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REVIEW 4 major objections 3 minor 2 cited by

Frame dragging forces retrograde accretion flows to reverse, and the reversal leaves three distinct, non-coincident markers in a black hole's polarized image.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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Frame dragging flips an initially retrograde equatorial flow around a Kerr black hole, and the polarized image shows three distinct critical locations whose spatial hierarchy is derived analytically for an on-axis observer.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection The abstract promises a novel frame-dragging diagnostic for polarized black hole images, but the only full text supplied is an unrelated CS paper, so the derivation is unverifiable. the 4 major comments →

arxiv 2508.15178 v1 pith:WTIPYGRP submitted 2025-08-21 gr-qc

Semi-analytical Study on the Polarized Images of Black Hole due to Frame Dragging

Xinyu Wang , Songbai Chen , Minyong Guo , Bin Chen This is my paper
classification gr-qc MSC 83C5783C10 PACS 04.70.Bw95.30.Sf
keywords black holeframe draggingpolarized imageretrograde accretiongravitational lensinggravitational Faraday rotationgeodesic flowspin measurement
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

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 frame dragging does not just alter the motion of accreting gas around a spinning black hole: it leaves a readable imprint in the polarized image. For a thin equatorial disk of test particles that starts orbiting retrograde, the flow reverses to prograde before plunging, and the image contains three critical features—the turning point of the flow's primary image, the polarization-flip location, and the image position of the actual spacetime turning point. The paper argues that gravitational lensing and gravitational Faraday rotation push these three locations apart in a generic way, derives approximate expressions for their positions for an on-axis observer, and works out their spatial ordering. A sympathetic reader would care because the non-coincidence gives an observer a way to infer frame dragging, and with it the black hole's spin, from a single polarimetric image.

Core claim

The central claim is that in a thin equatorial accretion disk made of geodesic test particles that initially orbit retrograde, frame dragging transforms the flow into a prograde configuration before it plunges into the black hole. The polarized image of this flow then exhibits three critical locations: the turning point of the flow's primary image, the polarization-flip location on the image plane, and the position of the primary image that corresponds to the flow's actual turning point in spacetime. Because gravitational lensing distorts where the turning point appears and gravitational Faraday rotation shifts the polarization direction, these three positions do not generally coincide. For

What carries the argument

The central mechanism is frame dragging (the Lense-Thirring effect), which twists orbital motion and reverses the sign of the flow's angular momentum inside a certain radius. The argument is carried by the mapping between the spacetime turning point and image-plane locations under gravitational lensing, together with gravitational Faraday rotation of the polarization direction. These two effects are what separate the three critical locations; the paper's on-axis observer formulas express the radii of those locations approximately in terms of the black hole's rotation and the flow's trajectory.

Load-bearing premise

The load-bearing assumption is that the accretion flow is a thin equatorial disk of test particles following geodesics that begin in a retrograde orbit; real flows feel pressure, magnetic stress, and turbulence, so the reversal point and the image locations tied to it could move.

What would settle it

A ray-traced polarized image of a thin disk with initially retrograde geodesic motion would falsify the claimed hierarchy if the three critical locations coincided for all spins, or if their ordering reversed relative to the analytic expressions. Observationally, a high-resolution polarimetric image of an accreting black hole whose accretion direction is independently known to be retrograde should show the predicted polarization flip and image-plane turning point at the predicted radii; if they are absent or coincide, the frame-dragging imprint claim fails.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • A polarized black-hole image can be read as a frame-dragging detector: the three critical radii and their ordering are a spin-dependent signature.
  • Because the three locations are displaced by different physical effects, measuring their offsets can help separate gravitational lensing from gravitational Faraday rotation.
  • The approximate on-axis expressions provide a direct analytic map from observed image-plane radii to the spacetime radius where the flow turns around.
  • The prediction is testable with ray-traced polarized image models and, in principle, with high-resolution interferometric polarimetric observations of accreting black holes.

Where Pith is reading between the lines

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

  • If real accretion flows with pressure, magnetic stress, or turbulence still reverse direction, the three locations may shift from the geodesic prediction; comparing observed offsets with these formulas could yield a constraint on non-geodesic stresses.
  • Extending the same three-critical-location logic to off-axis observers would turn the radial hierarchy into an azimuthally modulated pattern, because projection mixes radii and angles.
  • Caution: the full-text body supplied with this record is an unrelated manuscript (a DSL-based puzzle-data synthesis paper), so this extraction is grounded in the abstract alone; if that body is authoritative, the paper's actual claims are those of the puzzle framework rather than the black-hole analysis.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 3 minor

Summary. The submission is advertised as a gr-qc study of polarized black-hole images, with the abstract claiming that frame dragging converts an initially retrograde thin equatorial accretion flow into a prograde configuration and that the polarized image then exhibits three generically non-coincident critical locations: the turning point of the flow's primary image, the polarization-flip location on the image plane, and the image position corresponding to the flow's actual spacetime turning point. The abstract further promises approximate analytic expressions for these locations for an on-axis observer. The supplied full text, however, is an unrelated arXiv:2508.15180v3 paper, 'PuzzleClone: A DSL-Powered Framework for Synthesizing Verifiable Data,' which contains no Kerr metric, no geodesic equations, no ray tracing, no polarization formalism, and no definitions of the three critical locations. The physical claims of the abstract are therefore not supported by any derivable content in the submitted manuscript.

Significance. If the abstract's claims were backed by a self-contained derivation, the spatial hierarchy among the three image-plane features could provide an interesting observational signature of frame dragging, especially because the three are conceptually distinct and their non-coincidence would not be an identity. The physical narrative is broadly compatible with established Kerr geodesic behavior and gravitational Faraday rotation. However, the submitted manuscript provides no equations, no numerical results, no code, and no derivations that could support or falsify the central claim. There is no strength to credit in the submission as currently constituted: the only verifiable content is the PuzzleClone dataset paper, which is irrelevant to the claimed physics.

major comments (4)
  1. [Full Text (entire submitted manuscript)] The manuscript body contains no physics content whatsoever: no Kerr metric, no geodesic equations, no ray-tracing or gravitational-lensing formalism, no polarization transport equations, and no definitions of the three critical locations. The submitted text is the PuzzleClone cs.AI paper. The abstract's claim of a 'semi-analytical study' and 'approximate analytic expressions' is thus an omitted-proof flag on the central claim. No amount of local revision can fix the absence of the actual derivation.
  2. [Abstract] The 'three distinctive critical locations' are named but never defined in the submitted text. In particular, 'turning point of the flow's primary image,' 'polarization-flip location on the image plane,' and 'position of the primary image corresponding to the flow's actual turning point in spacetime' require precise image-plane and spacetime coordinate conventions. Without these definitions, the claimed generic non-coincidence and the spatial hierarchy are not checkable statements.
  3. [Abstract] The promised 'approximate analytic expressions characterizing their positions' for an on-axis observer do not appear anywhere in the supplied manuscript. No equations are derived, no approximations are stated, and no comparison is made to numerical ray tracing. This is a load-bearing component of the central claim, not a presentation issue.
  4. [Abstract] The modeling assumptions are stated only at the abstract level: a thin equatorial accretion disk of initially retrograde, geodesically moving flows. The submitted text provides no equations of motion, no demonstration that frame dragging reverses the radial motion before plunge, and no specification of the Kerr spin parameter, observer inclination, or emission model. The physical scenario may be plausible, but the manuscript supplies no grounds for the predicted locations or their hierarchy.
minor comments (3)
  1. [Title/Abstract vs. Full Text] The title and abstract are for a black-hole polarization paper, while the full text is a paper on synthetic puzzle generation for large language models. This mismatch makes the manuscript internally incoherent as a submission.
  2. [References] The reference list is drawn entirely from the PuzzleClone paper and contains no entries for Kerr geometry, geodesic motion, gravitational lensing, or gravitational Faraday rotation, which would be essential for the claimed study.
  3. [Figures and tables] All figures and tables in the supplied text describe the PuzzleClone benchmark pipeline and model performance; there are no images, image-plane coordinates, polarization maps, or parameter scans relevant to the claimed physics.

Circularity Check

0 steps flagged

No circularity can be identified because the supplied full text contains no derivation chain for the claimed result.

full rationale

The abstract promises a gr-qc derivation about polarized black-hole images, but the full text supplied is arXiv:2508.15180v3, 'PuzzleClone: A DSL-Powered Framework for Synthesizing Verifiable Data', a CS/AI dataset-generation paper. It contains no Kerr metric, no geodesic equations, no ray tracing, no definitions of the three critical locations, and no approximate analytic expressions. There is therefore no derivation chain to walk and no equation-level reduction to exhibit. Circularity requires quoting a specific reduction, such as an input defined in terms of the output, a fitted parameter renamed as a prediction, or a load-bearing self-citation that substitutes for proof. None of these can be found because the relevant derivation is entirely absent. This is an omitted-proof and manuscript-integrity concern, not a circularity finding. If the actual gr-qc text were available, the three critical locations named in the abstract are distinct observables, so their non-coincidence would be a physical claim rather than an identity by construction. Accordingly, the circularity score is 0, with no circular steps identified.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 0 invented entities

Because only the abstract is available, the ledger records the physical and mathematical premises that the abstract itself states or directly implies. No numbers are fitted in the abstract, and no new entities are introduced. The main burden is the idealization of the accretion flow: thin, equatorial, geodesic, initially retrograde, plus the plasma and radiative assumptions hidden inside 'gravitational Faraday rotation' and the restriction to an on-axis observer for the analytic formulas.

axioms (4)
  • standard math Kerr spacetime is the correct stationary, axisymmetric vacuum exterior for the black hole
    The abstract's frame-dragging effect is a Kerr feature; the calculation treats the hole's rotation as the driver of the flow reversal.
  • domain assumption The accretion flow is a thin equatorial disk of test particles on geodesics, initially retrograde
    Stated in the abstract: 'a thin equatorial accretion disk composed of initially retrograde, geodesically moving flows'. Real magnetized, turbulent disks are not geodesic.
  • domain assumption Polarized image formation follows geometric optics with gravitational Faraday rotation through the disk plasma
    The abstract attributes the polarization flip to 'gravitational Faraday rotation'; the emission and plasma model behind it is not specified in the abstract.
  • domain assumption Analytic expressions are restricted to an on-axis observer
    The abstract states the approximate expressions are derived 'for an on-axis observer'; the general off-axis case is left to the numerical treatment.

reviewed 2026-08-05 · how reviews work

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Cite this review

Pith. "Pith review of Semi-analytical Study on the Polarized Images of Black Hole due to Frame Dragging." pith.science (2026). https://pith.science/paper/WTIPYGRP

@misc{pith2026250815178,
  author       = {Pith},
  title        = {Pith review of: Semi-analytical Study on the Polarized Images of Black Hole due to Frame Dragging},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WTIPYGRP}},
  note         = {Machine review of arXiv:2508.15178}
}
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read the original abstract

An initially retrograde accretion flow is transformed into a prograde configuration before plunging into the black hole, as a result of the frame-dragging effect induced by the black hole's rotation. The polarized image of a black hole shaped by such an accretion flow manifests three distinctive critical locations: the turning point of the flow's primary image, the polarization-flip location on the image plane, and the position of the primary image corresponding to the flow's actual turning point in spacetime. Due to the influences of gravitational lensing and gravitational Faraday rotation, these three positions generally do not coincide. In this work, we examine a thin equatorial accretion disk composed of initially retrograde, geodesically moving flows, and conduct a systematic investigation into the interrelations and discrepancies among these critical locations. We elucidate the spatial hierarchy among the three, and for an on-axis observer, we derive approximate analytic expressions characterizing their positions.

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.

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  2. Optical images of Kerr-Sen black hole illuminated by thick accretion disks

    astro-ph.HE 2026-04 unverdicted novelty 4.0

    Increasing charge Q shrinks photon rings and central shadows in Kerr-Sen black hole images while spin creates brightness asymmetry; polarization patterns follow lensing and frame dragging.

Reference graph

Works this paper leans on

49 extracted references · 13 canonical work pages · cited by 2 Pith papers · 3 internal anchors

  1. [1]

    U ber den Einflu der Eigenrotation der Zentralk \

    J. Lense and H. Thirring , `` \"U ber den Einflu der Eigenrotation der Zentralk \"o rper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie ,'' Physikalische Zeitschrift 19 (Jan., 1918) 156

    work page 1918

  2. [2]

    Ciufolini and E

    I. Ciufolini and E. C. Pavlis , `` A confirmation of the general relativistic prediction of the Lense-Thirring effect ,'' http://dx.doi.org/10.1038/nature03007 431 no. 7011, (Oct., 2004) 958--960

    work page doi:10.1038/nature03007 2004

  3. [3]

    C. W. F. Everitt et al. , `` Gravity Probe B: Final Results of a Space Experiment to Test General Relativity ,'' http://dx.doi.org/10.1103/PhysRevLett.106.221101 Phys. Rev. Lett. 106 (2011) 221101 , http://arxiv.org/abs/1105.3456 arXiv:1105.3456 [gr-qc]

    Pith/arXiv arXiv 2011

  4. [4]

    M. D. Johnson et al. , `` Universal interferometric signatures of a black hole s photon ring ,'' http://dx.doi.org/10.1126/sciadv.aaz1310 Sci. Adv. 6 no. 12, (2020) eaaz1310 , http://arxiv.org/abs/1907.04329 arXiv:1907.04329 [astro-ph.IM]

    Pith/arXiv arXiv 2020

  5. [5]

    X. Wang, Y. Hou, and M. Guo, `` How different are shadows of compact objects with and without horizons? ,'' http://dx.doi.org/10.1088/1475-7516/2023/05/036 JCAP 05 (2023) 036 , http://arxiv.org/abs/2301.04851 arXiv:2301.04851 [gr-qc]

    Pith/arXiv arXiv 2023

  6. [6]

    X. Wang, X. Wang, H.-Q. Zhang, and M. Guo, `` Is a photon ring invariably a closed structure? ,'' http://dx.doi.org/10.1140/epjc/s10052-024-13527-6 Eur. Phys. J. C 84 no. 11, (2024) 1168 , http://arxiv.org/abs/2405.05011 arXiv:2405.05011 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  7. [7]

    LIGO Scientific, Virgo Collaboration, B. P. Abbott et al. , `` Observation of Gravitational Waves from a Binary Black Hole Merger ,'' http://dx.doi.org/10.1103/PhysRevLett.116.061102 Phys. Rev. Lett. 116 no. 6, (2016) 061102 , http://arxiv.org/abs/1602.03837 arXiv:1602.03837 [gr-qc]

    Pith/arXiv arXiv 2016

  8. [8]

    Akiyama et al

    Event Horizon Telescope Collaboration, K. Akiyama et al. , `` First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole ,'' http://dx.doi.org/10.3847/2041-8213/ab0ec7 Astrophys. J. Lett. 875 (2019) L1 , http://arxiv.org/abs/1906.11238 arXiv:1906.11238 [astro-ph.GA]

    Pith/arXiv arXiv 2041

  9. [9]

    Akiyama et al

    Event Horizon Telescope Collaboration, K. Akiyama et al. , `` First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way ,'' http://dx.doi.org/10.3847/2041-8213/ac6674 Astrophys. J. Lett. 930 no. 2, (2022) L12 , http://arxiv.org/abs/2311.08680 arXiv:2311.08680 [astro-ph.HE]

    Pith/arXiv arXiv 2041

  10. [10]

    Akiyama et al

    Event Horizon Telescope Collaboration, K. Akiyama et al. , `` First M87 Event Horizon Telescope Results. VII. Polarization of the Ring ,'' http://dx.doi.org/10.3847/2041-8213/abe71d Astrophys. J. Lett. 910 no. 1, (2021) L12 , http://arxiv.org/abs/2105.01169 arXiv:2105.01169 [astro-ph.HE]

    Pith/arXiv arXiv 2041

  11. [11]

    Akiyama et al

    Event Horizon Telescope Collaboration, K. Akiyama et al. , `` First Sagittarius A* Event Horizon Telescope Results. VII. Polarization of the Ring ,'' http://dx.doi.org/10.3847/2041-8213/ad2df0 Astrophys. J. Lett. 964 no. 2, (2024) L25

    doi:10.3847/2041-8213/ad2df0 2041

  12. [12]

    Ricarte, M

    A. Ricarte, M. D. Johnson, Y. Y. Kovalev, D. C. M. Palumbo, and R. Emami, `` How Spatially Resolved Polarimetry Informs Black Hole Accretion Flow Models ,'' http://dx.doi.org/10.3390/galaxies11010005 Galaxies 11 no. 1, (2023) 5 , http://arxiv.org/abs/2211.03907 arXiv:2211.03907 [astro-ph.HE]

    Pith/arXiv arXiv 2023

  13. [13]

    Chael, A

    A. Chael, A. Lupsasca, G. N. Wong, and E. Quataert, `` Black Hole Polarimetry I. A Signature of Electromagnetic Energy Extraction ,'' http://dx.doi.org/10.3847/1538-4357/acf92d Astrophys. J. 958 no. 1, (2023) 65 , http://arxiv.org/abs/2307.06372 arXiv:2307.06372 [astro-ph.HE]

    Pith/arXiv arXiv 2023

  14. [14]

    Polarized images of charged particles in vortical motions around a magnetized Kerr black hole

    Z. Zhang, Y. Hou, Z. Hu, M. Guo, and B. Chen, `` Polarized images of charged particles in vortical motions around a magnetized Kerr black hole ,'' http://dx.doi.org/10.1088/1475-7516/2024/03/013 JCAP 03 (2024) 013 , http://arxiv.org/abs/2304.03642 arXiv:2304.03642 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  15. [15]

    S. Chen, J. Jing, W.-L. Qian, and B. Wang, `` Black hole images: A review ,'' http://dx.doi.org/10.1007/s11433-022-2059-5 Sci. China Phys. Mech. Astron. 66 no. 6, (2023) 260401 , http://arxiv.org/abs/2301.00113 arXiv:2301.00113 [astro-ph.HE]

    Pith/arXiv arXiv 2059

  16. [16]

    Huang, D.-J

    Y. Huang, D.-J. Liu, and H. Zhang, `` Lensing and light rings of parity-odd rotating boson stars ,'' http://dx.doi.org/10.1007/s11433-024-2577-0 Sci. China Phys. Mech. Astron. 68 no. 8, (2025) 280411 , http://arxiv.org/abs/2410.20867 arXiv:2410.20867 [gr-qc]

    Pith/arXiv arXiv 2025

  17. [17]

    D. H. Roberts , J. F. C. Wardle , and L. F. Brown , `` Linear Polarization Radio Imaging at Milliarcsecond Resolution ,'' http://dx.doi.org/10.1086/174180 427 (June, 1994) 718

    work page doi:10.1086/174180 1994

  18. [18]

    Himwich, M

    E. Himwich, M. D. Johnson, A. Lupsasca, and A. Strominger, `` Universal polarimetric signatures of the black hole photon ring ,'' http://dx.doi.org/10.1103/PhysRevD.101.084020 Phys. Rev. D 101 no. 8, (2020) 084020 , http://arxiv.org/abs/2001.08750 arXiv:2001.08750 [gr-qc]

    Pith/arXiv arXiv 2020

  19. [19]

    F. H. Vincent, M. Wielgus, N. Aimar, T. Paumard, and G. Perrin, `` Polarized signatures of orbiting hot spots: Special relativity impact and probe of spacetime curvature ,'' http://dx.doi.org/10.1051/0004-6361/202348016 Astron. Astrophys. 684 (2024) A194 , http://arxiv.org/abs/2309.10053 arXiv:2309.10053 [astro-ph.HE]

    Pith/arXiv arXiv 2024

  20. [20]

    B. Chen, Y. Hou, Y. Song, and Z. Zhang, `` Polarization patterns of the hot spots plunging into a Kerr black hole ,'' http://dx.doi.org/10.1103/PhysRevD.111.083045 Phys. Rev. D 111 no. 8, (2025) 083045 , http://arxiv.org/abs/2407.14897 arXiv:2407.14897 [astro-ph.HE]

    Pith/arXiv arXiv 2025

  21. [21]

    Gelles, E

    Z. Gelles, E. Himwich, D. C. M. Palumbo, and M. D. Johnson, `` Polarized image of equatorial emission in the Kerr geometry ,'' http://dx.doi.org/10.1103/PhysRevD.104.044060 Phys. Rev. D 104 no. 4, (2021) 044060 , http://arxiv.org/abs/2105.09440 arXiv:2105.09440 [gr-qc]

    Pith/arXiv arXiv 2021

  22. [22]

    Y. Hou, J. Huang, M. Guo, Y. Mizuno, and B. Chen, `` Near-horizon Polarization as a Diagnostic of Black Hole Spacetime ,'' http://dx.doi.org/10.3847/2041-8213/adee09 Astrophys. J. Lett. 988 no. 2, (2025) L51 , http://arxiv.org/abs/2409.07248 arXiv:2409.07248 [gr-qc]

    Pith/arXiv arXiv 2041

  23. [23]

    Yang, K.-J

    C.-Y. Yang, K.-J. He, X.-X. Zeng, and L.-F. Li, `` Observational signatures and polarized images of rotating charged black holes in Kalb-Ramond Gravity ,'' http://arxiv.org/abs/2508.07393 arXiv:2508.07393 [gr-qc]

    Pith/arXiv arXiv

  24. [24]

    X. Qin, S. Chen, Z. Zhang, and J. Jing, `` Polarized Image of a Rotating Black Hole in Scalar Tensor Vector Gravity Theory ,'' http://dx.doi.org/10.3847/1538-4357/ac8f49 Astrophys. J. 938 no. 1, (2022) 2 , http://arxiv.org/abs/2207.12034 arXiv:2207.12034 [gr-qc]

    Pith/arXiv arXiv 2022

  25. [25]

    Y. Chen, L. Cheng, P. Wang, and H. Yang, `` Polarized image of a synchrotron-emitting ring in an Einstein-Maxwell-scalar theory ,'' http://dx.doi.org/10.1103/kbkh-xgp7 Phys. Rev. D 112 no. 2, (2025) 024044 , http://arxiv.org/abs/2409.05304 arXiv:2409.05304 [gr-qc]

    Pith/arXiv arXiv 2025

  26. [26]

    Ricarte, D

    A. Ricarte, D. C. M. Palumbo, R. Narayan, F. Roelofs, and R. Emami, `` Observational Signatures of Frame Dragging in Strong Gravity ,'' http://dx.doi.org/10.3847/2041-8213/aca087 Astrophys. J. Lett. 941 no. 1, (2022) L12 , http://arxiv.org/abs/2211.01810 arXiv:2211.01810 [gr-qc]

    Pith/arXiv arXiv 2041

  27. [27]

    Ruffini and J

    R. Ruffini and J. R. Wilson, ``Relativistic magnetohydrodynamical effects of plasma accreting into a black hole,'' http://dx.doi.org/10.1103/PhysRevD.12.2959 Phys. Rev. D 12 (Nov, 1975) 2959--2962 . https://link.aps.org/doi/10.1103/PhysRevD.12.2959

    doi:10.1103/physrevd.12.2959 1975

  28. [28]

    Y. Hou, Z. Zhang, M. Guo, and B. Chen, `` A new analytical model of magnetofluids surrounding rotating black holes ,'' http://dx.doi.org/10.1088/1475-7516/2024/02/030 JCAP 02 (2024) 030 , http://arxiv.org/abs/2309.13304 arXiv:2309.13304 [gr-qc]

    Pith/arXiv arXiv 2024

  29. [29]

    D. C. M. Palumbo, G. N. Wong, and B. S. Prather, `` Discriminating Accretion States via Rotational Symmetry in Simulated Polarimetric Images of M87 ,'' http://dx.doi.org/10.3847/1538-4357/ab86ac Astrophys. J. 894 no. 2, (2020) 156 , http://arxiv.org/abs/2004.01751 arXiv:2004.01751 [astro-ph.HE]

    Pith/arXiv arXiv 2020

  30. [30]

    S. E. Gralla and A. Lupsasca, `` Lensing by Kerr Black Holes ,'' http://dx.doi.org/10.1103/PhysRevD.101.044031 Phys. Rev. D 101 no. 4, (2020) 044031 , http://arxiv.org/abs/1910.12873 arXiv:1910.12873 [gr-qc]

    Pith/arXiv arXiv 2020

  31. [31]

    Pineault and R

    S. Pineault and R. C. Roeder , `` Applications of Geometrical Optics to the Kerr Metric. Analytical Results ,'' http://dx.doi.org/10.1086/155073 212 (Mar., 1977) 541--549

    work page doi:10.1086/155073 1977

  32. [32]

    Fayos and J

    F. Fayos and J. Llosa , `` Gravitational effects on the polarization plane ,'' http://dx.doi.org/10.1007/BF00756802 General Relativity and Gravitation 14 no. 10, (Oct., 1982) 865--877

    work page doi:10.1007/bf00756802 1982

  33. [33]

    Photon polarization and geometric phase in general relativity

    A. Brodutch, T. F. Demarie, and D. R. Terno, `` Photon polarization and geometric phase in general relativity ,'' http://dx.doi.org/10.1103/PhysRevD.84.104043 Phys. Rev. D 84 (2011) 104043 , http://arxiv.org/abs/1108.0973 arXiv:1108.0973 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  34. [34]

    Ishihara, M

    H. Ishihara, M. Takahashi, and A. Tomimatsu, `` GRAVITATIONAL FARADAY ROTATION INDUCED BY KERR BLACK HOLE ,'' http://dx.doi.org/10.1103/PhysRevD.38.472 Phys. Rev. D 38 (1988) 472

    work page doi:10.1103/physrevd.38.472 1988

  35. [35]

    J. M. Bardeen, `` Timelike and null geodesics in the Kerr metric ,'' Proceedings, Ecole d'Et\'e de Physique Th\'eorique: Les Astres Occlus : Les Houches, France, August, 1972, 215-240 (1973) 215--240

    work page 1972

  36. [36]

    K. S. Thorne , `` Disk-Accretion onto a Black Hole. II. Evolution of the Hole ,'' http://dx.doi.org/10.1086/152991 191 (July, 1974) 507--520

    doi:10.1086/152991 1974

  37. [37]

    R. D. Blandford and R. L. Znajek, `` Electromagnetic extractions of energy from Kerr black holes ,'' http://dx.doi.org/10.1093/mnras/179.3.433 Mon. Not. Roy. Astron. Soc. 179 (1977) 433--456

    doi:10.1093/mnras/179.3.433 1977

  38. [38]

    Z. Hu, Z. Zhong, P.-C. Li, M. Guo, and B. Chen, `` QED effect on a black hole shadow ,'' http://dx.doi.org/10.1103/PhysRevD.103.044057 Phys. Rev. D 103 no. 4, (2021) 044057 , http://arxiv.org/abs/2012.07022 arXiv:2012.07022 [gr-qc]

    Pith/arXiv arXiv 2021

  39. [39]

    Y. Hou, Z. Zhang, H. Yan, M. Guo, and B. Chen, `` Image of a Kerr-Melvin black hole with a thin accretion disk ,'' http://dx.doi.org/10.1103/PhysRevD.106.064058 Phys. Rev. D 106 no. 6, (2022) 064058 , http://arxiv.org/abs/2206.13744 arXiv:2206.13744 [gr-qc]

    Pith/arXiv arXiv 2022

  40. [40]

    Zhong, Z

    Z. Zhong, Z. Hu, H. Yan, M. Guo, and B. Chen, `` QED effects on Kerr black hole shadows immersed in uniform magnetic fields ,'' http://dx.doi.org/10.1103/PhysRevD.104.104028 Phys. Rev. D 104 no. 10, (2021) 104028 , http://arxiv.org/abs/2108.06140 arXiv:2108.06140 [gr-qc]

    Pith/arXiv arXiv 2021

  41. [41]

    Li, M.-Q

    G.-P. Li, M.-Q. Wu, K.-J. He, and Q.-Q. Jiang, `` Observational features of massive boson stars with thin disk accretion ,'' http://arxiv.org/abs/2505.14734 arXiv:2505.14734 [gr-qc]

    Pith/arXiv arXiv

  42. [42]

    W.-Q. Zhen, H. Guo, M.-H. Wu, and X.-M. Kuang, `` Orbital precession and Lense-Thirring effect of Horndeski rotating spacetimes ,'' http://dx.doi.org/10.1016/j.physletb.2025.139307 Phys. Lett. B 862 (2025) 139307

    work page arXiv 2025

  43. [43]

    W. Liu, H. Huang, D. Wu, and J. Wang, `` Lorentz violation signatures in the low-energy sector of Ho r ava gravity from black hole shadow observations ,'' http://arxiv.org/abs/2506.13504 arXiv:2506.13504 [gr-qc]

    work page arXiv

  44. [44]

    V. P. Frolov and I. D. Novikov, eds., http://dx.doi.org/10.1007/978-94-011-5139-9 Black hole physics: Basic concepts and new developments . 1998

    doi:10.1007/978-94-011-5139-9 1998

  45. [45]

    P. V. P. Cunha, C. A. R. Herdeiro, E. Radu, and H. F. Runarsson, `` Shadows of Kerr black holes with and without scalar hair ,'' http://dx.doi.org/10.1142/S0218271816410212 Int. J. Mod. Phys. D 25 no. 09, (2016) 1641021 , http://arxiv.org/abs/1605.08293 arXiv:1605.08293 [gr-qc]

    Pith/arXiv arXiv 2016

  46. [46]

    R. W. Lindquist, `` Relativistic transport theory ,'' http://dx.doi.org/10.1016/0003-4916(66)90207-7 Annals Phys. 37 no. 3, (1966) 487--518

    doi:10.1016/0003-4916(66)90207-7 1966

  47. [47]

    Walker and R

    M. Walker and R. Penrose, `` On quadratic first integrals of the geodesic equations for type [22] spacetimes ,'' http://dx.doi.org/10.1007/BF01649445 Commun. Math. Phys. 18 (1970) 265--274

    doi:10.1007/bf01649445 1970

  48. [48]

    D. E. A. Gates, S. Hadar, and A. Lupsasca, `` Maximum observable blueshift from circular equatorial Kerr orbiters ,'' http://dx.doi.org/10.1103/PhysRevD.102.104041 Phys. Rev. D 102 no. 10, (2020) 104041 , http://arxiv.org/abs/2009.03310 arXiv:2009.03310 [gr-qc]

    Pith/arXiv arXiv 2020

  49. [49]

    write newline

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    work page

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.