Pith. sign in

REVIEW 2 major objections 5 minor 69 references

Signatures of Lorentz violation in bright ring for Sgr A* images by radiation ineffective accretion flows

T0 review · 2 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 A single Lorentz-violating parameter in a rotating black hole metric shrinks Sgr A*'s bright-ring diameter while widening, brightening, and asymmetrizing the ring, and the measured diameter can be turned into an allowed range for that param

desk verdict The parameter study is competent, but Eq. (1) as printed does not reduce to Kerr at l=0, so the EHT-based l constraint is not reproducible from the manuscript. read the letter →

arxiv 2608.01413 v1 pith:FMWEYKM2 submitted 2026-08-02 astro-ph.HE gr-qc

Cuiyu Zhao , Songbai Chen , Jiliang Jing This is my paper
classification astro-ph.HEgr-qc PACS 04.70.Dy95.30.Sf97.60.Lf
keywords LorentzviolationblackholeimageSgrA*brightringradiativelyinefficientaccretionflowsynchrotronradiationphotonLorentz-violatinggravity
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 tries to establish that Lorentz violation leaves a measurable imprint on the bright ring of Sgr A* images. Working with a rotating black hole metric from a low-energy Lorentz-violating gravity theory and a radiatively inefficient accretion flow model, it claims that increasing the Lorentz-violating parameter $l$ monotonically shrinks the ring diameter while increasing its width, brightness, azimuthal asymmetry, and orientation angle, and that these trends grow with black hole spin and disk thickness. It then uses the measured ring diameter of Sgr A* to derive allowed ranges for $l$ that depend on spin and disk thickness, and shows that nonzero $l$ shifts and narrows the allowed spin range. A sympathetic reader would care because this turns a single image observable into a concrete, quantifiable constraint on Planck-scale Lorentz symmetry breaking.

What carries the argument

The load-bearing object is the rotating Lorentz-violating black hole metric of Eq. (1), whose time-time and off-diagonal $t\varphi$ components carry the parameter $l$ multiplied by powers of the spin $a$; this product structure makes $l$ mimic spin effects without being identical to them. Around this spacetime the paper places a semi-analytic radiatively inefficient accretion flow (RIAF) with power-law electron density and temperature profiles, a disk-thickness parameter $H$, and velocities interpolated between Keplerian and radial free-fall. Images are produced by general-relativistic ray tracing of thermal synchrotron emission, blurred to observational resolution, and the ring features are

What would settle it

Substitute Eq. (1) into the field equations of the low-energy Lorentz-violating gravity theory and verify it as an exact solution; a failed check would show the $l$-dependence is an artifact of the metric ansatz. Observationally, measure the Sgr A* ring at higher resolution and compare the diameter and width changes as the accretion state varies: if the diameter does not shrink while the width grows along the suggested $l$ direction, the predicted correlations are excluded.

Watch

Extended reading notes

Core claim

The paper's central claim is that the Lorentz-violating parameter $l$ in the rotating black hole metric produces a systematic, spin-like change in the simulated 230 GHz image of Sgr A*: the bright-ring diameter decreases monotonically with $l$, while the ring's width, intensity, azimuthal asymmetry, orientation angle, and brightness asymmetry all increase. Because $l$ enters the metric functions in products with the spin parameter $a$, its imaging effects track those of spin. Comparing the simulated ring diameter with the observed value $51.8 \pm 2.3\,\mu\mathrm{as}$, the paper derives, for each disk thickness, an allowed interval in $l$ that first broadens and then contracts as $a$ grows an

Load-bearing premise

Everything rests on the rotating Lorentz-violating metric being a genuine, correctly transcribed solution of the underlying gravity theory, especially the off-diagonal term where $a^2$ appears; if that metric is not an exact solution or contains a typographical error, the quoted ring properties and the derived allowed range for $l$ are invalid.

Editorial extensions

If this is right

  • The observed Sgr A* ring diameter can be translated, at fixed disk thickness, into an allowed interval for the Lorentz-violating parameter $l$, so a single image measurement becomes a quantitative bound on Lorentz violation.
  • Nonzero $l$ narrows the allowed spin range of the black hole: negative $l$ pushes spin upward and positive $l$ pushes it downward, meaning the two parameters are observationally entangled.
  • Thicker disks shrink the predicted ring diameter and amplify the $l$-dependence of the diameter, so disk thickness must be known or marginalized before a reliable $l$ constraint can be quoted.
  • The primary image and $n=1$ photon ring respond differently to $l$: their peak positions and widths decrease with $l$ except in narrow angular windows, and Keplerian versus radial free-fall flows produce different sensitivities, so future resolution of these subcomponents could separate Lorentz violation from flow geometry.

Reading between the lines

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

  • The paper implicitly treats $l$ and $a$ as degenerate in the ring diameter; an independent measurement of Sgr A*'s spin, for instance from quasi-periodic variability or jet orientation, would break that degeneracy and sharpen the $l$ bound.
  • The same RIAF-plus-ring-extraction pipeline could be applied to other Lorentz-violating black hole solutions to test whether the monotonic diameter/width/asymmetry trends are generic to Lorentz violation or specific to this metric's particular coupling structure.
  • The semi-analytic flow is a fixed idealization; replacing it with turbulent GRMHD snapshots would test whether the claimed $l$ trends survive realistic velocity and magnetic-field fluctuations before the bounds are used as exclusion limits.
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

2 major / 5 minor

Summary. The manuscript studies 230 GHz images of Sgr A* produced by a semi-analytic radiatively inefficient accretion flow (RIAF) around a rotating Lorentz-violating (LV) black hole in low-energy Hořava gravity. Using the EHT REx algorithm on ray-traced and blurred images, it reports that increasing the LV parameter l decreases the bright-ring diameter and increases ring width, luminosity, azimuthal asymmetry, and orientation angle; that spin and disk thickness affect these trends; and that comparing with EHT's Sgr A* diameter (51.8 ± 2.3 μas) yields a model-dependent allowed l range. It also analyzes how l shifts peak positions and widths of the n=0 primary image and n=1 photon ring for Keplerian, mixed, and radial free-fall flows.

Significance. The forward-modeling strategy is sensible and connects a modified-gravity parameter to a specific EHT observable. The use of a semi-analytic RIAF, thermal synchrotron emissivity, and the REx ring extractor is appropriate, and the paper explicitly scans multiple spins, disk thicknesses, and l values. If Eq. (1) were correctly transcribed and the simulations rerun, the qualitative trends could provide a useful template for LV searches in horizon-scale images. However, the paper gives no code or data release, and the central line element as printed is internally inconsistent, which currently prevents reproducibility and undermines the physical interpretation of the LV constraints.

major comments (2)
  1. [Section II, Eq. (1)] The metric as printed does not have the claimed Kerr limit. Setting l=0 gives g_{tφ} = -4 M a^2 r sin^2θ / ρ^2, whereas Kerr in Boyer-Lindquist coordinates has g_{tφ} = -2 M a r sin^2θ / ρ^2. Thus the statement that the solution 'can be returned to the Kerr solution when l=0' is false for the printed line element; the extra power of a also makes g_{tφ} dimensionally inconsistent if a is the usual specific angular momentum. Because every ray-tracing result and the EHT-derived allowed range for l (Figs. 1-6 and the Section V summary) are computed in this spacetime, the central claim is not reproducible from the manuscript. The authors must verify the metric against Ref. [50], correct the transcription, and rerun the simulations; as written the paper cannot be accepted.
  2. [Section III, Fig. 4] The allowed-range analysis only propagates the 1σ statistical diameter uncertainty (51.8 ± 2.3 μas) for fixed fiducial model parameters (Table I). The diameter d varies by only a few μas over the quoted l ranges, so EHT systematic uncertainties (calibration, imaging, source variability) and model uncertainties in n_{e,0}, T_{e,0}, κ, inclination, and disk thickness could shift or erase the allowed range. The abstract and Section V present the l interval as a constraint rather than as a conditional illustration. This conclusion should be softened or supplemented by an explicit systematic-error treatment.
minor comments (5)
  1. [Title, Abstract, Section V] 'Radiation ineffective accretion flows' should be 'radiatively inefficient accretion flows'; this typo appears in the title, abstract, and summary.
  2. [Section II, Eq. (2)] The sentence 'From grr = ∆r/ρ² = 0' is garbled. The horizon condition is Δ=0, i.e. g^{rr}=0, not g_{rr}=0; please fix the notation.
  3. [Section IV, Fig. 7] 'Isohypse' appears to be a typo for 'isophote' or 'isocontour' in the description of temperature contours.
  4. [Fig. 6 label] The label 'Lv parameter' should be 'LV parameter'.
  5. [Section III, Eq. (8)] The definition of ring width w as 'FWHM[I(r,θ)-I_floor]' is ambiguous: it should specify the radial coordinate over which the FWHM is computed, and the role of the azimuthal average.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper is a forward-model study whose constrained LV parameter is not fitted or defined in terms of the target observable.

full rationale

The paper's central derivation is self-contained in the forward-modeling sense. The rotating Lorentz-violating black hole metric is imported as an external solution from Devecioglu-Park [50] and subsequent studies [51,52]; it is an input assumption, not derived in this paper. The RIAF model [21,22], synchrotron emissivity fits [61], and ray-tracing codes [53,54] are all external. The LV parameter l is a free parameter of the input metric; varying it and computing ring properties is a forward prediction, not a fit. The electron density and temperature are calibrated to the Sgr A* flux, but the paper does not present that flux calibration as a prediction; the ring diameter constraint uses the independent EHT diameter measurement. No fitted parameter is renamed as a prediction, no uniqueness theorem is invoked from the authors' prior work, and no ansatz is smuggled in through self-citation. The paper's self-citations (e.g., Refs. [10,12-14,16]) appear only as background references and are not load-bearing for the main derivation. A possible concern that Eq. (1) does not reduce to Kerr at l=0 as printed is a metric-consistency/correctness issue, not a circularity of the derivation chain; it does not make the constraint on l circular.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central results rest on the cited LV metric, the semi-analytic RIAF model, and several fixed astrophysical inputs. No new entities are introduced. The free parameters include the LV parameter itself and the normalization constants ne,0 and Te,0 that are calibrated to the observed Sgr A* flux, as well as the explored disk thickness and spin.

free parameters (5)
  • LV parameter l = constrained; paper samples -0.99 to 0.99
    Target parameter of the theory; the central claim is how ring properties depend on it and what values are allowed by EHT data.
  • Electron number density normalization ne,0 = approximately 1e7 cm^-3
    Set so that simulated flux matches measured Sgr A* flux (Sec. II).
  • Electron temperature normalization Te,0 = approximately 1e11 K
    Set together with ne,0 to match observed flux (Sec. II).
  • Disk thickness H = 0.1, 0.3, 0.5 studied
    Chosen to explore thickness dependence; central to the constraint analysis via H.
  • Spin parameter a = 0, 0.5, 0.99 sampled
    Varied; the LV parameter range depends on spin; also constrained by ring diameter.
assumptions (5)
  • domain assumption Eq. (1) is the exact rotating LV black hole solution in low-energy Horava gravity
    Taken from Devecioglu-Park [50]; the paper's results inherit this.
  • domain assumption Semi-analytic RIAF model of Pu and Broderick describes Sgr A* accretion flow
    Adopted to avoid GRMHD; fixes ne, Te radial profiles and velocity interpolation (Sec. II).
  • domain assumption Electron distribution is relativistic thermal Maxwell-Juttner at 230 GHz
    Non-thermal emission assumed subdominant (Sec. II).
  • domain assumption MAD-like configuration is favored for Sgr A*
    Cited to EHT [9]; affects magnetic field structure in radiative transfer.
  • domain assumption EHT measured ring diameter 51.8 ± 2.3 microarcseconds corresponds to the REX diameter d=2<r_pk> of blurred simulated images
    Used for the allowed-range analysis (Sec. III).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Signatures of Lorentz violation in bright ring for Sgr A* images by radiation ineffective accretion flows." pith.science (2026). https://pith.science/paper/FMWEYKM2

@misc{pith2026260801413,
  author       = {Pith},
  title        = {Pith review of: Signatures of Lorentz violation in bright ring for Sgr A* images by radiation ineffective accretion flows},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FMWEYKM2}},
  note         = {Machine review of arXiv:2608.01413}
}
abstract

We have investigated effects of Lorentz violation (LV) on bright ring in Sgr A* images illuminated by the 230 GHz thermal synchrotron emission from radiation ineffective accretion flows around a rotating LV black hole within the low-energy Ho\v{r}ava gravity framework. Our results reveal that the LV parameter reduces the bright ring diameter yet increases its width, luminosity, azimuthal asymmetry and orientation angle. Higher spin parameter strengthens the LV-induced effects on bright ring properties.Increasing disk thickness reduces the ring diameter and enhances the LV parameter's effects on this diameter. The ring width shows no systematic dependence on the disk thickness. These quantities of bright ring display similar trends against black hole spin and the LV parameter for the rotating LV black hole. Using EHT observational data of Sgr A*, we find that, at fixed disk thickness, the allowed range of the LV parameter first broadens and then contracts with growing black hole spin, and shifts toward smaller LV parameter values. In addition, the LV parameter narrows the permitted range of black hole spin: negative LV parameter values shift this range to higher spin, while positive values shift it to lower spin. Finally, we probe effects of the LV parameter on the peak position value and the width of the primary image and the $n=1$ photon ring for the rotating LV black hole. The peak positions and their widths decrease with the LV parameter, except for a narrow range. The peak position differences for various LV parameter are more pronounced for pure Keplerian accretion flow. In additional, the primary image and the $n=1$ photon ring produced by pure radially free-falling flows are broader than their counterparts generated by pure Keplerian flows.

Figures

Figures reproduced from arXiv: 2608.01413 by the authors.

Figure 1
Figure 1. FIG. 1: Images of a rotating LV black hole under different spin [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Black hole images (in the top row) and the corresponding blurred images (in the bottom row), with [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Unwrapped ring profiles of the simulated blurred LV black hole images for different black hole spin [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: The one-dimensional radial brightness profiles corresponding to the same parameters as in Fig. 3. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Relationship between brightness asymmetry [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Intensity profiles for the direct image and the [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Positions of the [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Positions of the [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

69 extracted references · 10 canonical work pages

  1. [50]

    D. O. Devecioglu and M.-I. Park, Eur. Phys. J. C 84, 852 (2024), 2402.02253

    work page Pith review arXiv 2024

  2. [1]

    Akiyama et al

    K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 875, L1 (2019), 1906.11238

    arXiv 2019

  3. [2]

    Akiyama et al

    K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 875, L4 (2019), 1906.11241

    arXiv 2019

  4. [3]

    Akiyama et al

    K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 875, L5 (2019), 1906.11242

    arXiv 2019

  5. [4]

    Akiyama et al

    K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 875, L6 (2019), 1906.11243. 16

    arXiv 2019

  6. [5]

    Akiyama et al

    K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 930, L12 (2022), 2311.08680

    arXiv 2022

  7. [6]

    Akiyama et al

    K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 930, L14 (2022), 2311.09479

    arXiv 2022

  8. [7]

    Akiyama et al

    K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 930, L15 (2022), 2311.08697

    arXiv 2022

Show all 69 references
  1. [8]

    Akiyama et al

    K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 930, L16 (2022), 2311.09478

    2022 arXiv

  2. [9]

    Akiyama et al

    K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 930, L17 (2022), 2311.09484

    2022 arXiv

  3. [10]

    H. Yin, S. Chen, and J. Jing, JCAP 04, 071 (2026), 2507.03857

    2026 arXiv

  4. [11]

    Zhang, S

    Z. Zhang, S. Chen, and J. Jing, JCAP 09, 027 (2024), 2404.12223

    2024 arXiv

  5. [12]

    S. Chen, J. Jing, W.-L. Qian, and B. Wang, Sci. China Phys. Mech. Astron. 66, 260401 (2023), 2301.00113

    2023 arXiv

  6. [13]

    X. Qin, S. Chen, Z. Zhang, and J. Jing, Eur. Phys. J. C 83, 159 (2023), 2301.01551

    2023 arXiv

  7. [14]

    Zhang, S

    Z. Zhang, S. Chen, and J. Jing, Eur. Phys. J. C 82, 835 (2022), 2205.13696

    2022 arXiv

  8. [15]

    Vagnozzi et al., Class

    S. Vagnozzi et al., Class. Quant. Grav. 40, 165007 (2023), 2205.07787

    2023 arXiv

  9. [16]

    M. Wang, G. Guo, P. Yan, S. Chen, and J. Jing, Chin. Phys. C 48, 105103 (2024), 2307.16748

    2024 arXiv

  10. [17]

    Desire, A

    T. Desire, A. C´ ardenas-Avenda˜ no, and A. Chael, The Astrophysical Journal980, 262 (2025)

    2025

  11. [18]

    M. D. Johnson et al., Sci. Adv. 6, eaaz1310 (2020), 1907.04329

    2020 arXiv

  12. [19]

    A. A. Chael, Ph.D. thesis, Harvard University (2019)

    2019

  13. [20]

    J. B. Achour, E. Gourgoulhon, and H. Roussille, Black hole photon ring beyond general relativity: an integrable parametrization (2025), 2506.09882

    2025

  14. [21]

    F. Yuan, E. Quataert, and R. Narayan, The Astrophysical Journal 598, 301–312 (2003)

    2003

  15. [22]

    Pu and A

    H.-Y. Pu and A. E. Broderick, Astrophys. J. 863, 148 (2018), 1807.01817

    2018 arXiv

  16. [23]

    Jiang, C

    H.-X. Jiang, C. Liu, I. K. Dihingia, Y. Mizuno, H. Xu, T. Zhu, and Q. Wu, JCAP 01, 059 (2024), 2312.04288

    2024 arXiv

  17. [24]

    J.-M. Yan, T. Zhu, and Q. Wu (2025), 2504.10956

    2025 arXiv

  18. [25]

    H.-Y. Pu, K. Akiyama, and K. Asada, Astrophys. J. 831, 4 (2016), 1608.03035

    2016 arXiv

  19. [26]

    Casana, A

    R. Casana, A. Cavalcante, F. Poulis, and E. Santos, Phys. Rev. D 97, 104001 (2018)

    2018

  20. [27]

    Bluhm, S.-H

    R. Bluhm, S.-H. Fung, and V. A. Kostelecky, Phys. Rev. D 77, 065020 (2008), 0712.4119

    2008 arXiv

  21. [28]

    V. A. Kostelecky and R. Potting, Gen. Rel. Grav. 37, 1675 (2005), gr-qc/0510124

    2005 arXiv

  22. [29]

    Bertolami and J

    O. Bertolami and J. Paramos, Phys. Rev. D 72, 044001 (2005), hep-th/0504215

    2005 arXiv

  23. [30]

    Kalb and P

    M. Kalb and P. Ramond, Phys. Rev. D 9, 2273 (1974)

    1974

  24. [31]

    Yang, Y.-Z

    K. Yang, Y.-Z. Chen, Z.-Q. Duan, and J.-Y. Zhao, Phys. Rev. D 108, 124004 (2023), 2308.06613

    2023 arXiv

  25. [32]

    Altschul, Q

    B. Altschul, Q. G. Bailey, and V. A. Kostelecky, Phys. Rev. D 81, 065028 (2010), 0912.4852

    2010 arXiv

  26. [33]

    L. A. Lessa, J. E. G. Silva, R. V. Maluf, and C. A. S. Almeida, Eur. Phys. J. C 80, 335 (2020), 1911.10296

    2020 arXiv

  27. [34]

    S. K. Jha, Int. J. Mod. Phys. D 34, 2550055 (2025), 2404.15808

    2025 arXiv

  28. [35]

    Horava, Phys

    P. Horava, Phys. Rev. D 79, 084008 (2009), 0901.3775

    2009 arXiv

  29. [36]

    Aharony, S

    O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, Phys. Rept. 323, 183 (2000), hep-th/9905111

    2000 arXiv

  30. [37]

    Colladay and V

    D. Colladay and V. A. Kostelecky, Phys. Rev. D 58, 116002 (1998), hep-ph/9809521

    1998 arXiv

  31. [38]

    Lin, J.-Z

    Y.-X. Lin, J.-Z. Liu, and Y.-X. Liu (2026), 2605.18371

    2026 arXiv

  32. [39]

    Zeng, C.-Y

    X.-X. Zeng, C.-Y. Yang, M. I. Aslam, and R. Saleem, Eur. Phys. J. C 86, 383 (2026), 2511.00586

    2026

  33. [40]

    M. Xu, R. Li, J. Lu, S. Yang, and S.-M. Wu, Eur. Phys. J. C 85, 676 (2025), 2506.17075

    2025 arXiv

  34. [41]

    Kumar, S

    R. Kumar, S. G. Ghosh, and A. Wang, Phys. Rev. D 101, 104001 (2020), 2001.00460

    2020 arXiv

  35. [42]

    W. Liu, D. Wu, and J. Wang, JCAP 05, 017 (2025), 2407.07416

    2025 arXiv

  36. [43]

    Kuang and A

    X.-M. Kuang and A. ¨Ovg¨ un, Annals Phys.447, 169147 (2022), 2205.11003

    2022 arXiv

  37. [44]

    Wang and S.-W

    H.-M. Wang and S.-W. Wei, Eur. Phys. J. Plus 137, 571 (2022), 2106.14602

    2022 arXiv

  38. [45]

    C. Liu, C. Ding, and J. Jing (2019), 1910.13259

    2019 arXiv

  39. [46]

    Chen and H.-S

    Y.-Q. Chen and H.-S. Liu, Phys. Rev. D 112, 084040 (2025), 2505.23104

    2025 arXiv

  40. [47]

    A. A. Ara´ ujo Filho, J. R. Nascimento, A. Y. Petrov, and P. J. Porf ´ ırio, JCAP07, 004 (2024), 2402.13014

    2024 arXiv

  41. [48]

    W. Liu, X. Fang, J. Jing, and J. Wang, Eur. Phys. J. C 83, 83 (2023), 2211.03156

    2023 arXiv

  42. [49]

    A. A. A. Filho, J. R. Nascimento, A. Y. Petrov, and P. J. Porf ´ ırio, Phys. Rev. D108, 085010 (2023), 2211.11821

    2023 arXiv

  43. [51]

    W. Liu, H. Huang, D. Wu, and J. Wang, Phys. Lett. B 868, 139812 (2025), 2506.13504

    2025

  44. [52]

    Zhao, Y.-Y

    M.-D. Zhao, Y.-Y. Wang, K.-J. He, and G.-P. Li, Eur. Phys. J. C 86, 329 (2026), 2511.23117

    2026 arXiv

  45. [53]

    S. C. Noble, P. K. Leung, C. F. Gammie, and L. G. Book, Class. Quant. Grav. 24, S259 (2007), astro-ph/0701778

    2007 arXiv

  46. [54]

    Moscibrodzka and C

    M. Moscibrodzka and C. F. Gammie, Mon. Not. Roy. Astron. Soc. 475, 43 (2018), 1712.03057

    2018 arXiv

  47. [55]

    A. E. Broderick, V. L. Fish, S. S. Doeleman, and A. Loeb, Astrophys. J. 735, 110 (2011), 1011.2770

    2011 arXiv

  48. [56]

    A. I. Yfantis, M. Wielgus, and M. A. Mo´ scibrodzka, Astron. Astrophys. 691, A327 (2024), 2408.07120

    2024 arXiv

  49. [57]

    Narayan, A

    R. Narayan, A. Sadowski, R. F. Penna, and A. K. Kulkarni, Mon. Not. Roy. Astron. Soc. 426, 3241 (2012), 1206.1213

    2012 arXiv

  50. [58]

    F. Yuan, H. Wang, and H. Yang, Astrophys. J. 924, 124 (2022), 2201.00512

    2022 arXiv

  51. [59]

    M. C. Begelman, N. Scepi, and J. Dexter, Mon. Not. Roy. Astron. Soc. 511, 2040 (2022), 2111.02439

    arXiv

  52. [60]

    Y. Chen, Y. Liu, R.-S. Lu, Y. Mizuno, J. Shu, X. Xue, Q. Yuan, and Y. Zhao, Nature Astronomy 6, 592–598 (2022)

    2022

  53. [61]

    Pandya, Z

    A. Pandya, Z. Zhang, M. Chandra, and C. F. Gammie, Astrophys. J. 822, 34 (2016), 1602.08749

    2016 arXiv

  54. [62]

    I. Urso, F. H. Vincent, M. Wielgus, T. Paumard, and G. Perrin, Astron. Astrophys. 700, A193 (2025), 2506.13482

    2025 arXiv

  55. [63]

    Saurabh, M

    S. Saurabh, M. Wielgus, A. Tursunov, A. P. Lobanov, and R. Emami, Astron. Astrophys. 705, A166 (2026), 2508.11760

    2026

  56. [64]

    A. A. Chael, M. D. Johnson, K. L. Bouman, L. L. Blackburn, K. Akiyama, and R. Narayan, Astrophys. J. 857, 17 23 (2018), 1803.07088

    2018 arXiv

  57. [65]

    Paugnat, A

    H. Paugnat, A. Lupsasca, F. Vincent, and M. Wielgus, Astron. Astrophys. 668, A11 (2022), 2206.02781

    2022 arXiv

  58. [66]

    M. H. Khan and V. Perlick, Phys. Rev. D 112, 124066 (2025), 2508.20575

    2025

  59. [67]

    J. M. Bardeen, Proceedings, Ecole d’Et´ e de Physique Th´ eorique: Les Astres Occlus : Les Houches, France, August, 1972, 215-240 pp. 215–240 (1973)

    1972

  60. [68]

    S. E. Gralla, D. E. Holz, and R. M. Wald, Phys. Rev. D 100, 024018 (2019), 1906.00873

    2019 arXiv

  61. [69]

    A. A. Chael, M. D. Johnson, and A. Lupsasca, Astrophys. J. 918, 6 (2021), 2106.00683

    2021 arXiv

Pith tools

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