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Transition from Regular Black Holes to Wormholes in Covariant Effective Quantum Gravity: Scattering, Quasinormal Modes, and Hawking Radiation

T0 review · 2 major / 7 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read Quantum corrections to black holes predict ultra-long-lived wormhole ringdown modes near the black-hole–wormhole transition.

desk verdict Useful first QNM/grey-body computation for the Zhang et al. metric, but the 'arbitrarily long-lived' threshold claim outruns the numerics and several tables have copy-paste errors. read the letter →

arxiv 2502.05689 v2 pith:ZPUFQ45M submitted 2025-02-08 gr-qc

R. A. Konoplya , O. S. Stashko This is my paper · ORCID
classification gr-qc
keywords quasinormalmodesregularblackholestraversablewormholesquantum-correctedspacetimesgrey-bodyfactorsHawkingradiationringdownechoesRegge-Wheelerperturbations
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

Using a quantum-corrected spacetime family derived from Hamiltonian-constraint quantum gravity, this paper computes how black holes and wormholes ring when perturbed. For the black-hole branch, the fundamental quasinormal mode stays within about 10–15% of the Schwarzschild value while higher overtones deviate from Schwarzschild by more than 30%, encoding near-horizon quantum corrections. At the transition value $\xi \approx 3.93M$, the solution becomes a traversable wormhole and the spectrum changes abruptly: the fundamental mode becomes exceptionally long-lived, with its damping rate decreasing as $\xi$ approaches the threshold, and time-domain signals show early echoes followed by a slowly decaying ringdown. The same calculation yields grey-body factors, absorption cross-sections, and Hawking radiation rates. If these features survive in the full quantum theory, they would give gravitational-wave observables that distinguish quantum-corrected compact objects from classical black holes.

What carries the argument

The central object is the quantum-corrected line element with metric functions $f(r)$ and $\mu(r)$ controlled by the quantum parameter $\xi$; for $\xi/M < \pi^{3/2}/\sqrt{2} \approx 3.937$ it describes a regular black hole, and for larger values a traversable wormhole with throat radius $r_m = \sqrt[6]{2 M \xi^2/3}$. The argument runs by reducing axial gravitational, scalar, and electromagnetic perturbations to a single master wave equation with the potentials of equations (13)–(15), then solving the boundary-value problem with a pseudospectral method and with time-domain integration. The mechanism that produces long-lived modes is the double-peaked effective potential in the wormhole regime: waves bounce between the two peaks, producing echoes and trapping slowly decaying modes, and as $\xi$ approaches the critical value from above, the fundamental damping rate tends to zero. Analytic eikonal/WKB expansions provide control at large multipole number $\ell$.

What would settle it

Compute the axial gravitational quasinormal spectrum directly from the full Hamiltonian-constraint perturbation equations for the same metric family. If the fundamental $\ell=2$ mode at $\xi=3.94M$ has a damping rate far from $|\mathrm{Im}\,\omega| \approx 5.7\times 10^{-6}$ (the effective-theory value), then the predicted long-lived wormhole modes are an artifact of the effective fluid treatment.

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Extended reading notes

Core claim

On its own terms, the paper establishes that the quasinormal spectrum sharply encodes the quantum parameter $\xi$ of the metric family given by equations (1)–(3). For regular black holes, the fundamental axial mode is close to Schwarzschild ($\omega_0 \approx 0.3737 - 0.0890i$ for $\ell=2$ at small $\xi$), but overtones drift increasingly, with the third overtone departing by more than 30% from its Schwarzschild counterpart. In the wormhole regime $\xi > \xi_{\mathrm{cr}} \approx 3.93M$, the spectrum is not a smooth continuation of the black-hole spectrum: it forms a new set of modes that are non-perturbative in $\xi$, and near the threshold the fundamental mode becomes arbitrarily long-lived, for example $\omega_0 \approx 0.1330 - 5.7\times 10^{-6} i$ for $\ell=2$ at $\xi=3.94M$. Time-domain evolution shows echoes at early times followed by a late-time ringdown controlled by these slowly decaying modes. The paper also reports that for wormholes the quasinormal-mode/grey-body-factor correspondence breaks down because the effective potential has two peaks, while for black holes it holds for larger $\ell$; and it provides Hawking-temperature, grey-body, and energy-emission profiles that vary strongly with $\xi$.

Load-bearing premise

The computation treats the quantum-corrected metric as a solution of Einstein's equations with an anisotropic fluid and perturbs it with standard Regge-Wheeler theory, because perturbing the underlying Hamiltonian constraint theory directly has not been done; if that effective description is not what the full quantum theory produces, the predicted overtones and long-lived modes would not be the real signal.

Editorial extensions

If this is right

  • Ringdown waveforms from a quantum-corrected black hole would look nearly Schwarzschild in the fundamental mode but show growing deviations in the first overtones, so searches that include overtones could expose near-horizon quantum structure.
  • Near the transition to a wormhole, the signal would contain early echoes followed by a very slowly decaying tone; detecting such a pattern in a gravitational-wave event would be evidence for a black-hole-to-wormhole transition rather than a classical remnant.
  • Wormhole grey-body factors are non-monotonic in frequency with narrow quasi-resonances, so the absorption and emission spectra carry a clear wormhole fingerprint.
  • The Hawking energy emission rate peaks at $\xi \approx 3.86M$, beyond the peak of the Hawking temperature at $\xi \approx 3.08M$, showing that grey-body factors, not just temperature, set the observed flux.

Reading between the lines

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

  • A natural extension is to test whether the long-lived modes survive direct Hamiltonian-constraint perturbation theory; if they do, they would provide a target for low-frequency gravitational-wave searches that is free of the tail-suppression problem noted for massive-field long-lived modes.
  • The abrupt spectral change and overtone reconnection at the transition suggest an analogy with level crossing in quantum systems; searches could look for a discontinuous shift in the ringdown frequency as a compact object's parameters evolve.
  • Because the wormhole potential is double-peaked and symmetric, the long-lived modes are symmetric or antisymmetric about the throat; a rotating generalization could break this symmetry and split or destabilize the modes, which would be a concrete next test.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 7 minor

Summary. The paper studies axial gravitational, scalar, and electromagnetic perturbations of the quantum-corrected black hole and wormhole spacetimes derived by Zhang et al. from a Hamiltonian-constraint approach. Using Chebyshev pseudospectral and time-domain (Gundlach–Price–Pullin) methods, it computes quasinormal frequencies for the black-hole branch (ξ < ξ_c ≈ 3.937) and the wormhole branch (ξ > ξ_c), finds that the wormhole fundamental modes become extremely long-lived near the transition (Table II gives Im(ω) = −6.6×10⁻⁹ at ξ = 3.94 for ℓ = 3), and reports grey-body factors, absorption cross-sections, and Hawking emission rates. It also derives eikonal WKB expansions for the quasinormal modes to order ξ⁴ and 1/κ². The paper concludes that the black-hole-to-wormhole transition leaves an observable late-time signature with echoes and long-lived modes, potentially relevant for pulsar timing array experiments.

Significance. The background metric is motivated by a covariant effective quantum-gravity construction and interpolates between regular black holes and traversable wormholes, making the perturbation study timely. The main results—overtone deviations in the black-hole branch and long-lived wormhole modes near the transition—are physically interesting and, if confirmed, could serve as an observational discriminant for this class of quantum-corrected compact objects. The analytic WKB expansions and the explicit test of the quasinormal-mode/grey-body correspondence for black holes are useful additions. The numerical setup follows standard methods and the master equations appear correctly reduced. However, the headline claim of 'arbitrarily long-lived' modes rests on a single pseudospectral eigenvalue at ξ = 3.94 with no convergence study and no closer-to-threshold calculation, and there are data-quality issues in the appendix tables; the quantitative support is therefore incomplete.

major comments (2)
  1. [§V.B, Table II, Conclusions] The statement that wormhole modes become 'arbitrarily long-lived' as ξ approaches the critical threshold is an extrapolation from a single computation at ξ = 3.94, the closest value to ξ_c ≈ 3.937. At that point Table II gives the ℓ = 3 fundamental mode as Im(ω) = −6.6×10⁻⁹, more than three orders of magnitude smaller than the ℓ = 3 fundamental at ξ = 4.0, but no grid-convergence data, no time-domain integration, and no intermediate points (e.g., ξ = 3.95, 3.945) are reported. Because pseudospectral eigenvalues with exponentially small imaginary parts are susceptible to contamination, the numerical evidence does not yet establish the 'arbitrarily long-lived' limit. The authors should either provide a convergence study at ξ = 3.94, compute values closer to ξ_c, and confirm one near-threshold mode with an independent method (time-domain integration or a WKB estimate of the inter-barrier trapping time), or temper the conclusion to 'very long-lived at the closest computed point'.
  2. [§IV.A, Appendix A] The pseudospectral section states that calculations are performed on two grids and only the overlapping eigenvalues are retained, but the manuscript never reports the grid sizes N, the differences between the two grids, or error estimates for the quoted frequencies. Given that the central quantitative claim rests on Table II entries with |Im(ω)| as small as 10⁻⁶–10⁻⁹, a convergence table (e.g., values of the ℓ = 3 fundamental at ξ = 3.94 and ξ = 4.0 for N = 200, 250, 300, 350) is necessary. Without such data, the reader cannot distinguish genuine long-lived modes from numerical artifacts near the transition.
minor comments (7)
  1. [§III.A] The phrase 'The of the axial gravitational perturbations' is missing a word; it should read 'The axial gravitational perturbations' or 'The perturbation of the axial gravitational field'.
  2. [§IV, §V, §VI] There are several typographical errors: 'domians' should be 'domains' (§IV), 'pertrubations' should be 'perturbations' (§V), and 'absorbtion' should be 'absorption' (§VI and figure captions).
  3. [Appendix A, Table IV] The caption of Table IV states 'ℓ = 0 and 1', but the table lists ℓ = 1 and 2; moreover, electromagnetic perturbations have no ℓ = 0 mode, so the caption should be corrected to 'ℓ = 1 and 2'.
  4. [Appendix A, Tables IV and V] Several entries are duplicated across different ℓ values: in Table IV the ξ = 3.5 and ξ = 3.9 rows are identical for ℓ = 1 and ℓ = 2, and in Table V the ξ = 4.6 row is identical for ℓ = 2 and ℓ = 3. These appear to be copy-paste errors and must be corrected, as they undermine confidence in the time-domain data used to support the quasinormal-mode values.
  5. [Figures 9 and 14] Fig. 9 and Fig. 14 appear to be the same figure, with the same caption and the same panels. One should be removed and the figure numbering checked throughout the manuscript.
  6. [§VI.B, Eq. (36)] The correction term Σ(ω₀,ω₁) in Eq. (36) is not defined, and the symbol Γₗ(ω) is not used elsewhere in the text. Please define the notation and specify how many correction terms from Ref. [33] are included in the numerical comparison.
  7. [§II] The expression for the throat radius r_m in Section II is typeset ambiguously; please rewrite it in standard notation so that the dependence on M and ξ is unambiguous.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the quasinormal-mode and grey-body results are obtained by solving the fixed background wave equation with standard numerical methods, and the cited self-references are methodological rather than load-bearing.

full rationale

The paper's central claims are self-contained numerical computations rather than refits of target outputs. The quasinormal modes are obtained by solving the master wave equation (16) for the fixed quantum-corrected metric (1)-(3), using the Chebyshev pseudospectral method and independent time-domain integration, with standard purely-ingoing/purely-outgoing boundary conditions (17). The grey-body factors and absorption cross-sections are likewise computed by direct numerical integration of (16) with scattering boundary conditions (30). No parameter is fitted to the QNM or grey-body data, and the long-lived wormhole modes emerge from the double-peaked effective potential for xi > xi_c rather than being imposed by an ansatz. The eikonal WKB expressions (25)-(29) are analytic approximations derived by expanding the potential maximum and applying standard WKB formulas; they are not used as inputs to the numerical spectra that support the headline claims. The grey-body/QNM correspondence (36) is cited from the authors' prior work, but it is only checked against independently computed numerical data, and in the wormhole case it is found to break down, so it is not a load-bearing input. Self-citations such as [5], [33], [78], and [83] are methodological or contextual and do not constitute a uniqueness argument or a fitted-input reduction. The noted limitation that direct perturbations in the Hamiltonian approach have not been carried out is an explicit model assumption, not a circular step. The near-threshold extrapolation to 'arbitrarily long-lived modes' is a robustness concern about numerical convergence, but it is not circularity under the definitions used here.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new particles or forces and fits no data. It borrows the quantum-corrected metric, with its free parameter xi, from prior work; the main assumptions are the effective-fluid description of perturbations and the standard QNM/scattering framework.

free parameters (1)
  • xi (quantum parameter)
    Free parameter of the metric from arXiv:2412.02487; varied over 0.01 <= xi/M <= 100, with transition at xi/M ~ 3.93. Not fitted to data in this paper, but the central results depend on it.
assumptions (4)
  • domain assumption The quantum-corrected metric (1)-(3) from Zhang et al. is a valid spacetime for perturbations; it solves Einstein equations with an effective anisotropic fluid.
    Section III A: perturbations are modeled by treating the metric as a solution of Einstein equations with stress-energy (8), an effective approach not derived from the Hamiltonian constraint theory in this paper.
  • standard math Standard Regge-Wheeler perturbation equations for spherically symmetric backgrounds apply to the axial sector.
    Section III: master equations (12)-(15) are taken from standard black-hole perturbation theory [6,7,42,43].
  • standard math WKB eikonal expansion [83-85] provides accurate QNM approximation for large ell.
    Section V: analytic expressions (25)-(29) are used; the WKB method is prior standard, and the authors note its breakdown for double-peaked wormhole potentials.
  • domain assumption The wormhole potential's symmetry allows reducing boundary conditions to symmetric/antisymmetric modes at the throat.
    Section IV: for WH case, they impose Psi(0)=0 or Psi'(0)=0 after noting V(r*)=V(-r*). This is justified by symmetry but assumes the full solution is decomposed into these sectors.

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Cite this review

Pith. "Pith review of Transition from Regular Black Holes to Wormholes in Covariant Effective Quantum Gravity: Scattering, Quasinormal Modes, and Hawking Radiation." pith.science (2026). https://pith.science/paper/ZPUFQ45M

@misc{pith2026250205689,
  author       = {Pith},
  title        = {Pith review of: Transition from Regular Black Holes to Wormholes in Covariant Effective Quantum Gravity: Scattering, Quasinormal Modes, and Hawking Radiation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZPUFQ45M}},
  note         = {Machine review of arXiv:2502.05689}
}
read the original abstract

Utilizing the Hamiltonian constraints approach, a quantum-corrected solution has been derived \cite{Zhang:2024ney}, which describes either a regular black hole or a traversable wormhole, contingent upon the value of the quantum parameter. In this work, we compute the quasinormal modes associated with axial gravitational and test fields' perturbations of these objects. We see that due to quantum corrections near the event horizon, the first several overtones deviate from their Schwarzschild values at an increasing rate. The transition between the black hole and wormhole states is marked by modifications in the late-time signal. Our findings reveal that the fundamental quasinormal modes of quantum-corrected black holes exhibit only slight deviations from those of the classical Schwarzschild solution. However, at the transition, the spectrum undergoes significant changes, with the wormhole state characterized by exceptionally long-lived quasinormal modes. In addition, we calculate absorption cross-sections of partial waves, grey-body factors and energy emission rates of Hawking radiation.

Figures

Figures reproduced from arXiv: 2502.05689 by the authors.

Figure 1
Figure 1. FIG. 1. The effective potentials (left) and time-domain profiles for [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The effective potential (left) and the time-domain profile of perturbations (right) for [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The effective potential (left) and the time-domain profiles of perturbations (middle and right) for [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The fundamental mode and the first five overtones as a function of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The QNMs trajectories in the complex [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The fundamental mode and the first seven overtones as a function of [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The typical behavior of overtone curves near the [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. The QNMs trajectories in the complex [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. The typical behavior of the total absorption cross-section for different values of [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. The Hawking temperature as a function of [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Typical dependencies of the energy emission rate per unit frequency for various values of [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Typical behavior of greybody factors for various values of [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. The typical behavior of the grey-body factors for different values of [PITH_FULL_IMAGE:figures/full_fig_p010_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. The typical behavior of the total absorption cross-section for different values of [PITH_FULL_IMAGE:figures/full_fig_p011_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. The typical behavior of the total absorption cross [PITH_FULL_IMAGE:figures/full_fig_p011_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. The contributions of the partial cross-sections with different [PITH_FULL_IMAGE:figures/full_fig_p012_16.png]

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Reference graph

Works this paper leans on

111 extracted references · 12 canonical work pages · cited by 11 Pith papers

  1. [1]

    changes relatively mildly—by about10−15%—the third overtone deviates from its Schwarzschild limit by more than30%, with the deviation increasing as the over- tone number grows. For smaller multipole numbersℓ, which correspond to the dynamical degrees of freedom of fields with lower spin (such as scalar, electromagnetic, and Dirac fields), the deviation of...

  2. [2]

    T.Thiemann,Modern Canonical Quantum General Rel- ativity(Cambridge University Press, Cambridge, UK, 2007)

    2007

  3. [3]

    Ashtekar and J

    A. Ashtekar and J. Lewandowski, Class. Quant. Grav. 21, R53 (2004), arXiv:gr-qc/0404018 [gr-qc]

    arXiv 2004

  4. [4]

    C.Zhang, J.Lewandowski, Y.Ma, andJ.Yang, (2024), arXiv:2412.02487 [gr-qc]

    arXiv 2024

  5. [5]

    R. A. Konoplya and O. S. Stashko, (2024), arXiv:2408.02578 [gr-qc]

    arXiv 2024

  6. [6]

    K. D. Kokkotas and B. G. Schmidt, Living Rev. Rel.2, 2 (1999), arXiv:gr-qc/9909058

    arXiv 1999

  7. [7]

    C.Zhang, J.Lewandowski, Y.Ma, andJ.Yang, (2024), arXiv:2407.10168 [gr-qc]

    arXiv 2024

  8. [8]

    D. N. Page, Phys. Rev. D13, 198 (1976)

    1976

Show all 111 references
  1. [9]

    D. N. Page, Phys. Rev. D14, 3260 (1976)

    1976

  2. [10]

    R. A. Konoplya and A. Zhidenko, Rev. Mod. Phys.83, 793 (2011), arXiv:1102.4014 [gr-qc]

    2011 arXiv

  3. [11]

    Simpson and M

    A. Simpson and M. Visser, JCAP02, 042 (2019), arXiv:1812.07114 [gr-qc]

    2019 arXiv

  4. [12]

    Casadio, A

    R. Casadio, A. Fabbri, and L. Mazzacurati, Phys. Rev. D65, 084040 (2002), arXiv:gr-qc/0111072

    2002 arXiv

  5. [13]

    Kanti, N

    P. Kanti, N. E. Mavromatos, J. Rizos, K. Tamvakis, and E. Winstanley, Phys. Rev. D54, 5049 (1996), arXiv:hep-th/9511071

    1996 arXiv

  6. [14]

    K. A. Bronnikov and R. K. Walia, Phys. Rev. D105, 044039 (2022), arXiv:2112.13198 [gr-qc]

    2022 arXiv

  7. [15]

    Alencar, A

    G. Alencar, A. Duran-Cabacés, D. Rubiera-Garcia, and D. Sáez-Chillón Gómez, (2025), arXiv:2501.03909 [gr- qc]

    2025 arXiv

  8. [16]

    K. A. Bronnikov and S.-W. Kim, Phys. Rev. D67, 064027 (2003), arXiv:gr-qc/0212112

    2003 arXiv

  9. [17]

    M. S. Churilova and Z. Stuchlik, Class. Quant. Grav. 37, 075014 (2020), arXiv:1911.11823 [gr-qc]

    2020 arXiv

  10. [18]

    R. A. Konoplya and A. Zhidenko, JHEAp44, 419 (2024), arXiv:2209.00679 [gr-qc]

    2024 arXiv

  11. [19]

    K. A. Bronnikov and R. A. Konoplya, Phys. Rev. D 101, 064004 (2020), arXiv:1912.05315 [gr-qc]

    2020 arXiv

  12. [20]

    R. A. Konoplya, A. F. Zinhailo, J. Kunz, Z. Stuch- lik, and A. Zhidenko, JCAP10, 091 (2022), arXiv:2206.14714 [gr-qc]

    2022 arXiv

  13. [21]

    A. F. Zinhailo, (2024), 10.13140/RG.2.2.26785.01124

    2024

  14. [22]

    R. A. Konoplya, Int. J. Mod. Phys. D32, 2342014 (2023), arXiv:2312.16249 [gr-qc]

    2023 arXiv

  15. [23]

    S. V. Bolokhov, Phys. Rev. D110, 024010 (2024), arXiv:2311.05503 [gr-qc]

    2024 arXiv

  16. [24]

    R. A. Konoplya and A. Zhidenko, Phys. Rev. D109, 043014 (2024), arXiv:2310.19205 [gr-qc]

    2024 arXiv

  17. [25]

    R. A. Konoplya, Z. Stuchlik, A. Zhidenko, and A. F. Zinhailo, Phys. Rev. D107, 104050 (2023), arXiv:2303.01987 [gr-qc]

    2023 arXiv

  18. [26]

    R. A. Konoplya, JCAP07, 001 (2023), arXiv:2305.09187 [gr-qc]

    2023 arXiv

  19. [27]

    R. A. Konoplya, Phys. Rev. D107, 064039 (2023), arXiv:2210.14506 [gr-qc]

    2023 arXiv

  20. [28]

    R. A. Konoplya, D. Ovchinnikov, and B. Ahmedov, Phys. Rev. D108, 104054 (2023), arXiv:2307.10801 [gr- qc]

    2023 arXiv

  21. [29]

    Luo, Phys

    S. Luo, Phys. Rev. D110, 084071 (2024), arXiv:2408.08139 [gr-qc]

    2024

  22. [30]

    Zhang, H

    D. Zhang, H. Gong, G. Fu, J.-P. Wu, and Q. Pan, Eur. Phys. J. C84, 564 (2024), arXiv:2402.15085 [gr-qc]

    2024 arXiv

  23. [31]

    𝐴𝑙≡|𝒯| 2 = 1−|ℛ| 2 .(32) In the BH case the use of grey-body factors is necessary ingredient for the estimation of the intensity of Hawking radiation

    The grey-body factor𝐴𝑙 is defined as the transmis- sion coefficient. 𝐴𝑙≡|𝒯| 2 = 1−|ℛ| 2 .(32) In the BH case the use of grey-body factors is necessary ingredient for the estimation of the intensity of Hawking radiation. The quasi-thermal energy emission rate from the black hol...

  24. [32]

    L.-G. Zhu, G. Fu, S. Li, D. Zhang, and J.-P. Wu, (2024), arXiv:2410.00543 [gr-qc]

    2024 arXiv

  25. [33]

    R. A. Konoplya and A. Zhidenko, JCAP09, 068 (2024), arXiv:2406.11694 [gr-qc]

    2024 arXiv

  26. [34]

    Oshita, Phys

    N. Oshita, Phys. Rev. D109, 104028 (2024), arXiv:2309.05725 [gr-qc]

    2024 arXiv

  27. [35]

    R. F. Rosato, K. Destounis, and P. Pani, Phys. Rev. D 110, L121501 (2024), arXiv:2406.01692 [gr-qc]

    2024 arXiv

  28. [36]

    Paul, (2025), arXiv:2501.03745 [gr-qc]

    S. Paul, (2025), arXiv:2501.03745 [gr-qc]

    2025

  29. [37]

    R. A. Konoplya and A. Zhidenko, Phys. Lett. B861, 139288 (2025), arXiv:2408.11162 [gr-qc]

    2025 arXiv

  30. [38]

    W. Liu, D. Wu, and J. Wang, (2024), arXiv:2412.18083 [gr-qc]

    2024

  31. [39]

    Bouhmadi-López, S

    M. Bouhmadi-López, S. Brahma, C.-Y. Chen, P. Chen, and D.-h. Yeom, JCAP07, 066 (2020), arXiv:2004.13061 [gr-qc]

    2020 arXiv

  32. [40]

    Ashtekar, J

    A. Ashtekar, J. Olmedo, and P. Singh, Phys. Rev. Lett. 121, 241301 (2018), arXiv:1806.00648 [gr-qc]

    2018 arXiv

  33. [41]

    Ashtekar, J

    A. Ashtekar, J. Olmedo, and P. Singh, Phys. Rev. D 98, 126003 (2018), arXiv:1806.02406 [gr-qc]

    2018 arXiv

  34. [42]

    Grav.26, 163001 (2009), arXiv:0905.2975 [gr-qc]

    E.Berti, V.Cardoso, andA.O.Starinets,Class.Quant. Grav.26, 163001 (2009), arXiv:0905.2975 [gr-qc]

    2009 arXiv

  35. [43]

    Bonanno and M

    A. Bonanno and M. Reuter, Phys. Rev. D62, 043008 (2000), arXiv:hep-th/0002196

    2000 arXiv

  36. [44]

    Regge and J

    T. Regge and J. A. Wheeler, Phys. Rev.108, 1063 (1957)

    1957

  37. [45]

    Boyd,Chebyshev and Fourier Spectral Methods: Sec- ond Revised Edition, Dover Books on Mathematics (Dover Publications, 2013)

    J. Boyd,Chebyshev and Fourier Spectral Methods: Sec- ond Revised Edition, Dover Books on Mathematics (Dover Publications, 2013)

    2013

  38. [46]

    Chen and P

    C.-Y. Chen and P. Chen, Phys. Rev. D99, 104003 (2019), arXiv:1902.01678 [gr-qc]

    2019 arXiv

  39. [47]

    R. A. Konoplya and C. Molina, Phys. Rev. D71, 124009 (2005), arXiv:gr-qc/0504139

    2005 arXiv

  40. [48]

    Alfaro, P

    S. Alfaro, P. A. González, D. Olmos, E. Papantonopou- los, and Y. Vásquez, Phys. Rev. D109, 104009 (2024), arXiv:2402.15575 [gr-qc]

    2024 arXiv

  41. [49]

    Gundlach, R

    C. Gundlach, R. H. Price, and J. Pullin, Phys. Rev. D 49, 883 (1994), arXiv:gr-qc/9307009

    1994 arXiv

  42. [50]

    F. S. Khoo, B. Azad, J. L. Blázquez-Salcedo, L. M. González-Romero, B. Kleihaus, J. Kunz, and F. Navarro-Lérida, Phys. Rev. D109, 084013 (2024), arXiv:2401.02898 [gr-qc]

    2024 arXiv

  43. [51]

    M. S. Churilova, R. A. Konoplya, and A. Zhidenko, Phys. Lett. B802, 135207 (2020), arXiv:1911.05246 [gr- qc]

    2020 arXiv

  44. [52]

    Batic and D

    D. Batic and D. Dutykh, Classical and Quantum Grav- ity41, 215003 (2024)

    2024

  45. [53]

    B. Azad, J. L. Blázquez-Salcedo, X. Y. Chew, J. Kunz, and D.-h. Yeom, Phys. Rev. D107, 084024 (2023), arXiv:2212.12601 [gr-qc]

    2023 arXiv

  46. [54]

    S.Aneesh, S.Bose, andS.Kar,Phys.Rev.D97,124004 (2018), arXiv:1803.10204 [gr-qc]

    2018 arXiv

  47. [55]

    M. S. Churilova, R. A. Konoplya, Z. Stuchlik, and A. Zhidenko, JCAP10, 010 (2021), arXiv:2107.05977 [gr-qc]

    2021 arXiv

  48. [56]

    R. A. Konoplya, Phys. Lett. B784, 43 (2018), arXiv:1805.04718 [gr-qc]

    2018 arXiv

  49. [57]

    Jusufi, Gen

    K. Jusufi, Gen. Rel. Grav.53, 87 (2021), arXiv:2007.16019 [gr-qc]

    2021 arXiv

  50. [58]

    M. A. Cuyubamba, R. A. Konoplya, and A. Zhidenko, Phys. Rev. D98, 044040 (2018), arXiv:1804.11170 [gr- qc]

    2018 arXiv

  51. [59]

    J. L. Blázquez-Salcedo, X. Y. Chew, and J. Kunz, Phys. 16 Rev. D98, 044035 (2018), arXiv:1806.03282 [gr-qc]

    2018 arXiv

  52. [60]

    P. D. Roy, Eur. Phys. J. C82, 673 (2022), arXiv:2110.05019 [gr-qc]

    2022 arXiv

  53. [61]

    P. A. González, E. Papantonopoulos, A. Rincón, and Y. Vásquez, Phys. Rev. D106, 024050 (2022), arXiv:2205.06079 [gr-qc]

    2022 arXiv

  54. [62]

    R. A. Konoplya, A. Khrabustovskyi, J. Kříž, and A. Zhidenko, (2025), arXiv:2501.16134 [gr-qc]

    2025 arXiv

  55. [63]

    R. A. Konoplya and A. Zhidenko, Phys. Rev. D81, 124036 (2010), arXiv:1004.1284 [hep-th]

    2010 arXiv

  56. [64]

    S. H. Völkel and K. D. Kokkotas, Class. Quant. Grav. 35, 105018 (2018), arXiv:1802.08525 [gr-qc]

    2018 arXiv

  57. [65]

    Bueno, P

    P. Bueno, P. A. Cano, F. Goelen, T. Hertog, and B. Vercnocke, Phys. Rev. D97, 024040 (2018), arXiv:1711.00391 [gr-qc]

    2018 arXiv

  58. [66]

    K.G.e.a.Arun,LivingReviewsinRelativity25(2022), 10.1007/s41114-022-00036-9

    2022 doi

  59. [67]

    K. A. Bronnikov, R. A. Konoplya, and A. Zhidenko, Phys. Rev. D86, 024028 (2012), arXiv:1205.2224 [gr- qc]

    2012 arXiv

  60. [68]

    K. A. Bronnikov, R. A. Konoplya, and T. D. Pappas, Phys. Rev. D103, 124062 (2021), arXiv:2102.10679 [gr- qc]

    2021 arXiv

  61. [69]

    Chirenti, A

    C. Chirenti, A. Saa, and J. Skakala, Phys. Rev. D86, 124008 (2012), arXiv:1206.0037 [gr-qc]

    2012 arXiv

  62. [70]

    Cardoso, E

    V. Cardoso, E. Franzin, and P. Pani, Phys. Rev. Lett. 116, 171101 (2016), [Erratum: Phys.Rev.Lett. 117, 089902 (2016)], arXiv:1602.07309 [gr-qc]

    2016 arXiv

  63. [71]

    O. S. Stashko, O. V. Savchuk, and V. I. Zhdanov, Phys. Rev. D109, 024012 (2024), arXiv:2307.04295 [gr-qc]

    2024 arXiv

  64. [72]

    R. A. Konoplya, Z. Stuchlík, and A. Zhidenko, (2024), arXiv:2411.09014 [gr-qc]

    2024

  65. [73]

    Franzin, S

    E. Franzin, S. Liberati, and V. Vellucci, Journal of Cosmology and Astroparticle Physics2024, 020 (2024)

    2024

  66. [74]

    Ohashi and M.-a

    A. Ohashi and M.-a. Sakagami, Class. Quant. Grav.21, 3973 (2004), arXiv:gr-qc/0407009

    2004 arXiv

  67. [75]

    Davlataliev, B

    A. Davlataliev, B. Narzilloev, I. Hussain, A. Abdujab- barov, and B. Ahmedov, (2024), arXiv:2412.09464 [gr- qc]

    2024 arXiv

  68. [76]

    R. A. Konoplya and A. V. Zhidenko, Phys. Lett. B609, 377 (2005), arXiv:gr-qc/0411059

    2005 arXiv

  69. [77]

    A. F. Zinhailo, Phys. Lett. B853, 138682 (2024), arXiv:2403.06867 [gr-qc]

    2024 arXiv

  70. [78]

    R. A. Konoplya and A. Zhidenko, Class. Quant. Grav. 40, 245005 (2023), arXiv:2309.02560 [gr-qc]

    2023 arXiv

  71. [79]

    R. A. Konoplya and A. Zhidenko, Phys. Lett. B853, 138685 (2024), arXiv:2307.01110 [gr-qc]

    2024 arXiv

  72. [80]

    M. H.-Y. Cheung, K. Destounis, R. P. Macedo, E. Berti, and V. Cardoso, Physical Review Letters128(2022), 10.1103/physrevlett.128.111103

    2022 doi

  73. [81]

    Malik, Int

    Z. Malik, Int. J. Theor. Phys.63, 128 (2024), arXiv:2409.09872 [gr-qc]

    2024 arXiv

  74. [82]

    Malik, EPL147, 69001 (2024), arXiv:2410.04306 [gr- qc]

    Z. Malik, EPL147, 69001 (2024), arXiv:2410.04306 [gr- qc]

    2024 arXiv

  75. [83]

    Malik, Z

    Z. Malik, Z. Naturforsch. A79, 1063 (2024)

    2024

  76. [84]

    Iyer and C

    S. Iyer and C. M. Will, Phys. Rev. D35, 3621 (1987)

    1987

  77. [85]

    Malik, Int

    Z. Malik, Int. J. Theor. Phys.64, 30 (2025)

    2025

  78. [86]

    R. A. Konoplya, Phys. Rev. D68, 024018 (2003), arXiv:gr-qc/0303052

    2003 arXiv

  79. [87]

    R. A. Konoplya and A. F. Zinhailo, Eur. Phys. J. C80, 1049 (2020), arXiv:2003.01188 [gr-qc]

    2020 arXiv

  80. [88]

    B. F. Schutz and C. M. Will, Astrophys. J. Lett.291, L33 (1985)

    1985

  81. [89]

    Cardoso, A

    V. Cardoso, A. S. Miranda, E. Berti, H. Witek, and V. T. Zanchin, Phys. Rev. D79, 064016 (2009), arXiv:0812.1806 [hep-th]

    2009 arXiv

  82. [90]

    S. V. Bolokhov, Phys. Lett. B856, 138879 (2024), arXiv:2310.12326 [gr-qc]

    2024 arXiv

  83. [91]

    R. A. Konoplya and Z. Stuchlík, Phys. Lett. B771, 597 (2017), arXiv:1705.05928 [gr-qc]

    2017 arXiv

  84. [92]

    R. A. Konoplya, Phys. Lett. B838, 137674 (2023), arXiv:2210.08373 [gr-qc]

    2023 arXiv

  85. [93]

    J. A. H. Futterman, F. A. Handler, and R. A. Matzner, SCATTERING FROM BLACK HOLES, Cambridge Monographs on Mathematical Physics (Cambridge Uni- versity Press, 2012)

    2012

  86. [94]

    J. L. Jaramillo, R. Panosso Macedo, and L. Al Sheikh, Phys. Rev. X11, 031003 (2021), arXiv:2004.06434 [gr- qc]

    2021 arXiv

  87. [95]

    Oshita, K

    N. Oshita, K. Takahashi, and S. Mukohyama, Phys. Rev. D110, 084070 (2024), arXiv:2406.04525 [gr-qc]

    2024 arXiv

  88. [96]

    L. K. S. Furuta, R. B. Magalhães, H. C. D. Lima, Ju- nior., and L. C. B. Crispino, Phys. Rev. D110, 124039 (2024)

    2024

  89. [97]

    B. Azad, F. Loran, and A. Mostafazadeh, Eur. Phys. J. C80, 1097 (2020), arXiv:2010.15023 [gr-qc]

    2020 arXiv

  90. [98]

    H. C. D. Lima, C. L. Benone, and L. C. B. Crispino, Phys. Rev. D101, 124009 (2020), arXiv:2006.03967 [gr- qc]

    2020 arXiv

  91. [99]

    M. A. A. de Paula, L. C. S. Leite, S. R. Dolan, and L. C. B. Crispino, Phys. Rev. D109, 064053 (2024), arXiv:2401.01767 [gr-qc]

    2024 arXiv

  92. [100]

    Q. Li, Q. Wang, and J. Jia, Phys. Rev. D111, 024059 (2025), arXiv:2411.02987 [gr-qc]

    2025 arXiv

  93. [101]

    R. B. Magalhães, A. Masó-Ferrando, G. J. Olmo, and L. C. B. Crispino, Phys. Rev. D108, 024063 (2023), arXiv:2303.03924 [gr-qc]

    2023 arXiv

  94. [102]

    R.A.Konoplya, A.Zhidenko, andA.F.Zinhailo,Class. Quant. Grav.36, 155002 (2019), arXiv:1904.10333 [gr- qc]

    2019 arXiv

  95. [103]

    Cardoso and R

    V. Cardoso and R. Vicente, Phys. Rev. D100, 084001 (2019)

    2019

  96. [104]

    Wu, R.-G

    L.-B. Wu, R.-G. Cai, and L. Xie, (2024), arXiv:2411.07734 [gr-qc]

    2024 arXiv

  97. [105]

    This correspondence has been inves- tigated in several recent studies [106–108]

    for wormholes. This correspondence has been inves- tigated in several recent studies [106–108]. From the pre- cise numerical data obtained here for quasinormal modes and grey-body factors, we confirm that, if the multipole numberℓis not small, the correspondence holds with hig...

  98. [106]

    S. V. Bolokhov, K. A. Bronnikov, and R. A. Konoplya, (2023), arXiv:2306.11083 [gr-qc]

    2023 arXiv

  99. [107]

    R. A. Konoplya and A. F. Zinhailo, Phys. Rev. D99, 104060 (2019), arXiv:1904.05341 [gr-qc]

    2019 arXiv

  100. [108]

    S. V. Bolokhov and M. Skvortsova, (2024), arXiv:2412.11166 [gr-qc]

    2024 arXiv

  101. [109]

    Malik, (2024), 10.13140/RG.2.2.33693.01768, arXiv:2412.19443 [gr-qc]

    Z. Malik, (2024), 10.13140/RG.2.2.33693.01768, arXiv:2412.19443 [gr-qc]

    2024

  102. [110]

    Skvortsova, (2024), arXiv:2411.06007 [gr-qc]

    M. Skvortsova, (2024), arXiv:2411.06007 [gr-qc]

    2024 arXiv

  103. [111]

    Dubinsky, (2024), arXiv:2412.00625 [gr-qc]

    A. Dubinsky, (2024), arXiv:2412.00625 [gr-qc]

    2024

Pith tools

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