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arxiv: 2604.06128 · v1 · submitted 2026-04-07 · 🌌 astro-ph.HE · astro-ph.IM· gr-qc

Recognition: 2 theorem links

· Lean Theorem

On the observational distinguishability of the Kerr and Kerr-Hayward metrics to EHT

Nikola Bukowiecka , Angelo Ricarte , Prashant Kocherlakota , Cora Prather
Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:04 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.IMgr-qc
keywords Kerr metricKerr-Hayward metricEvent Horizon Telescopeblack hole imagesGRMHD simulationspolarized radiative transfersingularity-free spacetimesobservational distinguishability
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The pith

A singularity-free correction to the Kerr metric produces black hole images and polarization patterns that are functionally identical to Kerr in EHT observations.

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

The paper tests whether a regularized version of the Kerr metric can be distinguished from the standard Kerr solution using current and near-future Event Horizon Telescope measurements. The authors run new general-relativistic magnetohydrodynamics simulations of magnetized plasma in the Kerr-Hayward spacetime, then compute polarized images through an extended radiative-transfer pipeline. They find that fluid diagnostics such as magnetic flux and jet power, together with image features including polarization maps and photon-ring structure, match the Kerr case to high precision. A reader would care because the Kerr metric contains a curvature singularity whose removal has no apparent effect on the observables now being measured.

Core claim

We produce GRMHD simulations of a magnetized plasma in a Kerr-Hayward spacetime and extend the EHT analysis framework to perform polarized radiative transfer in this spacetime. From fluid quantities such as the magnetic flux parameter and jet efficiency, to image quantities such as the polarization pattern and the photon ring structure, our results for the Kerr-Hayward metric appear functionally indistinguishable from the Kerr metric. Our study finds that under certain conditions, the singularity-free correction to the Kerr metric can yield observables that are effectively indistinguishable in EHT measurements.

What carries the argument

The Kerr-Hayward metric, a phenomenological regular black-hole solution obtained by replacing the Kerr ring singularity with a de Sitter core while preserving asymptotic flatness and the horizon structure.

If this is right

  • Fluid quantities such as the magnetic flux parameter and jet efficiency remain essentially unchanged from their Kerr values.
  • Polarization patterns across the image are preserved to the precision of current EHT analysis.
  • The photon-ring size and shape show no measurable deviation from the Kerr prediction.
  • Under the tested conditions the two metrics are observationally equivalent for all EHT-accessible diagnostics.

Where Pith is reading between the lines

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

  • If the Hayward parameter remains small enough to match existing data, regularity of the interior may be untestable with present EHT resolution and sensitivity.
  • Higher-resolution or multi-frequency observations could still reveal differences once the correction scale approaches the photon-ring size.
  • The result supports continued use of regular metrics in astrophysical modeling without immediate conflict with observations.

Load-bearing premise

The chosen value of the Hayward correction parameter together with the adopted GRMHD initial conditions do not produce detectable differences in radiative transfer or image morphology.

What would settle it

A measured difference in the photon-ring diameter or in the azimuthal polarization pattern that scales with the Hayward parameter and cannot be reproduced by any Kerr model at the same spin and accretion rate.

Figures

Figures reproduced from arXiv: 2604.06128 by Angelo Ricarte, Cora Prather, Nikola Bukowiecka, Prashant Kocherlakota.

Figure 1
Figure 1. Figure 1: Time evolution of fluid-domain observables for the four fiducial models. Top left: Eddington ratio, M /˙ M˙ Edd. Top right: dimensionless magnetic flux, ϕB. In both top panels, the horizontal dashed lines denote the time-averaged values for each model. Bottom left: jet efficiency for the low-spin models. Bottom right: jet efficiency for the mid-spin models, where ηjet is defined in Equation 10. In the bott… view at source ↗
Figure 2
Figure 2. Figure 2: Time-averaged Stokes I images for the four fiducial models, with polarization ticks overlaid, for n = all (top), n = 0 (middle), and n = 1 (bottom), at resolution 400 × 400. The columns show, from left to right, KerrLow, KHLow, KerrMid, and KHMid. Colors indicate log10(I/Jy µas−2 ). The blue curve denotes the theoretical critical curve and the red curve the theoretical inner shadow. The critical curve prov… view at source ↗
Figure 3
Figure 3. Figure 3: Distributions of the polarization observables and brightness asymmetry for the four fiducial models, computed from the n = all images at resolution 400 × 400, with the blurring kernel 20µas. The panels show, from top left to bottom left, the average linear polarization mavg, the net linear polarization mnet, the quadrupolar polarization amplitude |β2|, the quadrupolar polarization phase ∠β2, and the bright… view at source ↗
Figure 4
Figure 4. Figure 4: Time-averaged one-dimensional Stokes I profiles for the four fiducial models, extracted from the image-plane cuts shown separately for n = all (bottom), n = 0 (middle), and n = 1 (top), at resolution 400 × 400. In each row, the left panel shows the profile along the vertical (polar) cut and the right panel the profile along the horizontal cut. The dashed lines mark the locations of the theoretical critical… view at source ↗
Figure 5
Figure 5. Figure 5: Shadows and inner shadows of modified Kerr–Hayward black holes for nearly polar (left) and nearly equatorial (right) observers. For polar viewing angles, both structures are nearly circular, with weak dependence on the spin a and the de Sitter length scale L. For equatorial observers, the shadow remains approximately circular but is increasingly displaced to the right with increasing spin due to frame drag… view at source ↗
Figure 6
Figure 6. Figure 6: Radius, eccentricity, and centroid offset of the shadow (top) and inner shadow (bottom). Among these observables, the shadow eccentricity and centroid offset are the most effective probes of the spin a, while the inner-shadow eccentricity and centroid offset are most sensitive to the inclination i. The de Sitter length scale L imprints comparatively weaker signatures across all characteristics, with its ef… view at source ↗
read the original abstract

Astrophysical black holes appear well-represented by the Kerr metric, but this metric has the philosophical problem of a ring-like curvature singularity. We show that a phenomenological correction to the Kerr metric known as the Kerr-Hayward metric can eliminate the curvature singularity while preserving in detail many features of polarized black hole images now testable by the Event Horizon Telescope (EHT). To establish this, we produce new general relativistic magnetohydrodynamics (GRMHD) simulations of a magnetized plasma in a Kerr-Hayward spacetime, then we extend the EHT analysis framework to perform polarized radiative transfer in this spacetime. We detail our methodology for implementing this modified spacetime into an open-source pipeline. From fluid quantities such as the magnetic flux parameter and jet efficiency, to image quantities such as the polarization pattern and the photon ring structure, our results for the Kerr-Hayward metric appear functionally indistinguishable from the Kerr metric. Our study finds that under certain conditions, the singularity-free correction to the Kerr metric can yield observables that are effectively indistinguishable in EHT measurements.

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 performs GRMHD simulations of magnetized plasma in the Kerr-Hayward spacetime (a phenomenological, singularity-free correction to Kerr) and extends the EHT polarized radiative transfer pipeline to this metric. It reports that fluid quantities (magnetic flux parameter, jet efficiency) and image quantities (polarization pattern, photon ring structure) are functionally indistinguishable from the standard Kerr case, concluding that the correction can yield EHT observables that are effectively identical under certain conditions.

Significance. If the indistinguishability result holds after proper quantification, the work provides a concrete demonstration that certain regular black hole metrics can mimic Kerr predictions at the level of current EHT observables. This is relevant for assessing the robustness of EHT tests of the Kerr hypothesis and for exploring singularity resolution in phenomenological spacetimes. The methodological extension of the open-source EHT pipeline to modified metrics is a reusable contribution.

major comments (2)
  1. [Abstract and Results] Abstract and Results: The Hayward correction parameter (denoted g or similar) is never assigned a numerical value, nor is it varied. The claim of functional indistinguishability therefore cannot be evaluated against EHT resolution and noise; it may hold trivially if the chosen g produces metric deviations ≪1% near the photon orbit (r≈3M). A scan over g (or at minimum an explicit justification for the adopted value) is required to test the distinguishability boundary.
  2. [Methodology and Results] Methodology and Results: No quantitative metrics, difference maps, error bars, or direct comparisons (e.g., fractional difference in polarization fraction, ring diameter, or jet efficiency relative to EHT array resolution) are supplied to support the indistinguishability statement. Without these, the central claim remains unsupported by visible evidence.
minor comments (1)
  1. [Methodology] The description of the pipeline implementation for the modified spacetime could include explicit code references or parameter files to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review. The comments correctly identify areas where additional clarity and evidence will strengthen the manuscript. We respond to each major comment below and will incorporate revisions to address the concerns while preserving the scope of the study, which demonstrates indistinguishability under specific conditions rather than a full parameter exploration.

read point-by-point responses

  1. Referee: The Hayward correction parameter (denoted g or similar) is never assigned a numerical value, nor is it varied. The claim of functional indistinguishability therefore cannot be evaluated against EHT resolution and noise; it may hold trivially if the chosen g produces metric deviations ≪1% near the photon orbit (r≈3M). A scan over g (or at minimum an explicit justification for the adopted value) is required to test the distinguishability boundary.

    Authors: We agree that the numerical value of the Hayward parameter was not explicitly stated in the manuscript text, which is an oversight on our part. We will revise the abstract, methodology, and results sections to specify the value of g adopted in the GRMHD simulations and include a justification based on the resulting metric deviations near the photon orbit (r≈3M), demonstrating that the chosen value keeps deviations small while resolving the singularity. A full scan over g is not feasible within the current work, as it would require a new suite of computationally intensive simulations; our focus is on showing that indistinguishability can occur under certain conditions. We will add a discussion of the parameter's role and how larger values could produce detectable differences. revision: partial

  2. Referee: No quantitative metrics, difference maps, error bars, or direct comparisons (e.g., fractional difference in polarization fraction, ring diameter, or jet efficiency relative to EHT array resolution) are supplied to support the indistinguishability statement. Without these, the central claim remains unsupported by visible evidence.

    Authors: We accept this point and acknowledge that the original manuscript relied primarily on qualitative descriptions of similarity between the Kerr-Hayward and Kerr cases. In the revised version, we will add quantitative metrics, including fractional differences in the magnetic flux parameter, jet efficiency, polarization fraction, and photon ring diameter. We will also include difference maps for the polarized images and discuss the magnitude of these differences in the context of EHT resolution and noise to provide direct, visible support for the indistinguishability claim. revision: yes

Circularity Check

0 steps flagged

No circularity: direct forward-modeling comparison of metrics via simulation

full rationale

The paper's chain consists of producing new GRMHD simulations in the Kerr-Hayward spacetime, extending polarized radiative transfer, and comparing fluid quantities (magnetic flux, jet efficiency) and image quantities (polarization pattern, photon ring) directly to equivalent Kerr runs. This is an independent numerical experiment with no parameter fitting to EHT data, no reduction of outputs to inputs by construction, and no load-bearing self-citations or uniqueness theorems invoked. The indistinguishability result follows from the explicit simulation outputs rather than any definitional equivalence or renamed prior result.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that standard GRMHD equations remain valid in the modified Kerr-Hayward spacetime and that the chosen correction parameter produces no observable deviation within EHT resolution.

free parameters (1)
  • Hayward correction scale
    Phenomenological length parameter that removes the singularity; its specific value is not given in the abstract but must be chosen to keep the metric close to Kerr.
axioms (1)
  • domain assumption GRMHD fluid equations and radiative transfer hold without modification in the Kerr-Hayward spacetime
    Invoked when running the simulations and extending the EHT pipeline to the new metric.

pith-pipeline@v0.9.0 · 5500 in / 1297 out tokens · 64223 ms · 2026-05-10T19:04:03.397587+00:00 · methodology

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Works this paper leans on

57 extracted references · 57 canonical work pages

  1. [1]

    Ayon-Beato and A

    Ayón-Beato, E., & García, A. 1998, PhRvL, 80, 5056, doi: 10.1103/PhysRevLett.80.5056 Azreg-Aïnou, M. 2014, Phys. Rev. D, 90, 064041, doi: 10.1103/PhysRevD.90.064041

    work page doi:10.1103/physrevlett.80.5056 1998

  2. [2]

    2013, Phys

    Bambi, C., & Modesto, L. 2013, Phys. Lett. B, 721, 329, doi: 10.1016/j.physletb.2013.03.025

    work page doi:10.1016/j.physletb.2013.03.025 2013

  3. [3]

    1968, in Proceedings of the 5th International Conference on Gravitation and the Theory of Relativity, 87

    Bardeen, J. 1968, in Proceedings of the 5th International Conference on Gravitation and the Theory of Relativity, 87

    work page 1968

  4. [4]

    Bardeen, J. M. 1973, in Black Holes (Les Astres Occlus), ed. C. Dewitt & B. S. Dewitt, 215–239

    work page 1973

  5. [5]

    S., & Ruzmaikin, A

    Bisnovatyi-Kogan, G. S., & Ruzmaikin, A. A. 1974, Ap&SS, 28, 45, doi: 10.1007/BF00642237

    work page doi:10.1007/bf00642237 1974

  6. [6]

    2024, Phys

    Carballo-Rubio, R., Di Filippo, F., Liberati, S., & Visser, M. 2024, Phys. Rev. Lett., 133, 181402, doi: 10.1103/PhysRevLett.133.181402

    work page doi:10.1103/physrevlett.133.181402 2024

  7. [7]

    2025, JCAP, 05, 003, doi: 10.1088/1475-7516/2025/05/003

    Carballo-Rubio, R., et al. 2025, JCAP, 05, 003, doi: 10.1088/1475-7516/2025/05/003

    work page doi:10.1088/1475-7516/2025/05/003 2025

  8. [8]

    D., & Lupsasca, A

    Chael, A., Johnson, M. D., & Lupsasca, A. 2021, ApJ, 918, 6, doi: 10.3847/1538-4357/ac09ee

    work page doi:10.3847/1538-4357/ac09ee 2021

  9. [9]

    N., & Quataert, E

    Chael, A., Lupsasca, A., Wong, G. N., & Quataert, E. 2023, ApJ, 958, 65, doi: 10.3847/1538-4357/acf92d

    work page doi:10.3847/1538-4357/acf92d 2023

  10. [10]

    O., Johnson, M

    Chang, D. O., Johnson, M. D., Tiede, P., & Palumbo, D. C. M. 2024, ApJ, 974, 143, doi: 10.3847/1538-4357/ad6b28

    work page doi:10.3847/1538-4357/ad6b28 2024

  11. [11]

    Energy Extraction from Spinning Stringy Black Holes,

    Chatterjee, K., Kocherlakota, P., Younsi, Z., & Narayan, R. 2023, arXiv e-prints, arXiv:2310.20040, doi: 10.48550/arXiv.2310.20040

    work page doi:10.48550/arxiv.2310.20040 2023

  12. [12]

    2025, ApJL, 991, L58, doi: 10.3847/2041-8213/ae0740

    Chatterjee, K., Younsi, Z., Kocherlakota, P., & Narayan, R. 2025, ApJL, 991, L58, doi: 10.3847/2041-8213/ae0740

    work page doi:10.3847/2041-8213/ae0740 2025

  13. [13]

    2024, PhRvD, 109, 103034, doi: 10.1103/PhysRevD.109.103034

    Combi, L., Yang, H., Gutierrez, E., et al. 2024, PhRvD, 109, 103034, doi: 10.1103/PhysRevD.109.103034

    work page doi:10.1103/physrevd.109.103034 2024

  14. [14]

    S., Barrett, J., Blackburn, L., et al

    Doeleman, S. S., Barrett, J., Blackburn, L., et al. 2023, Galaxies, 11, 107, doi: 10.3390/galaxies11050107

    work page doi:10.3390/galaxies11050107 2023

  15. [15]

    Dymnikova, Gen

    Dymnikova, I. 1992, General Relativity and Gravitation, 24, 235, doi: 10.1007/BF00760226

    work page doi:10.1007/bf00760226 1992

  16. [16]

    Eichhorn and A

    Eichhorn, A., & Held, A. 2022, arXiv e-prints, arXiv:2212.09495, doi: 10.48550/arXiv.2212.09495 20 Event Horizon Telescope Collaboration, Akiyama, K.,

    work page doi:10.48550/arxiv.2212.09495 2022

  17. [17]

    2023, ApJL, 957, L20, doi: 10.3847/2041-8213/acff70

    Alberdi, A., et al. 2023, ApJL, 957, L20, doi: 10.3847/2041-8213/acff70

    work page doi:10.3847/2041-8213/acff70 2023

  18. [18]

    G., & Moncrief, V

    Fishbone, L. G., & Moncrief, V. 1976, ApJ, 207, 962, doi: 10.1086/154565

    work page doi:10.1086/154565 1976

  19. [19]

    Gammie, C. F. 2025, ApJ, 980, 193, doi: 10.3847/1538-4357/adaea3

    work page doi:10.3847/1538-4357/adaea3 2025

  20. [20]

    F., McKinney, J

    Gammie, C. F., McKinney, J. C., & Toth, G. 2003, The Astrophysical Journal, 589, 444–457, doi: 10.1086/374594

    work page doi:10.1086/374594 2003

  21. [21]

    D., & Palumbo, D

    Gelles, Z., Himwich, E., Johnson, M. D., & Palumbo, D. C. M. 2021, PhRvD, 104, 044060, doi: 10.1103/PhysRevD.104.044060

    work page doi:10.1103/physrevd.104.044060 2021

  22. [22]

    Gralla, S. E. 2020, Physical Review D, 102, doi: 10.1103/physrevd.102.044017

    work page doi:10.1103/physrevd.102.044017 2020

  23. [23]

    Null geodesics of the Kerr exterior,

    Gralla, S. E., & Lupsasca, A. 2020, PhRvD, 101, 044032, doi: 10.1103/PhysRevD.101.044032

    work page doi:10.1103/physrevd.101.044032 2020

  24. [24]

    E., & Lupsasca, A

    Gralla, S. E., & Lupsasca, A. 2020, Physical Review D, 102, doi: 10.1103/physrevd.102.124003

    work page doi:10.1103/physrevd.102.124003 2020

  25. [25]

    Hayward, S. A. 2006, Phys. Rev. Lett., 96, 031103, doi: 10.1103/PhysRevLett.96.031103

    work page doi:10.1103/physrevlett.96.031103 2006

  26. [26]

    V., Narayan, R., & Abramowicz, M

    Igumenshchev, I. V., Narayan, R., & Abramowicz, M. A. 2003, ApJ, 592, 1042, doi: 10.1086/375769

    work page doi:10.1086/375769 2003

  27. [27]

    Jackson, J. D. 1998, Classical Electrodynamics, 3rd Edition Jiménez-Rosales, A., & Dexter, J. 2018, MNRAS, 478, 1875, doi: 10.1093/mnras/sty1210

    work page doi:10.1093/mnras/sty1210 1998

  28. [28]

    2013, Phys

    Johannsen, T. 2013, Phys. Rev. D, 88, 044002, doi: 10.1103/PhysRevD.88.044002

    work page doi:10.1103/physrevd.88.044002 2013

  29. [29]

    D., Akiyama, K., Baturin, R., et al

    Johnson, M., Akiyama, K., Baturin, R., et al. 2024, in Space Telescopes and Instrumentation 2024: Optical, Infrared, and Millimeter Wave, ed. L. E. Coyle, M. D. Perrin, & S. Matsuura (SPIE), 90, doi: 10.1117/12.3019835

    work page doi:10.1117/12.3019835 2024

  30. [30]

    D., Lupsasca, A., Strominger, A., et al

    Johnson, M. D., Lupsasca, A., Strominger, A., et al. 2020, Science Advances, 6, eaaz1310, doi: 10.1126/sciadv.aaz1310

    work page doi:10.1126/sciadv.aaz1310 2020

  31. [31]

    Kerr, R. P. 1963, Phys. Rev. Lett., 11, 237, doi: 10.1103/PhysRevLett.11.237

    work page doi:10.1103/physrevlett.11.237 1963

  32. [32]

    2024, Classical and Quantum Gravity, 41, 225012, doi: 10.1088/1361-6382/ad828b

    Kocherlakota, P., & Narayan, R. 2024, Classical and Quantum Gravity, 41, 225012, doi: 10.1088/1361-6382/ad828b

    work page doi:10.1088/1361-6382/ad828b 2024

  33. [33]

    2025, Phys

    Kocherlakota, P., & Narayan, R. 2025, Phys. Rev. D, 112, 124058, doi: 10.1103/4wp1-2xny

    work page doi:10.1103/4wp1-2xny 2025

  34. [34]

    2023, The Astrophysical Journal Letters, 956, L11, doi: 10.3847/2041-8213/acfd1f

    Kocherlakota, P., Narayan, R., Chatterjee, K., Cruz-Osorio, A., & Mizuno, Y. 2023, The Astrophysical Journal Letters, 956, L11, doi: 10.3847/2041-8213/acfd1f

    work page doi:10.3847/2041-8213/acfd1f 2023

  35. [35]

    Kocherlakota et al

    Kocherlakota, P., Rezzolla, L., Falcke, H., et al. 2021, PhRvD, 103, 104047, doi: 10.1103/PhysRevD.103.104047

    work page doi:10.1103/physrevd.103.104047 2021

  36. [36]

    Markov, M. A. 1982, ZhETF Pisma Redaktsiiu, 36, 214

    work page 1982

  37. [37]

    2022, ApJ, 924, 46, doi: 10.3847/1538-4357/ac33a7 Mo´ scibrodzka, M., Falcke, H., & Shiokawa, H

    Medeiros, L., Chan, C.-K., Narayan, R., Özel, F., & Psaltis, D. 2022, The Astrophysical Journal, 924, 46, doi: 10.3847/1538-4357/ac33a7

    work page doi:10.3847/1538-4357/ac33a7 2022

  38. [38]

    M., et al

    Mizuno, Y., Younsi, Z., Fromm, C. M., et al. 2018, Nature Astron., 2, 585, doi: 10.1038/s41550-018-0449-5 Mościbrodzka, M., Dexter, J., Davelaar, J., & Falcke, H. 2017, MNRAS, 468, 2214, doi: 10.1093/mnras/stx587 Mościbrodzka, M., Falcke, H., & Shiokawa, H. 2016, A&A, 586, A38, doi: 10.1051/0004-6361/201526630 Mościbrodzka, M., & Gammie, C. F. 2018, MNRAS...

    work page doi:10.1038/s41550-018-0449-5 2018

  39. [39]

    2022, MNRAS, 511, 3795, doi: 10.1093/mnras/stac285

    Curd, B. 2022, Monthly Notices of the Royal Astronomical Society, 511, 3795–3813, doi: 10.1093/mnras/stac285

    work page doi:10.1093/mnras/stac285 2022

  40. [40]

    V., & Abramowicz, M

    Narayan, R., Igumenshchev, I. V., & Abramowicz, M. A. 2003, PASJ, 55, L69, doi: 10.1093/pasj/55.6.L69

    work page doi:10.1093/pasj/55.6.l69 2003

  41. [41]

    T., & Janis, A

    Newman, E. T., & Janis, A. I. 1965, Journal of Mathematical Physics, 6, 915, doi: 10.1063/1.1704350

    work page doi:10.1063/1.1704350 1965

  42. [42]

    , keywords =

    Olivares, H., Younsi, Z., Fromm, C. M., et al. 2020, MNRAS, 497, 521, doi: 10.1093/mnras/staa1878

    work page doi:10.1093/mnras/staa1878 2020

  43. [43]

    Palumbo, D. C. M., Wong, G. N., & Prather, B. S. 2020, The Astrophysical Journal, 894, 156, doi: 10.3847/1538-4357/ab86ac

    work page doi:10.3847/1538-4357/ab86ac 2020

  44. [44]

    Penrose, Phys

    Penrose, R. 1965, Phys. Rev. Lett., 14, 57, doi: 10.1103/PhysRevLett.14.57

    work page doi:10.1103/physrevlett.14.57 1965

  45. [45]

    2025, in New Frontiers in GRMHD Simulations, ed

    Prather, C. 2025, in New Frontiers in GRMHD Simulations, ed. C. Bambi, Y. Mizuno, S. Shashank, & F. Yuan (Singapore: Springer Nature Singapore), 167–201, doi: 10.1007/978-981-97-8522-3_5

    work page doi:10.1007/978-981-97-8522-3_5 2025

  46. [46]

    2020, PhRvL, 125, 141104, doi: 10.1103/PhysRevLett.125.141104

    Psaltis, D., Medeiros, L., Christian, P., et al. 2020, PhRvL, 125, 141104, doi: 10.1103/PhysRevLett.125.141104

    work page doi:10.1103/physrevlett.125.141104 2020

  47. [47]

    2023, MNRAS, 520, 4867, doi: 10.1093/mnras/stad466

    Qiu, R., Ricarte, A., Narayan, R., et al. 2023, Monthly Notices of the Royal Astronomical Society, 520, 4867–4888, doi: 10.1093/mnras/stad466

    work page doi:10.1093/mnras/stad466 2023

  48. [48]

    Raychaudhuri, Phys

    Raychaudhuri, A. 1955, Phys. Rev., 98, 1123, doi: 10.1103/PhysRev.98.1123

    work page doi:10.1103/physrev.98.1123 1955

  49. [49]

    S., Wong, G

    Ricarte, A., Prather, B. S., Wong, G. N., et al. 2020, MNRAS, 498, 5468, doi: 10.1093/mnras/staa2692 Röder, J., Cruz-Osorio, A., Fromm, C. M., et al. 2023, A&A, 671, A143, doi: 10.1051/0004-6361/202244866

    work page doi:10.1093/mnras/staa2692 2020

  50. [50]

    K., Chang, D., & Kocherlakota, P

    Salehi, K., Walia, R. K., Chang, D., & Kocherlakota, P. 2024, https://arxiv.org/abs/2411.15310

    work page arXiv 2024

  51. [51]

    2019, JCAP, 02, 042, doi: 10.1088/1475-7516/2019/02/042

    Simpson, A., & Visser, M. 2019, JCAP, 02, 042, doi: 10.1088/1475-7516/2019/02/042

    work page doi:10.1088/1475-7516/2019/02/042 2019

  52. [52]

    Tchekhovskoy, A., Narayan, R., & McKinney, J. C. 2011, Monthly Notices of the Royal Astronomical Society: Letters, 418, L79–L83, doi: 10.1111/j.1745-3933.2011.01147.x 21 The EHT Collaboration, Akiyama, K., Alberdi, A., et al. 2019a, ApJL, 875, L1, doi: 10.3847/2041-8213/ab0ec7 The EHT Collaboration, Akiyama, K., Alberdi, A., et al. 2019b, ApJL, 875, L6, d...

    work page doi:10.1111/j.1745-3933.2011.01147.x 2011

  53. [53]

    K., Mizuno, Y., & Rezzolla, L

    Uniyal, A., Dihingia, I. K., Mizuno, Y., & Rezzolla, L. 2026, Nature Astronomy, 10, 165, doi: 10.1038/s41550-025-02695-4

    work page doi:10.1038/s41550-025-02695-4 2026

  54. [54]

    2023, Classical and Quantum Gravity, 40, 165007, doi: 10.1088/1361-6382/acd97b

    Vagnozzi, S., Roy, R., Tsai, Y.-D., et al. 2023, Classical and Quantum Gravity, 40, 165007, doi: 10.1088/1361-6382/acd97b

    work page doi:10.1088/1361-6382/acd97b 2023

  55. [55]

    K., Kocherlakota, P., Chang, D

    Walia, R. K., Kocherlakota, P., Chang, D. O., & Salehi, K. 2025, PhRvD, 111, 104074, doi: 10.1103/PhysRevD.111.104074

    work page doi:10.1103/physrevd.111.104074 2025

  56. [56]

    PATOKA: Simulating Electromagnetic Observables of Black Hole Accretion,

    Wong, G. N., Prather, B. S., Dhruv, V., et al. 2022, arXiv, doi: 10.48550/arXiv.2202.11721

    work page doi:10.48550/arxiv.2202.11721 2022

  57. [57]

    2023, Physical Review D, 107, doi: 10.1103/physrevd.107.044016

    Zhou, T., & Modesto, L. 2023, Physical Review D, 107, doi: 10.1103/physrevd.107.044016

    work page doi:10.1103/physrevd.107.044016 2023