3. [§3, Eq. (11)] The effective potential—the single physical input for all QNM and grey-body results—is taken from the anisotropic-fluid construction of refs. [14,16] without a derivation for the BR metric, which is not presented as a solution of the Einstein equations for any specified matter content. The paper explicitly calls this a 'practical workaround' and justifies it only by the assertion that it 'reliably captures the leading quantum corrections' for small deviations from Schwarzschild. This is a load-bearing assumption: if Eq. (11) is not the correct axial gravitational perturbation potential of the RG-improved geometry, then Tables 1–4 and Figs. 6–8 do not describe gravitational perturbations of the BR black hole. The authors should either (i) derive the axial perturbation equations for the improved metric, specifying the effective matter and its perturbation properties, or (ii) clearly reframe the paper as an analysis of the Regge–Wheeler-type equation (11) associated with the effective geometry, as done in refs. [14,16], and state the attendant limitation prominently.
  4. [§5, Eqs. (20)–(22)] The agreement between the two grey-body factor computations does not by itself validate the transmission coefficients, because both methods are WKB-type approximations built from the same potential V(r): the WKB formula (20) uses V₀ and V₀′′ at the barrier, while the QNM-correspondence formula (22) uses the WKB-Padé quasinormal frequencies of that same potential. Sub-percent agreement therefore tests the internal consistency of two approximations to the same scattering problem and cannot rule out a common systematic error from Eq. (11) or from the WKB barrier treatment. An independent check—direct numerical integration of the scattering problem (18) for real ω—should be added before the grey-body factor plots are presented as quantitative results.
minor comments (5)
  1. [§5 (near Eq. (22))] The text refers to 'the QNM–grey-body correspondence (equation (23))', but the correspondence formula is Eq. (22); the equation number should be corrected.
  2. [§4.4] The sentence 'the quantum corrected black hole of the same mass as its classical counterpart has longer lived modes with slightly smaller oscillations rate' is contradicted by Tables 1–3, which show Re ω slightly larger than the Schwarzschild value at the same mass (e.g., M=5, ℓ=2, γ=0.1: 0.075714 versus ≈0.07473); the wording should be aligned with the tabulated values.
  3. [Figs. 2–3] The axis labels of Figs. 2–3 appear garbled ('V/LParen1r/Star/RParen1', 'r/Star') and the captions contain spacing artifacts ('γ = 0 .1'); the figures should be regenerated with standard notation so that the potential plots are legible.
  4. [Tables 2–4] The captions read 'of the gravitational perturbations the Bonanno–Reuter black hole' and omit the word 'of'; each table caption should also state the fixed γ value explicitly.
  5. [§4.4; Tables 1–4] Since the central claim is convergence to Schwarzschild, the authors should tabulate the corresponding Schwarzschild fundamental frequencies explicitly (e.g., Mω≈0.37367−0.08896i for ℓ=2, n=0, axial) so that statements such as 'indistinguishable from Schwarzschild' have a stated numerical reference.

Circularity Check

1 steps flagged · score 4.0 of 10

Grey-body 'cross-check' is circular by construction; QNM claims rest on an independent time-domain integration.

  1. other [Section 5, Eqs. (20)-(22)]
    "Γℓ(ω)=(1+e^{2πK})^{-1}, K=i(ω²−V0)/√(−2V0′′)+··· (20)-(21); Γℓ(ω)≈[1+exp(2π(ω²−Re[ω0]²)/(4Re[ω0]|Im[ω0]|))]^{-1}+O(ℓ^{-1}) (22)"

    For a parabolic barrier, the WKB QNM condition (Eq. 15) gives Re[ω0]²≈V0 and 4Re[ω0]|Im[ω0]|≈√(2V0′′) for the fundamental mode. Substituting these into Eq. (22) reduces it to the leading-order WKB transmission formulas (20)-(21). Since ω0 in Eq. (22) is taken from the same sixth-order WKB calculation on the same effective potential, the 'correspondence' grey-body factors are not independent of the direct WKB grey-body factors. Their agreement is therefore expected by construction and cannot serve as a validation of the grey-body results or of the underlying potential.

full rationale

No fitting to data and no load-bearing self-citation chain occur. The quasinormal frequencies are computed from the effective potential via WKB and independently checked against time-domain integration of the same wave equation, with <0.005% agreement; that is a genuine numerical validation. The effective potential (Eq. 11) is imported from external references [14,16] rather than derived here, which is an assumption about the physics, not a circular step. The one circular element is the grey-body 'cross-check': the QNM-correspondence formula (Eq. 22) is algebraically equivalent to the WKB transmission formula (Eqs. 20-21) when the QNM frequency is obtained from the same WKB calculation, so the claimed concordance of the two grey-body methods is by construction. This does not undermine the WKB grey-body numbers themselves, which are still computed from the potential, but it does mean the paper's validation of the grey-body factors is redundant. The abstract's 'large γ' convergence claim is inconsistent with Eq. (3) and the tables, but that is a correctness issue, not circularity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 1 invented entities

The central results rest on the RG-improved metric and on the borrowed axial perturbation potential. No constants are fitted to data in this paper, but the free interpolation parameter gamma and the fixed RG parameter omega_tilde are model inputs. The effective-fluid description and the approximate nature of the WKB and eikonal methods are the main unproven ingredients.

free parameters (2)
  • gamma (interpolation parameter)
    Controls the RG scale interpolation in the metric (Eq. 1); treated as free and scanned over 0.01 to 10 in all results.
  • omega_tilde (RG parameter) = 118/(15*pi)
    Fixed to the phenomenologically motivated one-loop value from ref [9]; not fitted here, but all quantitative results depend on it.
assumptions (5)
  • domain assumption The Bonanno-Reuter metric (Eq. 3) correctly represents an asymptotically safe quantum black hole.
    Used throughout; adopted from ref [9] without derivation or independent test.
  • domain assumption Quantum corrections can be described as an effective anisotropic fluid, so the axial gravitational potential (Eq. 11) from refs [14,16] applies to this background.
    Explicitly called a 'practical workaround' in Section 3; the metric is not an exact Einstein solution, and the validity of the borrowed potential is the load-bearing assumption.
  • standard math Sixth/seventh-order WKB with Pade approximants is accurate for these potentials at low multipoles.
    Used to compute all QNM frequencies; accuracy is checked only by order differences and a single time-domain case.
  • domain assumption The QNM-grey-body correspondence (Eq. 22) holds at l=2 and l=3 within the claimed accuracy.
    This is an eikonal/geometric-optics approximation with O(1/l) corrections; used as the second grey-body method.
  • domain assumption A positive effective potential implies linear stability of the perturbations.
    The paper infers stability from Figures 2-3, but no rigorous stability proof is given.
invented entities (1)
  • Effective anisotropic fluid description of quantum corrections
    purpose: Provides a standard GR framework for deriving axial gravitational perturbation equations for a metric that is not an exact Einstein solution.
    Introduced in Section 3 as a workaround; no observational or theoretical independent evidence is provided for this specific fluid stress-energy.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Gravitational Quasinormal Modes and Grey-Body Factors of Bonanno-Reuter Regular Black Holes." pith.science (2026). https://pith.science/paper/KYMAALGJ

@misc{pith2026250707196,
  author       = {Pith},
  title        = {Pith review of: Gravitational Quasinormal Modes and Grey-Body Factors of Bonanno-Reuter Regular Black Holes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KYMAALGJ}},
  note         = {Machine review of arXiv:2507.07196}
}
abstract

We study gravitational perturbations of the Bonanno--Reuter quantum-corrected black hole arising in the asymptotic safety scenario, focusing on QNMs and grey-body factors. Assuming the RG parameter $\tilde{\omega}$ is fixed to its phenomenologically motivated value, we treat the interpolation parameter $\gamma$ as free and investigate how it modifies the black hole's response to axial gravitational perturbations. Quasinormal frequencies are computed using the sixth-order WKB method with Pad\'e approximants, and their dependence on $\gamma$ and the black hole mass $M$ is analyzed. We find that the Schwarzschild limit is rapidly recovered for large $M$ or large $\gamma$, while significant deviations arise in the quantum regime. The accuracy of the WKB results is confirmed by time-domain integration of the wave equation. Comparison of grey-body factors computed via both the WKB method and the quasinormal mode correspondence are in a good concordance. Our findings indicate that quantum corrections can leave significant imprints in the ringdown and radiation spectra, while preserving consistency with classical results in the appropriate limit.

Figures

Figures reproduced from arXiv: 2507.07196 by the authors.

Figure 1
Figure 1. Parametric range allowing for existence of the event horizon in the 𝑀-𝛾-plane. 3. Effective Potential for Gravitational Perturbations The analysis of axial gravitational perturbations in quantum-corrected black hole spacetimes derived from the Hamiltonian constraints approach is challenging, since the background metrics do not arise as exact solutions of the Einstein field equations, but rather from effective modifi… view at source ↗
Figure 2
Figure 2. Effective potentials for ℓ = 2 𝛾 = 0.1: 𝑀 = 1.66 (blue, top), 𝑀 = 2 (black, middle), 𝑀 = 10 (red, bottom). -50 50 100 150 rø 0.05 0.10 0.15 VHrøL [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Effective potentials for ℓ = 3 𝛾 = 0.1: 𝑀 = 1.66 (blue, top), 𝑀 = 2 (black, middle), 𝑀 = 10 (red, bottom). 4. Quasinormal Modes Quasinormal modes (QNMs) are characteristic oscillations of perturbed black holes, governed by linear field equations subject to specific boundary conditions. They dominate the intermediate ringdown phase of a black hole’s https://doi.org/10.xxxx/xxx 4 of 12 [PITH_FULL_IMAGE:figures/full_f… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Real and imaginary part of the dominant (𝑛 = 0) QNMs of the ℓ = 2 gravitational perturbations for the Bonanno-Reuter black hole calculated by WKB6Pade3 as functions of 𝑀, 𝛾 = 0.01 (blue), 𝛾 = 1 (red), 𝛾 = 9/2 (black), 𝛾 = 10 (green). The WKB method with Padé approximan…
Figure 5
Figure 5. Figure 5: Real and imaginary part of the dominant (𝑛 = 0) QNMs of the ℓ = 3 gravitational perturbations for the Bonanno-Reuter black hole calculated by WKB6Pade3 as functions of 𝑀, 𝛾 = 0.01 (blue), 𝛾 = 1 (red), 𝛾 = 9/2 (black), 𝛾 = 10 (green). 5. Grey-Body Factors In the semicla…
Figure 6
Figure 6. Figure 6: Time-domain profile for ℓ = 2 𝛾 = 0.1: 𝑀 = 1.66. The Prony method gives 𝜔 = 0.263305−0.042429𝑖, while the WKB data is 𝜔 = 0.263295 − 0.042414𝑖. https://doi.org/10.xxxx/xxx 9 of 12 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Grey-body factors for ℓ = 2 case calculated via the 6th order method and with the help of the correspon￾dence with QNMs (left) and the difference between the results obtained by the two methods (right): 𝛾 = 0.01 (blue), 𝛾 = 9/2 (red), 𝛾 = 10 (black). 0.05 0.10 0.15 0.2…
Figure 8
Figure 8. Figure 8: Grey-body factors for ℓ = 3 case calculated via the 6th order method and with the help of the correspon￾dence with QNMs (left) and the difference between the results obtained by the two methods (right): 𝛾 = 0.01 (blue), 𝛾 = 9/2 (red), 𝛾 = 10 (black). Moreover, the comp…

Discussion (0). Sign in to comment.

Forward citations

Cited by 6 Pith papers

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

  1. Where Do the Returns to Schooling Come From? Educational Transitions and Labor Market Payoffs

    stat.AP 2025-08 unverdicted novelty 6.0 of 10

    Abstract-only review: the announced additive mediation decomposition of education's ATE is unsupported by the attached full text, which is an unrelated physics manuscript.

  2. Hawking Emission from Black Holes Evaporating toward Wormholes and the Accuracy of the WKB Approximation

    gr-qc 2026-06 unverdicted novelty 5.5 of 10

    Numerical greybody factors for photons and massless Dirac fields in Simpson-Visser and Casadio-Fabbri-Mazzacurati geometries reveal that WKB overestimates luminosities by orders of magnitude near wormhole endpoints, i...

  3. Wave and particle probes of a regular T-duality-inspired black hole with gravitational self-energy

    gr-qc 2026-07 conditional novelty 4.0 of 10

    Increasing zero-point length makes photon and ISCO orbits more compact in ADM units while heavier scalars raise oscillation frequency and suppress damping on this regular self-energy black hole.

  4. Gravitational perturbations of a regular T-duality inspired black hole: Quasinormal modes, excitation factors, and time-domain evolution

    gr-qc 2026-07 conditional novelty 4.0 of 10

    Gravitational quasinormal-mode frequencies of a T-duality-inspired regular black hole are computed, showing the zero-point length makes the ringdown oscillate faster and alters damping non-monotonically.

  5. Long-lived quasinormal modes and grey-body factors of supermassive black holes with a dark matter halo

    gr-qc 2025-11 conditional novelty 4.0 of 10

    Massive scalar fields around a Schwarzschild black hole with a dark matter halo ring longer as field mass grows, while realistic halo parameters leave quasinormal frequencies and grey-body factors almost unchanged.

  6. Bonanno-Reuter regular black hole: quasi-resonances, grey-body factors and absorption cross-sections of a massive scalar field

    gr-qc 2025-10 conditional novelty 4.0 of 10

    Damping of massive scalar quasinormal modes decreases with field mass in the Bonanno-Reuter black hole, and grey-body factors shift to higher frequencies.

Reference graph

Works this paper leans on

37 extracted references · 33 canonical work pages · cited by 6 Pith papers

  1. [1]

    Quasinormal modes of stars and black holes

    Kokkotas, K.D.; Schmidt, B.G. Quasinormal modes of stars and black holes. Living Rev. Rel. 1999, 2, 2

    work page 1999

  2. [2]

    Quasinormal modes of black holes and black branes

    Berti, E.; Cardoso, V .; Starinets, A.O. Quasinormal modes of black holes and black branes. Class. Quant. Grav. 2009, 26, 163001,

    work page 2009

  3. [3]

    Quasinormal modes of black holes: From astrophysics to string theory

    Konoplya, R.A.; Zhidenko, A. Quasinormal modes of black holes: From astrophysics to string theory. Rev. Mod. Phys. 2011, 83, 793–836

    work page 2011

  4. [4]

    Review of analytic results on quasinormal modes of black holes

    Bolokhov, S.V .; Skvortsova, M. Review of analytic results on quasinormal modes of black holes. arXiv 2025, arXiv:2504.05014

    arXiv 2025

  5. [5]

    Particle Emission Rates from a Black Hole: Massless Particles from an Uncharged, Nonrotating Hole

    Page, D.N. Particle Emission Rates from a Black Hole: Massless Particles from an Uncharged, Nonrotating Hole. Phys. Rev. D 1976, 13, 198–206

    work page 1976

  6. [6]

    Black holes in theories with large extra dimensions: A Review

    Kanti, P. Black holes in theories with large extra dimensions: A Review. Int. J. Mod. Phys. A 2004, 19, 4899–4951

    work page 2004

  7. [7]

    Particle Creation by Black Holes

    Hawking, S.W. Particle Creation by Black Holes. Commun. Math. Phys. 1975, 43, 199–220. Erratum: Commun. Math. Phys. 1976, 46, 206

    work page 1975

  8. [8]

    The Asymptotic Safety Scenario in Quantum Gravity

    Niedermaier, M.; Reuter, M. The Asymptotic Safety Scenario in Quantum Gravity. Living Rev. Rel. 2006, 9, 5–173

    work page 2006

Show all 37 references
  1. [9]

    Renormalization group improved black hole space-times

    Bonanno, A.; Reuter, M. Renormalization group improved black hole space-times. Phys. Rev. D 2000, 62, 043008

    2000

  2. [10]

    Quasinormal ringing of regular black holes in asymptotically safe gravity: the importance of overtones

    Konoplya, R.A.; Zinhailo, A.F.; Kunz, J.; et al. Quasinormal ringing of regular black holes in asymptotically safe gravity: the importance of overtones. JCAP 2022, 10, 91

    2022

  3. [11]

    Quasinormal modes of an improved Schwarzschild black hole

    Rincón, A.; Panotopoulos, G. Quasinormal modes of an improved Schwarzschild black hole. Phys. Dark Univ. 2020, 30, 100639

    2020

  4. [12]

    Quasinormal modes for asymptotic safe black holes

    Liu, D.J.; Yang, B.; Zhai, Y .J.; et al. Quasinormal modes for asymptotic safe black holes. Class. Quant. Grav. 2012, 29, 145009

    2012

  5. [13]

    Quasinormal Modes for Electromagnetic Field Perturbation of the Asymptotic Safe Black Hole

    Li, J.; Zhong, Y . Quasinormal Modes for Electromagnetic Field Perturbation of the Asymptotic Safe Black Hole. Int. J. Theor . Phys.2013, 52, 1583–1587

    2013

  6. [14]

    A consistent model of non-singular Schwarzschild black hole in loop quantum gravity and its quasinormal modes

    Bouhmadi-López, M.; Brahma, S.; Chen, C.Y .; et al. A consistent model of non-singular Schwarzschild black hole in loop quantum gravity and its quasinormal modes. JCAP 2020, 7, 66

    2020

  7. [15]

    Stability of a Schwarzschild singularity

    Regge, T.; Wheeler, J.A. Stability of a Schwarzschild singularity. Phys. Rev. 1957, 108, 1063–1069

    1957

  8. [16]

    Probing the effective quantum gravity via quasinormal modes and shadows of black holes

    Konoplya, R.A.; Stashko, O.S. Probing the effective quantum gravity via quasinormal modes and shadows of black holes. Phys. Rev. D 2025, 111, 104055

    2025

  9. [17]

    Black hole normal modes: A semianalytic approach

    Schutz, B.F.; Will, C.M. Black hole normal modes: A semianalytic approach. Astrophys. J. Lett. 1985, 291, L33–L36

    1985

  10. [18]

    Black Hole Normal Modes: A WKB Approach

    Iyer, S.; Will, C.M. Black Hole Normal Modes: A WKB Approach. 1. Foundations and Application of a Higher Order WKB Analysis of Potential Barrier Scattering. Phys. Rev. D 1987, 35, 3621

    1987

  11. [19]

    Quasinormal behavior of the d-dimensional Schwarzschild black hole and higher order WKB approach

    Konoplya, R.A. Quasinormal behavior of the d-dimensional Schwarzschild black hole and higher order WKB approach. Phys. Rev. D 2003, 68, 024018

    2003

  12. [20]

    Quasinormal modes of black holes

    Matyjasek, J.; Opala, M. Quasinormal modes of black holes. The improved semianalytic approach. Phys. Rev. D 2017, 96, 024011

    2017

  13. [21]

    Long-lived quasinormal modes and oscillatory tails of the Bardeen spacetime

    Bolokhov, S.V . Long-lived quasinormal modes and oscillatory tails of the Bardeen spacetime. Phys. Rev. D 2024, 109, 064017

    2024

  14. [22]

    Late time decay of scalar and Dirac fields around an asymptotically de Sitter black hole in the Eu- ler–Heisenberg electrodynamics

    Bolokhov, S.V . Late time decay of scalar and Dirac fields around an asymptotically de Sitter black hole in the Eu- ler–Heisenberg electrodynamics. Eur . Phys. J. C2024, 84, 634

  15. [23]

    Ringing of Extreme Regular Black Holes

    Skvortsova, M. Ringing of Extreme Regular Black Holes. Grav. Cosmol. 2024, 30, 279–288

    2024

  16. [24]

    Quasinormal Spectrum of (2+1)-Dimensional Asymptotically Flat, dS and AdS Black Holes

    Skvortsova, M. Quasinormal Spectrum of (2+1)-Dimensional Asymptotically Flat, dS and AdS Black Holes. F ortsch. Phys. 2024, 72, 2400036. https://doi.org/10.xxxx/xxx 11 of 12 Bolokhov and Skvortsova Int. J. Gravit. Theor . Phys. 2025, V olume(Issue), Page Number

    2024

  17. [25]

    Late time behavior of stellar collapse and explosions: 1

    Gundlach, C.; Price, R.H.; Pullin, J. Late time behavior of stellar collapse and explosions: 1. Linearized perturbations. Phys. Rev. D 1994, 49, 883–889

    1994

  18. [26]

    Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations

    Konoplya, R.A.; Zhidenko, A.; Zinhailo, A.F. Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations. Class. Quant. Grav. 2019, 36, 155002

    2019

  19. [27]

    Correspondence between grey-body factors and quasinormal modes

    Konoplya, R.A.; Zhidenko, A. Correspondence between grey-body factors and quasinormal modes. JCAP 2024, 09, 068

    2024

  20. [28]

    Correspondence between quasinormal modes and grey-body factors of spherically symmetric traversable wormholes

    Bolokhov, S.V .; Skvortsova, M. Correspondence between quasinormal modes and grey-body factors of spherically symmetric traversable wormholes. JCAP 2025, 4, 25

    2025

  21. [29]

    Quantum corrected black holes: testing the correspondence between grey-body factors and quasinormal modes

    Skvortsova, M. Quantum corrected black holes: testing the correspondence between grey-body factors and quasinormal modes. arXiv 2024, arXiv:2411.06007

    2024 arXiv

  22. [30]

    Grey-body factors for gravitational and electromagnetic perturbations around Gibbons-Maeda-Garfinkle- Horovits-Strominger black holes

    Dubinsky, A. Grey-body factors for gravitational and electromagnetic perturbations around Gibbons-Maeda-Garfinkle- Horovits-Strominger black holes. arXiv 2024, arXiv:2412.00625

    2024

  23. [31]

    Correspondence between quasinormal modes and grey-body factors for massive fields in Schwarzschild-de Sitter spacetime

    Malik, Z. Correspondence between quasinormal modes and grey-body factors for massive fields in Schwarzschild-de Sitter spacetime. JCAP 2025, 4, 42

    2025

  24. [32]

    Quasinormal Modes and Gray-Body Factors for Gravitational Perturbations in Asymptotically Safe Gravity

    Lütfüo˘glu, B.C. Quasinormal Modes and Gray-Body Factors for Gravitational Perturbations in Asymptotically Safe Gravity. arXiv 2025, arXiv:2505.06966

    2025

  25. [33]

    Non-minimal Einstein–Yang–Mills black holes: fundamental quasinormal mode and grey-body factors versus outburst of overtones

    Lütfüo˘glu, B.C. Non-minimal Einstein–Yang–Mills black holes: fundamental quasinormal mode and grey-body factors versus outburst of overtones. Eur . Phys. J. C2025, 85, 630

  26. [34]

    Long-lived quasinormal modes and gray-body factors of black holes and wormholes in dark matter inspired Weyl gravity

    Lütfüo˘glu, B.C. Long-lived quasinormal modes and gray-body factors of black holes and wormholes in dark matter inspired Weyl gravity. Eur . Phys. J. C2025, 85, 486

  27. [35]

    Quasinormal modes of renormalization group improved Dymnikova regular black holes

    Konoplya, R.A.; Stuchlik, Z.; Zhidenko, A.; Zinhailo, A.F. Quasinormal modes of renormalization group improved Dymnikova regular black holes. Phys. Rev. D 2023, 107, 104050

    2023

  28. [36]

    Quasinormal spectrum in the asymptotically safe gravity

    Zinhailo, A.F. Quasinormal spectrum in the asymptotically safe gravity. arXiv 2023, arXiv:2311.05380

    2023 arXiv

  29. [37]

    Quasinormal modes and gray-body factors of regular black holes in asymptotically safe gravity

    Stashko, O. Quasinormal modes and gray-body factors of regular black holes in asymptotically safe gravity. Phys. Rev. D 2024, 110, 084016. https://doi.org/10.xxxx/xxx 12 of 12

    2024

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.