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arxiv: 2605.24369 · v1 · pith:UW4TD2VXnew · submitted 2026-05-23 · 🌀 gr-qc

Imprints of Black Hole Shadows and Polarization Patterns of Various Thick Disks: Bumblebee gravity

Muhammad Israr Aslam , Nazek Alessa , Chen-Yu Yang , Xiao-Xiong Zeng This is my paper

Pith reviewed 2026-06-30 13:47 UTC · model grok-4.3

classification 🌀 gr-qc
keywords black hole shadowpolarizationBumblebee gravityKerr-Sen black holeaccretion disk modelsframe draggingmodified gravity
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The pith

Simulations of Kerr-Sen-like black holes in Bumblebee gravity reveal that central dark regions in the shadow shrink with the Lorentz symmetry breaking parameter while brightness asymmetry increases with the Bumblebee charge.

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

This study explores the shadow and polarization patterns of a Kerr-Sen-like black hole in Bumblebee gravity at 230 GHz using RIAF-like and BAAF thick disk models. It shows that increasing the Lorentz symmetry breaking parameter ℓ causes two central dark regions around the bright ring to shrink, while the Bumblebee charge Q enhances the brightness asymmetry due to frame-dragging. The BAAF model produces thinner rings and more distinct higher-order images than RIAF, and anisotropic emission creates elliptical structures. Polarization follows the intensity and depends on the parameters, reflecting the spacetime. These results indicate that such observations can probe the black hole and accretion physics in modified gravity.

Core claim

The main discovery is that both models depict the bright ring encircled by two central dark regions, each gradually shrinking with increasing ℓ. Frame-dragging gives rise to pronounced brightness asymmetry enhanced with increasing Q. In anisotropic emission, a vertically stretched elliptical ring structure emerges. The BAAF disk shows a geometrically thinner bright ring with more pronounced separation between primary and higher-order images. Polarization patterns trace the brightness distribution and vary with ℓ and Q, reflecting the spacetime structure.

What carries the argument

Kerr-Sen-like black hole in Bumblebee gravity with LSB parameter ℓ and Bumblebee charge Q, modeled using RIAF-like phenomenological and BAAF analytical thick disk models for emission at 230 GHz.

If this is right

  • Both models show two central dark regions encircling the bright ring that shrink with increasing ℓ.
  • Frame-dragging produces brightness asymmetry enhanced with increasing Q.
  • Anisotropic emission leads to a vertically stretched elliptical ring.
  • The BAAF model has a geometrically thinner bright ring and more pronounced image separation than RIAF.
  • Polarization patterns trace brightness and vary with ℓ and Q.

Where Pith is reading between the lines

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

  • The described features offer a potential way to test Bumblebee gravity using existing millimeter telescope data.
  • Differences between the two disk models imply that accurate accretion modeling is needed to isolate gravity effects.
  • Polarization data could help measure the Bumblebee charge independently of the shadow size.

Load-bearing premise

The RIAF-like and BAAF models accurately capture the emission and geometry of accretion flows around the Kerr-Sen-like black hole in Bumblebee gravity.

What would settle it

If high-resolution images at 230 GHz fail to show the predicted shrinkage of central dark regions with ℓ or the enhancement of asymmetry with Q, the claimed imprints would not hold.

Figures

Figures reproduced from arXiv: 2605.24369 by Chen-Yu Yang, Muhammad Israr Aslam, Nazek Alessa, Xiao-Xiong Zeng.

Figure 1
Figure 1. Figure 1: FIG. 1: Imaging results of the thick accretion disk for isotropic radiation under the RIAF model, and the [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Intensity distribution for isotropic radiation under the RIAF model, and the accretion flow follows [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Intensity distribution for isotropic radiation under the RIAF model, and the accretion flow follows [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Imaging results of the thick accretion disk for anisotropic radiation under the RIAF model, and the [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Intensity distribution for anisotropic radiation under the RIAF model, and the accretion flow follows [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Intensity distribution for anisotropic radiation under the RIAF model, and the accretion flow follows [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Imaging results of the thick accretion disk for anisotropic radiation under the BAAF model, and [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Intensity distribution for anisotropic radiation under the BAAF model, and the accretion flow follows [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Intensity distribution for anisotropic radiation under the BAAF model, and the accretion flow follows [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Imaging results of the thick accretion disk for anisotropic radiation under the BAAF model, and [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Intensity distribution for anisotropic radiation under the BAAF model, and the accretion flow [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: The resulting Stokes parameters [PITH_FULL_IMAGE:figures/full_fig_p025_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Polarized images of the Kerr-Sen-like BH in the BAAF model with anisotropic emission. The [PITH_FULL_IMAGE:figures/full_fig_p026_13.png] view at source ↗
read the original abstract

The main objective of this study is to explore the shadow and polarization patterns of a Kerr-Sen-like BH induced from Bumblebee gravity, which, among other alternative theories of gravity beyond Einstein gravity, stands out as a promising candidate for explaining certain high-energy astrophysical phenomena. Specifically, we would like to probe the influence of the rate of LSB parameter $\ell$ and the Bumblebee charge $Q$ on the resulting image morphology at $230\mathrm{GHz}$. We adopt a phenomenological RIAF-like model and an analytical BAAF disk model. Both models depict that the bright ring is encircled by two central dark regions, each of which gradually shrinks with increasing $\ell$. Consequently, frame-dragging gives rise to a pronounced brightness asymmetry, which is more enhanced with increasing $Q$. A notable feature in the anisotropic emission case is the emergence of a vertically stretched, elliptical ring structure. Compared with the RIAF framework, the bright ring in the BAAF disk images appears geometrically thinner, and the separation between the primary and higher-order images becomes more pronounced. Finally, the polarization patterns trace the brightness distribution and vary with both $\ell$ and $Q$, reflecting the spacetime structure. These results demonstrate that intensity and polarization in thick disk models provide probes of Kerr-Sen-like BHs and near-horizon accretion physics

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

2 major / 1 minor

Summary. The paper investigates the shadow and polarization patterns of a Kerr-Sen-like black hole in Bumblebee gravity at 230 GHz. Using a phenomenological RIAF-like model and an analytical BAAF disk model, it reports that the bright ring is surrounded by two central dark regions that shrink with increasing LSB parameter ℓ, that frame-dragging produces brightness asymmetry enhanced by the Bumblebee charge Q, that the BAAF model yields a geometrically thinner ring with more pronounced image separation, and that polarization patterns trace the brightness distribution while varying with both ℓ and Q.

Significance. If the disk models remain valid in the modified spacetime, the work would indicate that intensity and polarization maps from thick accretion flows can serve as probes of the Bumblebee parameters ℓ and Q, offering potential observational tests of this alternative gravity theory near black-hole horizons.

major comments (2)
  1. [Model sections / abstract] The RIAF-like and BAAF models are imported and applied directly to the Bumblebee-modified Kerr-Sen-like metric without any derivation or consistency check that the underlying density, velocity, and emissivity profiles remain appropriate once the modified field equations and parameters ℓ, Q are introduced (abstract and model-adoption paragraphs). Because every reported morphological feature (shrinking dark regions, Q-enhanced asymmetry, thinner BAAF ring, polarization tracing) rests on these profiles, the absence of such validation is load-bearing for the central claims.
  2. [Results and abstract] No quantitative metrics, error bars, convergence tests with respect to grid resolution or ray-tracing parameters, or explicit comparisons to the ℓ = 0, Q = 0 limit (recovering the Kerr-Sen or Kerr case) are supplied; the results are stated only as qualitative trends. This omission prevents assessment of the magnitude and robustness of the reported effects on image morphology and polarization.
minor comments (1)
  1. Clarify the precise definitions and ranges of the free parameters ℓ and Q, and state whether any additional assumptions (e.g., on the magnetic field or plasma beta) are inherited unchanged from the original RIAF/BAAF constructions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the scope and presentation of our work. We address each major point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Model sections / abstract] The RIAF-like and BAAF models are imported and applied directly to the Bumblebee-modified Kerr-Sen-like metric without any derivation or consistency check that the underlying density, velocity, and emissivity profiles remain appropriate once the modified field equations and parameters ℓ, Q are introduced (abstract and model-adoption paragraphs). Because every reported morphological feature (shrinking dark regions, Q-enhanced asymmetry, thinner BAAF ring, polarization tracing) rests on these profiles, the absence of such validation is load-bearing for the central claims.

    Authors: We acknowledge that the RIAF-like and BAAF models are adopted phenomenologically from the literature without re-derivation from the Bumblebee field equations. This is standard practice for exploratory studies of image morphology in modified gravity, where the focus is on the impact of the modified spacetime geometry on ray-tracing rather than a self-consistent fluid solution. To address the concern, we will add a new paragraph in the model section explicitly stating the assumptions, noting that the density/velocity profiles are taken as given (as in prior works on Kerr-Sen and other alternatives), and discussing potential limitations. This will not change the reported trends but will better frame their applicability. revision: yes

  2. Referee: [Results and abstract] No quantitative metrics, error bars, convergence tests with respect to grid resolution or ray-tracing parameters, or explicit comparisons to the ℓ = 0, Q = 0 limit (recovering the Kerr-Sen or Kerr case) are supplied; the results are stated only as qualitative trends. This omission prevents assessment of the magnitude and robustness of the reported effects on image morphology and polarization.

    Authors: We agree that the current presentation is limited to qualitative trends. In the revised version we will add direct side-by-side comparisons with the ℓ=0, Q=0 (Kerr-Sen) case, including quantitative measures such as the fractional change in central dark-region area and the degree of brightness asymmetry as functions of ℓ and Q. Basic ray-tracing resolution checks will also be reported. Full error bars and exhaustive convergence studies lie beyond the scope of the present exploratory work but can be noted as future extensions. revision: partial

Circularity Check

0 steps flagged

No circularity; disk models applied to modified metric without self-referential reduction

full rationale

The paper adopts a phenomenological RIAF-like model and an analytical BAAF disk model, then computes shadow and polarization images for the Bumblebee-modified Kerr-Sen-like metric. The abstract states that both models show bright rings encircled by shrinking dark regions with increasing ℓ, with Q-enhanced asymmetry, but these are outputs of applying the chosen models to the new spacetime parameters rather than quantities defined in terms of themselves or fitted inputs renamed as predictions. No load-bearing self-citations, uniqueness theorems, or ansatzes smuggled via prior work are evident in the provided text that would make the central claims equivalent to the inputs by construction. The derivation remains self-contained for the purpose of this analysis.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the Bumblebee-derived metric and on the accuracy of two phenomenological disk models; no independent evidence for either is supplied in the abstract.

free parameters (2)
  • ℓ
    LSB parameter varied across simulations to produce reported trends
  • Q
    Bumblebee charge varied across simulations to produce reported trends
axioms (1)
  • domain assumption The Kerr-Sen-like solution is a valid vacuum solution of Bumblebee gravity
    Invoked as the background spacetime for all ray-tracing

pith-pipeline@v0.9.1-grok · 5780 in / 1314 out tokens · 41258 ms · 2026-06-30T13:47:13.456972+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

114 extracted references · 11 canonical work pages · 7 internal anchors

  1. [1]

    inner shadow

    dark matter spike [41] and the process of accretion disk [42] etc. The BH shadow is a dark region formed by the deflection of light in the strong gravitational field of a BH. Its morphology and radius are primarily evaluated by the underlying space-time geometry, allowing one to infer the significant properties of BHs with the analysis of shadow dynamics ...

    2021

  2. [2]

    Additionally, due to the frame-dragging effect induced by LSB parameterℓ, the intensity on the left side of the image becomes significantly enhanced with increasingℓ

    Comparing the rows of Fig.1with Fig.2, we observe that for a fixed value ofQ, both the bright ring and central region are slightly reduces with the augmentation ofℓ. Additionally, due to the frame-dragging effect induced by LSB parameterℓ, the intensity on the left side of the image becomes significantly enhanced with increasingℓ. On the contrary, by comp...

  3. [3]

    0.5 1.0 (b)Stokes parameterQ o -8 -4 0 4 8 -8 -4 0 4 8 x y -1.0 -0.5 0

    0.2 0.4 0.6 0.8 1.0 (a)Stokes parameterI o -8 -4 0 4 8 -8 -4 0 4 8 x y -0.5 0. 0.5 1.0 (b)Stokes parameterQ o -8 -4 0 4 8 -8 -4 0 4 8 x y -1.0 -0.5 0. 0.5 (c)Stokes parameterU o -8 -4 0 4 8 -8 -4 0 4 8 x y -0.5 0. 0.5 1.0 (d)Stokes parameterV o FIG. 12: The resulting Stokes parametersI o,Q o,U o, andV o under the BAAF disk model with an infalling motion. ...

  4. [4]

    0.001 0.002 0.003

    0.2 0.4 0.6 0.8 1.0 (a)Q= 0.1, ℓ=−0.5 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 y x 0. 0.001 0.002 0.003

  5. [5]

    0.001 0.002 0.003

    0.2 0.4 0.6 0.8 1.0 (b)Q= 0.1, ℓ= 0.1 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 y x 0. 0.001 0.002 0.003

  6. [6]

    0.001 0.002 0.003

    0.2 0.4 0.6 0.8 1.0 (c)Q= 0.1, ℓ= 0.5 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 y x 0. 0.001 0.002 0.003

  7. [7]

    0.001 0.002 0.003

    0.2 0.4 0.6 0.8 1.0 (d)Q= 0.3, ℓ=−0.5 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 y x 0. 0.001 0.002 0.003

  8. [8]

    0.001 0.002 0.003

    0.2 0.4 0.6 0.8 1.0 (e)Q= 0.3, ℓ= 0.1 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 y x 0. 0.001 0.002 0.003

  9. [9]

    0.001 0.002 0.003

    0.2 0.4 0.6 0.8 1.0 (f)Q= 0.3, ℓ= 0.5 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 y x 0. 0.001 0.002 0.003

  10. [10]

    0.001 0.002 0.003

    0.2 0.4 0.6 0.8 1.0 (g)Q= 0.5, ℓ=−0.5 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 y x 0. 0.001 0.002 0.003

  11. [11]

    0.001 0.002 0.003

    0.2 0.4 0.6 0.8 1.0 (h)Q= 0.5, ℓ= 0.1 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 y x 0. 0.001 0.002 0.003

  12. [12]

    13: Polarized images of the Kerr-Sen-like BH in the BAAF model with anisotropic emission

    0.2 0.4 0.6 0.8 1.0 (i)Q= 0.5, ℓ= 0.5 FIG. 13: Polarized images of the Kerr-Sen-like BH in the BAAF model with anisotropic emission. The accretion flow follows the infalling motion, and the observation is performed at a frequency of 230GHz with an inclination angle ofθ o = 75◦, and a spin parametera= 0.6. In Fig.12, we presents a representative example of...

  13. [13]

    Akiyama et al., Astrophys

    K. Akiyama et al., Astrophys. J. Lett.875, L1 (2019)

    2019

  14. [14]

    Akiyama et al., Astrophys

    K. Akiyama et al., Astrophys. J. Lett.910, L12 (2021)

    2021

  15. [15]

    Akiyama et al., Astrophys

    K. Akiyama et al., Astrophys. J. Lett.930, L12 (2022)

    2022

  16. [16]

    Akiyama et al., Astrophys

    K. Akiyama et al., Astrophys. J. Lett.964, L25 (2024)

    2024

  17. [17]

    Baub¨ ock et al., Astron

    M. Baub¨ ock et al., Astron. Astrophys.635, (2020) A143

    2020

  18. [18]

    Abuter et al., Astron

    R. Abuter et al., Astron. Astrophys.677, (2023) L10

    2023

  19. [19]

    M. D. Johnson et al., Sci. Adv.6(2020) eaaz1310

    2020

  20. [20]

    Gold et al., Astrophys

    R. Gold et al., Astrophys. J.897(2020) 148

    2020

  21. [21]

    Black Uniqueness Theorems

    P.O. Mazur,Black hole uniqueness theorems, hep-th/0101012

    work page internal anchor Pith review Pith/arXiv arXiv

  22. [22]

    C. M. Will, Living Rev. Rel.17(2014) 4

    2014

  23. [23]

    Yagi and L.C

    K. Yagi and L.C. Stein, Class. Quant. Grav.33(2016) 054001

    2016

  24. [24]

    Kerr, Phys

    R.P. Kerr, Phys. Rev. Lett.11(1963) 237

    1963

  25. [25]

    Penrose, Phys

    R. Penrose, Phys. Rev. Lett.14(1965) 57

    1965

  26. [26]

    Bambi, Mod

    C. Bambi, Mod. Phys. Lett. A26(2011) 2453

    2011

  27. [27]

    Cardoso and P

    V. Cardoso and P. Pani, Living Rev. Rel.22(2019) 4

    2019

  28. [28]

    V. A. Kostelecky, Phys. Rev. D69(2004) 105009

    2004

  29. [29]

    C. Ding, X. Chen and X. Fu, Nucl. Phys. B975(2022) 115688

    2022

  30. [30]

    V. A. Kostelecky and S. Samuel, Phys. Rev. D39(1989) 683

    1989

  31. [31]

    Jacobson, S

    T. Jacobson, S. Liberati and D. Mattingly, Annals Phys.321(2006) 150

    2006

  32. [32]

    V. A. Kosteleck´ y and M. Mewes, Phys. Lett. B757(2016) 510

    2016

  33. [33]

    Colladay and V

    D. Colladay and V. A. Kosteleck´ y, Phys. Rev. D58(1998) 116002

    1998

  34. [34]

    V. A. Kosteleck´ y and S. Samuel, Phys. Rev. Lett.63(1989) 224

    1989

  35. [35]

    A. V. Kosteleck´ y and J. D. Tasson, Phys. Rev. D83(2011) 016013

    2011

  36. [36]

    Casana, et al., Phys

    R. Casana, et al., Phys. Rev. D97(2018) 104001

    2018

  37. [37]

    G¨ ull¨ u and A.¨Ovg¨ un, Annals Phys.436(2022) 168721

    I. G¨ ull¨ u and A.¨Ovg¨ un, Annals Phys.436(2022) 168721

    2022

  38. [38]

    Q. G. Bailey, et al., Phys. Rev. D112(2025) 024069

    2025

  39. [39]

    C. Ding, C. Liu, R. Casana and A. Cavalcante, Eur. Phys. J. C80(2020) 178. 30

    2020

  40. [40]

    Ding and X

    C. Ding and X. Chen, Chin. Phys. C45(2021) 025106

    2021

  41. [41]

    Sen, Phys

    A. Sen, Phys. Rev. Lett.69(1992) 1006

    1992

  42. [42]

    S. K. Jha and A. Rahaman, Eur. Phys. J. C81(2021) 345

    2021

  43. [43]

    R. Xu, D. Liang, and L. Shao, Phys. Rev. D107(2023) 024011

    2023

  44. [44]

    X. Zhu, R. Xu, and D. Xu, arXiv:2411.18559

    work page arXiv

  45. [45]

    S. K. Jha, S. Aziz, and A. Rahaman, Eur. Phys. J. C82(2022) 106

    2022

  46. [46]

    Z. Wang, S. Chen, and J. Jing, Eur. Phys. J. C82(2022) 528

    2022

  47. [47]

    S. U. Islam, S. G. Ghosh, and S. D. Maharaj, JCAP12(2024) 047

    2024

  48. [48]

    J. Gu. et al., Eur. Phys. J. C82(2022) 708

    2022

  49. [49]

    H. Y. YuChih, and Y. Shen, Phys. Rev. D112(2025) 104016

    2025

  50. [50]

    J. P. Zhang, Y. Zhang, and L. Han, arXiv:2604.23721

    work page internal anchor Pith review Pith/arXiv arXiv

  51. [51]

    New Exact Vacuum Solutions in Extended Bumblebee Gravity

    J. Zhu and H. Li, arXiv:2604.09464

    work page internal anchor Pith review Pith/arXiv arXiv

  52. [52]

    Ahmed, S

    F. Ahmed, S. Kala and E. O. Silva, arXiv:2604.00883

    work page arXiv

  53. [53]

    Capozziello, et al., JCAP2023(2023) 027

    S. Capozziello, et al., JCAP2023(2023) 027

    2023

  54. [54]

    Lambiase, et al., JCAP2023(2023) 026

    G. Lambiase, et al., JCAP2023(2023) 026

    2023

  55. [55]

    R. D. Blandford and R. L. Znajek, Mon. Not. Roy. Astron. Soc.179(1977) 433

    1977

  56. [56]

    Narayan, M

    R. Narayan, M. D. Johnson, and C. F. Gammie, Astrophys. J. Lett.885(2019) L33

    2019

  57. [57]

    X. X. Zeng, H. Q. Zhang and H. Zhang, Eur. Phys. J. C80(2020) 872

    2020

  58. [58]

    X. X. Zeng, M. I. Aslam, R. Saleem, Eur. Phys. J. C83(2023) 129

    2023

  59. [59]

    Saleem and M

    R. Saleem and M. I. Aslam, Eur. Phys. J. C83(2023) 257

    2023

  60. [60]

    M. I. Aslam and R. Saleem, Eur. Phys. J. C84(2024) 37

    2024

  61. [61]

    Guo et al., Astrophys

    S. Guo et al., Astrophys. J.975(2024) 237

    2024

  62. [62]

    C. Y. Yang, M. I. Aslam and X. X. Zeng, et al., J. High Energy Astrophys.46(2025) 100345

    2025

  63. [63]

    X. X. Zeng, C. Y. Yang and M. I. Aslam, et al., J. Cosmol. Astropart. Phys.2025(2025) 066

    2025

  64. [64]

    Li and K.-J

    G.-P. Li and K.-J. He, JCAP06(2021) 037

    2021

  65. [65]

    X. X. Zeng et al., J. High Energy Astrophys.51(2026) 100540

    2026

  66. [66]

    M. I. Aslam et al., arXiv:2604.18628

    work page internal anchor Pith review Pith/arXiv arXiv

  67. [67]

    Hashimoto, S

    K. Hashimoto, S. Kinoshita and K. Murata, Phys. Rev. D101, 066018 (2020)

    2020

  68. [68]

    X. Y. Hu, M. I. Aslam and R. Saleem et al., J. Cosmol. Astropart. Phys.2023(2023) 013

    2023

  69. [69]

    M. I. Aslam, X. X. Zeng and R. Saleem et al., Chin. Phys. C48(2024) 115101

    2024

  70. [70]

    X. X. Zeng, M. I. Aslam and R. Saleem et al., Eur. Phys. J. C85(2025) 663

    2025

  71. [71]

    Narayan and I.-s

    R. Narayan and I.-s. Yi, Astrophys. J. Lett.428(1994) L13

    1994

  72. [72]

    Yuan and R

    F. Yuan and R. Narayan, Ann. Rev. Astron. Astrophys.52(2014) 529

    2014

  73. [73]

    Narayan, I

    R. Narayan, I. Yi, and R. Mahadevan, Nature374(1995) 623

    1995

  74. [74]

    Porth et al., Astrophys

    O. Porth et al., Astrophys. J. Suppl.243(2019) 26

    2019

  75. [75]

    Jiang et al., JCAP01(2024) 059

    H.-X. Jiang et al., JCAP01(2024) 059

    2024

  76. [76]

    Uniyal et al., Astrophys

    A. Uniyal et al., Astrophys. J.993(2025) 97. 31

    2025

  77. [77]

    F. Yuan, E. Quataert and R. Narayan, Astrophys. J.598, 301 (2003)

    2003

  78. [78]

    Broderick and A

    A. Broderick and A. Loeb, Astrophys. J.697, 1164 (2009)

    2009

  79. [79]

    H. Y. Pu and A. E. Broderick, Astrophys. J.863, 148 (2018)

    2018

  80. [80]

    H. X. Jiang et al., JCAP01, 059 (2024)

    2024

Showing first 80 references.