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arxiv: 2606.03842 · v1 · pith:PIWNGAEMnew · submitted 2026-06-02 · 🌀 gr-qc

Scattering and Hawking Radiation from Einstein--Euler--Heisenberg--de Sitter Black Holes

Jayden Tan This is my paper

Pith reviewed 2026-06-28 08:50 UTC · model grok-4.3

classification 🌀 gr-qc
keywords greybody factorsHawking radiationEuler-Heisenberg black holesde Sitter spacetimescalar fieldsDirac fieldsnumerical integrationcosmological constant
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The pith

Greybody factors for scalar and Dirac fields around Einstein-Euler-Heisenberg-de Sitter black holes rise with nonlinear coupling and fall with cosmological constant, while luminosity depends on the temperature prescription.

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

This paper calculates the transmission probabilities for waves scattering between the black hole horizon and the cosmological horizon in a spacetime that includes nonlinear electromagnetic effects and a positive cosmological constant. It finds that larger values of the Euler-Heisenberg coupling make the potential barriers higher, requiring higher frequencies for significant transmission. Increasing the cosmological constant shrinks the region and lowers the frequency thresholds for transmission. The amount of radiation emitted, however, changes depending on which formula is used for the temperature of the de Sitter space, with some choices making the emission brighter as the nonlinear term grows and others making it dimmer and reversing the effect. This shows that understanding how these black holes evaporate requires choosing a specific temperature convention.

Core claim

The paper establishes that neutral scalar and neutral massless Dirac greybody factors are computed by direct numerical integration of the wave equation in the static patch between horizons, checked with sixth-order WKB. Along the studied family, the Euler-Heisenberg coupling raises the dominant barriers and shifts half-transmission frequencies upward for both fields. At fixed charge and coupling, the cosmological constant contracts the patch and lowers the thresholds. Luminosity is controlled as much by the de Sitter temperature prescription as by the greybody factors, with event-horizon prescriptions brightening emission as nonlinear correction grows while effective static-patch temperature

What carries the argument

Numerical solution of the radial wave equation as a two-sided scattering problem across the finite static patch, yielding transmission coefficients that determine the greybody factors, together with separate choice of de Sitter temperature for the Hawking spectrum calculation.

If this is right

  • Increasing the Euler-Heisenberg coupling raises the dominant scalar and Dirac barriers and shifts the half-transmission frequencies upward.
  • At fixed charge and nonlinear coupling, increasing the cosmological constant contracts the static patch and lowers the dominant greybody thresholds.
  • Event-horizon temperature prescriptions brighten the emission as the nonlinear correction grows.
  • Effective static-patch temperatures give much smaller rates and can reverse the trend with nonlinear coupling.
  • The evaporation interpretation is not unique unless the temperature convention is specified explicitly.

Where Pith is reading between the lines

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

  • Different temperature prescriptions might correspond to different physical observer frames or coordinate choices in de Sitter space.
  • The sensitivity to temperature choice could influence models of black hole evolution in expanding universes.
  • Extending the numerical method to charged fields or including backreaction might test whether the prescription dependence persists in more general cases.

Load-bearing premise

The finite region between the black-hole and cosmological horizons can be treated as a two-sided scattering problem whose transmission coefficients are reliably obtained by direct numerical integration, and that a specific de Sitter temperature prescription can be chosen independently when interpreting luminosity.

What would settle it

A recalculation of the spectra using an alternative numerical method or exact solution for the transmission coefficients that produces luminosity trends independent of the chosen temperature prescription.

Figures

Figures reproduced from arXiv: 2606.03842 by Jayden Tan.

Figure 1
Figure 1. Figure 1: FIG. 1. Metric function and representative effective potentials for the reference family [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: the turn-on of the scalar and Dirac greybody factors shifts to larger frequency as the [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Direct numerical greybody factors for neutral scalar and Dirac test fields for [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Greybody factors for representative neutral scalar and Dirac channels at fixed [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Direct transmission coefficients compared with first- and sixth-order WKB estimates for [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Representative temperature prescriptions for the reference de Sitter static patch with [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Neutral scalar and Dirac emission spectra for [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Integrated neutral scalar-plus-Dirac power as a function of [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
read the original abstract

We compute neutral scalar and neutral massless Dirac greybody factors and Hawking spectra for the positive-cosmological-constant branch of the Einstein--Euler--Heisenberg black hole. The finite region between the black-hole and cosmological horizons is treated as a two-sided scattering problem, with direct numerical integrations providing the transmission coefficients and a sixth-order WKB calculation used as a local check near the barrier top. Along the reference family studied here, increasing the Euler--Heisenberg coupling raises the dominant scalar and Dirac barriers and shifts the half-transmission frequencies upward. At fixed charge and nonlinear coupling, increasing the cosmological constant contracts the static patch and lowers the dominant greybody thresholds. The luminosity is controlled as much by the de Sitter temperature prescription as by the greybody factors: event-horizon prescriptions brighten the emission as the nonlinear correction grows, whereas effective static-patch temperatures give much smaller rates and can reverse the trend. Thus the evaporation interpretation is not unique unless the temperature convention is specified explicitly.

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

0 major / 3 minor

Summary. The paper computes neutral scalar and neutral massless Dirac greybody factors and Hawking spectra for the positive-cosmological-constant branch of Einstein-Euler-Heisenberg black holes. The static patch between black-hole and cosmological horizons is treated as a two-sided scattering problem; transmission coefficients are obtained by direct numerical integration of the radial wave equation with a sixth-order WKB calculation used as a local check near the barrier peak. Along the reference family, increasing the Euler-Heisenberg coupling raises the dominant barriers and shifts half-transmission frequencies upward, while increasing the cosmological constant contracts the static patch and lowers greybody thresholds. Luminosities depend strongly on the chosen de Sitter temperature prescription, with event-horizon prescriptions yielding brighter emission that grows with nonlinear coupling and effective static-patch temperatures producing smaller rates that can reverse the trend.

Significance. If the numerical results hold, the work supplies concrete parameter trends for greybody factors and spectra in a nonlinear-electrodynamics de Sitter background and explicitly demonstrates the non-uniqueness of evaporation rates under different temperature conventions. Strengths include the use of two independent methods (direct integration plus WKB cross-check) and the clear separation of the greybody computation from the temperature choice, both of which are standard yet often under-emphasized in the de Sitter literature.

minor comments (3)
  1. The abstract and introduction would benefit from a brief statement of the precise numerical tolerances and convergence criteria used in the direct integrations, together with a short table or plot of sample transmission coefficients versus integration step size or grid resolution.
  2. Notation for the two temperature prescriptions (event-horizon versus effective static-patch) should be introduced once with explicit formulas and then used consistently in all luminosity plots and tables.
  3. A short discussion of the range of validity of the sixth-order WKB approximation relative to the numerical results (e.g., percentage deviation at the barrier peak for representative parameter values) would strengthen the cross-check claim.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive evaluation of our manuscript. The summary accurately describes the computations, methods, and main findings on greybody factors, transmission coefficients, and the sensitivity of luminosities to temperature prescriptions. We appreciate the recognition of the two-method verification and the explicit separation of greybody factors from temperature choices. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central results consist of direct numerical integration of the radial wave equation for scalar and Dirac fields on the fixed Einstein-Euler-Heisenberg-de Sitter metric between the black-hole and cosmological horizons, supplemented by a sixth-order WKB check near the barrier peak. Transmission coefficients, barrier heights, half-transmission frequencies, and luminosities under two explicit temperature prescriptions are obtained by varying the Euler-Heisenberg coupling, charge, and cosmological constant as independent inputs; none of these outputs are defined in terms of the others or obtained by fitting to a target quantity. No self-citations, uniqueness theorems, or ansatzes are invoked as load-bearing steps that reduce the claimed trends to the paper's own fitted parameters or prior definitions. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on the standard assumption that the wave equation for neutral scalar and massless Dirac fields can be separated and integrated numerically on the given background metric, plus the modeling choice of a de Sitter temperature prescription. No new entities are postulated.

free parameters (2)
  • Euler-Heisenberg coupling constant
    Varied along a reference family; specific values chosen for the study rather than derived from first principles.
  • Cosmological constant
    Varied at fixed charge and nonlinear coupling to explore contraction of the static patch.
axioms (2)
  • domain assumption The background is the Einstein-Euler-Heisenberg-de Sitter metric with positive cosmological constant
    Invoked as the fixed geometry on which the wave equations are solved.
  • standard math Neutral scalar and massless Dirac fields propagate according to the standard wave equations on this curved background
    Required to set up the scattering problem between horizons.

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discussion (0)

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

    gr-qc 2026-06 unverdicted novelty 5.0

    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...

  2. Hawking Radiation from the Dymnikova Regular Black Hole

    gr-qc 2026-06 unverdicted novelty 4.0

    Numerical greybody factors for the Dymnikova black hole show temperature-driven luminosity suppression near the extremal remnant, with increasing fermion dominance in the residual massless flux.

Reference graph

Works this paper leans on

89 extracted references · 40 linked inside Pith · cited by 2 Pith papers

  1. [1]

    S. W. Hawking, Commun. Math. Phys.43, 199 (1975)

    1975

  2. [2]

    W. G. Unruh, Phys. Rev. D14, 3251 (1976)

    1976

  3. [3]

    Jansen, Eur

    A. Jansen, Eur. Phys. J. Plus132, 546 (2017), arXiv:1709.09178 [gr-qc]

    Pith/arXiv arXiv 2017

  4. [4]

    R. A. Konoplya and A. Zhidenko, JHEP06, 037 (2004), arXiv:hep-th/0402080

    Pith/arXiv arXiv 2004

  5. [5]

    Arag´ on, R

    A. Arag´ on, R. B´ ecar, P. A. Gonz´ alez, and Y. V´ asquez, Eur. Phys. J. C80, 773 (2020), arXiv:2004.05632 [gr-qc]

    arXiv 2020

  6. [6]

    Zhidenko, Class

    A. Zhidenko, Class. Quant. Grav.21, 273 (2004), arXiv:gr-qc/0307012

    arXiv 2004

  7. [7]

    Dyatlov, Commun

    S. Dyatlov, Commun. Math. Phys.306, 119 (2011), arXiv:1003.6128 [math.AP]

    Pith/arXiv arXiv 2011

  8. [8]

    Kanti and R

    P. Kanti and R. A. Konoplya, Phys. Rev. D73, 044002 (2006), arXiv:hep-th/0512257

    Pith/arXiv arXiv 2006

  9. [9]

    Y. Mo, Y. Tian, B. Wang, H. Zhang, and Z. Zhong, Phys. Rev. D98, 124025 (2018), 25 arXiv:1808.03635 [gr-qc]

    Pith/arXiv arXiv 2018

  10. [10]

    Jing, Phys

    J.-l. Jing, Phys. Rev. D69, 084009 (2004), arXiv:gr-qc/0312079

    Pith/arXiv arXiv 2004

  11. [11]

    R. A. Konoplya and A. Zhidenko, Phys. Rev. Lett.103, 161101 (2009), arXiv:0809.2822 [hep- th]

    Pith/arXiv arXiv 2009

  12. [12]

    M. A. Cuyubamba, R. A. Konoplya, and A. Zhidenko, Phys. Rev. D93, 104053 (2016), arXiv:1604.03604 [gr-qc]

    Pith/arXiv arXiv 2016

  13. [13]

    Molina, Phys

    C. Molina, Phys. Rev. D68, 064007 (2003), arXiv:gr-qc/0304053

    Pith/arXiv arXiv 2003

  14. [14]

    R. A. Konoplya and A. Zhidenko, Nucl. Phys. B777, 182 (2007), arXiv:hep-th/0703231

    Pith/arXiv arXiv 2007

  15. [15]

    B. C. L¨ utf¨ uo˘ glu, J. Rayimbaev, N. Kurbonov, S. Murodov, and F. Javed, (2026), arXiv:2605.25076 [gr-qc]

    Pith/arXiv arXiv 2026

  16. [16]

    B. C. L¨ utf¨ uo˘ glu, Fortsch. Phys.74, e70074 (2026), arXiv:2510.10579 [gr-qc]

    arXiv 2026

  17. [17]

    R. A. Konoplya and A. Zhidenko, Phys. Rev. D89, 024011 (2014), arXiv:1309.7667 [hep-th]

    Pith/arXiv arXiv 2014

  18. [18]

    S. V. Bolokhov, (2026), arXiv:2605.21533 [gr-qc]

    Pith/arXiv arXiv 2026

  19. [19]

    S. V. Bolokhov, Eur. Phys. J. C84, 634 (2024), arXiv:2404.09364 [gr-qc]

    arXiv 2024

  20. [20]

    Skvortsova, Fortsch

    M. Skvortsova, Fortsch. Phys.72, 2400036 (2024), arXiv:2311.11650 [gr-qc]

    arXiv 2024

  21. [21]

    R. A. Konoplya and A. Zhidenko, Phys. Rev. D95, 104005 (2017), arXiv:1701.01652 [hep-th]

    Pith/arXiv arXiv 2017

  22. [22]

    Skvortsova, (2026), arXiv:2605.12113 [gr-qc]

    M. Skvortsova, (2026), arXiv:2605.12113 [gr-qc]

    Pith/arXiv arXiv 2026

  23. [23]

    Malik, (2026), arXiv:2604.00216 [gr-qc]

    Z. Malik, (2026), arXiv:2604.00216 [gr-qc]

    arXiv 2026

  24. [24]

    Malik, Annals Phys.482, 170238 (2025), arXiv:2504.12570 [gr-qc]

    Z. Malik, Annals Phys.482, 170238 (2025), arXiv:2504.12570 [gr-qc]

    arXiv 2025

  25. [25]

    Heisenberg and H

    W. Heisenberg and H. Euler, Z. Phys.98, 714 (1936), arXiv:physics/0605038

    Pith/arXiv arXiv 1936

  26. [26]

    B. C. L¨ utf¨ uo˘ glu, Phys. Lett. B871, 140026 (2025), arXiv:2508.13361 [gr-qc]

    arXiv 2025

  27. [27]

    Malik, Int

    Z. Malik, Int. J. Grav. Theor. Phys.1, 6 (2025), arXiv:2509.15995 [gr-qc]

    arXiv 2025

  28. [28]

    Magos and N

    D. Magos and N. Bret´ on, Phys. Rev. D102, 084011 (2020), arXiv:2009.05904 [gr-qc]

    arXiv 2020

  29. [29]

    Ye, Z.-Q

    X. Ye, Z.-Q. Chen, M.-D. Li, and S.-W. Wei, Chin. Phys. C46, 115102 (2022), arXiv:2202.09053 [gr-qc]

    arXiv 2022

  30. [30]

    H. Dai, Z. Zhao, and S. Zhang, Nucl. Phys. B991, 116219 (2023), arXiv:2202.14007 [gr-qc]

    arXiv 2023

  31. [31]

    N. J. Gogoi and P. Phukon, Phys. Dark Univ.44, 101456 (2024), arXiv:2312.13577 [hep-th]

    arXiv 2024

  32. [32]

    Zhao and H

    Y. Zhao and H. Cheng, Chin. Phys. C48, 125106 (2024), arXiv:2501.11075 [hep-th]

    arXiv 2024

  33. [33]

    Jafarzade, Z

    K. Jafarzade, Z. Bazyar, S. Saghafi, and K. Nozari, Eur. Phys. J. C85, 869 (2025), arXiv:2504.09690 [gr-qc]

    arXiv 2025

  34. [34]

    Yajima and T

    H. Yajima and T. Tamaki, Phys. Rev. D63, 064007 (2001), arXiv:gr-qc/0005016. 26

    Pith/arXiv arXiv 2001

  35. [35]

    Kanti and T

    P. Kanti and T. Pappas, Phys. Rev. D96, 024038 (2017), arXiv:1705.09108 [hep-th]

    Pith/arXiv arXiv 2017

  36. [36]

    Pappas and P

    T. Pappas and P. Kanti, Phys. Lett. B775, 140 (2017), arXiv:1707.04900 [hep-th]

    Pith/arXiv arXiv 2017

  37. [37]

    Bousso and S

    R. Bousso and S. W. Hawking, Phys. Rev. D54, 6312 (1996), arXiv:gr-qc/9606052

    Pith/arXiv arXiv 1996

  38. [38]

    Carter, Commun

    B. Carter, Commun. Math. Phys.10, 280 (1968)

    1968

  39. [39]

    R. A. Konoplya, Z. Stuchl´ ık, and A. Zhidenko, Phys. Rev. D97, 084044 (2018), arXiv:1801.07195 [gr-qc]

    Pith/arXiv arXiv 2018

  40. [40]

    R. A. Konoplya and A. Zhidenko, Phys. Rev. D97, 084034 (2018), arXiv:1712.06667 [gr-qc]

    Pith/arXiv arXiv 2018

  41. [41]

    H. T. Cho and Y. C. Lin, Class. Quant. Grav.22, 775 (2005), arXiv:gr-qc/0411090

    Pith/arXiv arXiv 2005

  42. [42]

    Kanti, R

    P. Kanti, R. A. Konoplya, and A. Zhidenko, Phys. Rev. D74, 064008 (2006), arXiv:gr- qc/0607048

    arXiv 2006

  43. [43]

    H. T. Cho, Phys. Rev. D68, 024003 (2003), arXiv:gr-qc/0303078

    Pith/arXiv arXiv 2003

  44. [44]

    R. A. Konoplya and A. Zhidenko, Phys. Rev. D76, 084018 (2007), [Erratum: Phys.Rev.D 90, 029901 (2014)], arXiv:0707.1890 [hep-th]

    Pith/arXiv arXiv 2007

  45. [45]

    Iyer and C

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

    1987

  46. [46]

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

    Pith/arXiv arXiv 2003

  47. [47]

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

    Pith/arXiv arXiv 2019

  48. [48]

    S. V. Bolokhov, (2026), arXiv:2605.03137 [gr-qc]

    Pith/arXiv arXiv 2026

  49. [49]

    R. A. Konoplya and A. Zhidenko, Phys. Rev. D82, 084003 (2010), arXiv:1004.3772 [hep-th]

    Pith/arXiv arXiv 2010

  50. [50]

    B. C. L¨ utf¨ uo˘ glu, Eur. Phys. J. C85, 630 (2025), arXiv:2504.18482 [gr-qc]

    arXiv 2025

  51. [51]

    Skvortsova, (2026), arXiv:2604.25471 [gr-qc]

    M. Skvortsova, (2026), arXiv:2604.25471 [gr-qc]

    Pith/arXiv arXiv 2026

  52. [52]

    Bret´ on, T

    N. Bret´ on, T. Clark, and S. Fernando, Int. J. Mod. Phys. D26, 1750112 (2017), arXiv:1703.10070 [gr-qc]

    Pith/arXiv arXiv 2017

  53. [53]

    Bolokhov, Eur

    S. Bolokhov, Eur. Phys. J. C85, 1166 (2025)

    2025

  54. [54]

    R. A. Konoplya and A. Zhidenko, Phys. Rev. D109, 104005 (2024), arXiv:2403.07848 [gr-qc]

    arXiv 2024

  55. [55]

    Fernando, Gen

    S. Fernando, Gen. Rel. Grav.48, 24 (2016), arXiv:1601.06407 [gr-qc]

    Pith/arXiv arXiv 2016

  56. [56]

    R. A. Konoplya and A. Zhidenko, Phys. Lett. B686, 199 (2010), arXiv:0909.2138 [hep-th]

    Pith/arXiv arXiv 2010

  57. [57]

    S. V. Bolokhov and M. Skvortsova, Int. J. Grav. Theor. Phys.1, 3 (2025), arXiv:2507.07196 [gr-qc]

    arXiv 2025

  58. [58]

    Karmakar and U

    R. Karmakar and U. D. Goswami, Phys. Scripta99, 055003 (2024), arXiv:2310.18594 [gr-qc]

    arXiv 2024

  59. [59]

    Skvortsova, EPL149, 59001 (2025), arXiv:2503.03650 [gr-qc]

    M. Skvortsova, EPL149, 59001 (2025), arXiv:2503.03650 [gr-qc]. 27

    arXiv 2025

  60. [60]

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

    arXiv 2023

  61. [61]

    Guo and Y.-G

    Y. Guo and Y.-G. Miao, Phys. Rev. D102, 064049 (2020), arXiv:2005.07524 [hep-th]

    arXiv 2020

  62. [62]

    S. V. Bolokhov, (2026), arXiv:2605.11013 [gr-qc]

    Pith/arXiv arXiv 2026

  63. [63]

    Kodama, R

    H. Kodama, R. A. Konoplya, and A. Zhidenko, Phys. Rev. D81, 044007 (2010), arXiv:0904.2154 [gr-qc]

    Pith/arXiv arXiv 2010

  64. [64]

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

    arXiv 2019

  65. [65]

    Skvortsova, Grav

    M. Skvortsova, Grav. Cosmol.30, 279 (2024), arXiv:2405.15807 [gr-qc]

    arXiv 2024

  66. [66]

    R. A. Konoplya and A. Zhidenko, Phys. Lett. B856, 138945 (2024), arXiv:2404.09063 [gr-qc]

    arXiv 2024

  67. [67]

    S. V. Bolokhov, (2026), arXiv:2604.11845 [gr-qc]

    Pith/arXiv arXiv 2026

  68. [68]

    R. A. Konoplya and O. S. Stashko, Phys. Rev. D111, 084031 (2025), arXiv:2502.05689 [gr-qc]

    arXiv 2025

  69. [69]

    Malik, Int

    Z. Malik, Int. J. Grav. Theor. Phys.2, 3 (2026), arXiv:2603.18887 [gr-qc]

    arXiv 2026

  70. [70]

    D. S. Eniceicu and M. Reece, Phys. Rev. D102, 044015 (2020), arXiv:1912.05553 [gr-qc]

    arXiv 2020

  71. [71]

    B. C. L¨ utf¨ uo˘ glu, Eur. Phys. J. C85, 486 (2025), arXiv:2503.16087 [gr-qc]

    arXiv 2025

  72. [72]

    S. V. Bolokhov and M. Skvortsova, Eur. Phys. J. C86, 374 (2026), arXiv:2508.19989 [gr-qc]

    arXiv 2026

  73. [73]

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

    arXiv 2024

  74. [74]

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

    Pith/arXiv arXiv 2010

  75. [75]

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

    arXiv 2024

  76. [76]

    S. V. Bolokhov, Phys. Rev. D109, 064017 (2024)

    2024

  77. [77]

    Skvortsova, EPL154, 49001 (2026), arXiv:2509.18061 [gr-qc]

    M. Skvortsova, EPL154, 49001 (2026), arXiv:2509.18061 [gr-qc]

    arXiv 2026

  78. [78]

    Skvortsova, Fortsch

    M. Skvortsova, Fortsch. Phys.72, 2400132 (2024), arXiv:2405.06390 [gr-qc]

    arXiv 2024

  79. [79]

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

    arXiv 2023

  80. [80]

    J. P. Arbelaez, JCAP05, 043 (2026), arXiv:2601.22340 [gr-qc]

    Pith/arXiv arXiv 2026

Showing first 80 references.