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REVIEW 4 major objections 5 minor 66 references

Dark Photon Polarimetry

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Using Event Horizon Telescope polarimetric images of M87* and Sgr A*, the paper derives 95% confidence-level exclusions on the photon–dark-photon kinetic mixing down to epsilon ~10^-11, in two barely explored dark-photon mass windows.

desk verdict A genuinely new polarimetric dark photon search, with an unquantified plasma-frame ambiguity that could shift the headline limits by orders of magnitude. read the letter →

arxiv 2501.13849 v2 pith:YGE6PM34 submitted 2025-01-23 hep-ph

Fiesta Ting Yan Leung , Tao Liu , Sida Lu , Jing Ren , Cheuk Kan Kelvin Yue , Kaifeng Zheng This is my paper · ORCID
classification hep-ph
keywords darkphotonkineticmixingpolarimetryFaradayrotationsuperradiancesupermassiveblackholeEventHorizonTelescopewavematter
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 proposes detecting dark photons through the polarization of light rather than its brightness. It argues that a dark-photon cloud grown by superradiance around a spinning supermassive black hole produces an oscillating magnetic field that imprints a characteristic Faraday-rotation pattern on the black hole's polarized image. Using existing Event Horizon Telescope images of M87* and Sgr A*, it derives 95% confidence-level exclusion limits on the photon–dark-photon kinetic mixing parameter in two mass windows that other non-gravitational searches have barely touched: $10^{-22}$ to $10^{-20}$ eV for M87* and $10^{-19}$ to $10^{-17}$ eV for Sgr A*. If correct, the method gives a new observational handle on ultralight wave dark matter and extends naturally to laboratory polarimetry and other astronomical polarization surveys.

What carries the argument

The load-bearing object is the effective current induced by photon–dark-photon kinetic mixing, $J'^\nu = -\varepsilon\mu^2 A'^\nu$, which turns the superradiant cloud profile—taken in its fastest-growing mode $(n,j,l,m)=(1,1,0,1)$—into an oscillating magnetic field $\vec{B}_{A'}$ near the disk. The signal that carries the argument is Faraday rotation: the rotation coefficient $\rho_V$ in the radiative-transfer equation is linear in the magnetic field, so $\vec{B}_{A'}$ modulates the polarization position angle at the cloud's eigenfrequency $\omega \simeq \mu(1-\alpha^2/2)$. The derivation uses a flat-spacetime Green's function as a leading-order approximation for the induced fields, public fitting functions for the transfer coefficients in the weak-field limit, a ray-tracing evolution of the Stokes parameters, and a radiatively inefficient accretion-flow electron-density profile calibrated to the EHT image intensities.

What would settle it

Compute the same Faraday rotation using the full Kerr Green's function from the rigorous eigenfunction treatment and compare the resulting limits; if the induced field changes by more than an order-one factor, the quoted exclusions are not stable. A direct check is also to search archival EHT visibility data for the predicted oscillatory polarization-angle pattern with period $2\pi/\omega$.

Watch

Extended reading notes

Core claim

The paper's central claim is that kinetic mixing between the photon and a massive dark photon ($A'$) effectively injects a current $J'^\nu = -\varepsilon\mu^2 A'^\nu$ into Maxwell's equations, so the fastest-growing superradiant cloud mode around a Kerr black hole sources an oscillating electromagnetic field near the accretion disk. The oscillating magnetic component $\vec{B}_{A'}$ rotates the polarization position angle of disk synchrotron radiation via Faraday rotation, and this rotation is tracked through a radiative-transfer calculation with the Stokes parameters. Applying that calculation to EHT data, the paper obtains 95% CL exclusion limits on the dimensionless mixing parameter $\varepsilon$ that scale as $\varepsilon \propto \mu^{7/2}$: for M87* in $10^{-22}$ to $10^{-20}$ eV with best reach $\sim 10^{-8}$ near $10^{-20}$ eV, and for Sgr A* in $10^{-19}$ to $10^{-17}$ eV with best reach $\sim 10^{-11}$ near $10^{-17}$ eV.

Load-bearing premise

The load-bearing premise is that the dark-photon-induced magnetic field near the black hole's disk can be computed with a flat-space Green's function, even though the curved spacetime there differs by a factor of order one; if the true field differs by that factor, the quoted limits on the mixing strength shift by the same factor.

Editorial extensions

If this is right

  • M87* polarimetric imaging excludes $\varepsilon$ down to $\sim 10^{-8}$ for dark-photon masses of $10^{-22}$ to $10^{-20}$ eV, and Sgr A* excludes down to $\sim 10^{-11}$ for $10^{-19}$ to $10^{-17}$ eV, covering windows that non-gravitational probes had left largely open.
  • Because the signal is an oscillation in time, longer or repeated polarimetric observing campaigns can convert the projected limits from total intensity and circular polarization into actual limits, and can push the reach to smaller $\varepsilon$ by phase-coherent stacking.
  • The same polarimetric mechanism applies to any magnetized astrophysical plasma, so the method is not tied to black holes; it can be deployed in laboratory polarization experiments and in astronomical or cosmological polarization surveys.
  • The $\varepsilon \propto \mu^{7/2}$ scaling means the strength of the limit is set by the line-of-sight electron density and the induced field amplitude, so higher-density targets or longer integration times directly improve the bound.

Reading between the lines

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

  • Beyond the paper: a full Kerr-metric Green's function would likely shift the quoted $\varepsilon$ bounds by an order-one factor; the authors flag the flat-spacetime choice as the leading approximation, so a Teukolsky-based calculation is the natural next check.
  • Beyond the paper: if the oscillatory polarization pattern predicted here is ever seen in several epochs, the period would measure the dark-photon mass and the phase would map the cloud's structure, effectively turning a limit into a tomographic probe of the gravitational atom.
  • Beyond the paper: the same Faraday-rotation template could be searched for in the visibility-domain data of the EHT, not just in reconstructed images, potentially improving sensitivity by avoiding imaging losses.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This Letter proposes a new polarimetric search for ultralight dark photons. For a superradiant DP cloud around a Kerr black hole, the kinetic-mixing effective current is argued to produce oscillating electromagnetic fields; the authors solve for these fields with a flat-spacetime Green's function (Eqs. 3-4), Lorentz-boost them into the plasma frame (Eq. 5), and inject an oscillating magnetic component into the public IPOLE/SYMPHONY radiative-transfer codes. Using EHT polarimetric images of M87* and Sgr A*, the paper derives 95% CL exclusion limits on the kinetic-mixing parameter epsilon in two mass windows, with best reaches of roughly 10^-8 at about 10^-20 eV and 10^-11 at about 10^-17 eV, and also gives projected limits from total intensity and circular polarization.

Significance. The observable is novel and targets DP mass ranges that are otherwise weakly constrained, so the proposed method would be a useful addition to the ultralight-DP toolbox if the signal calculation is reliable. The paper makes good use of public radiative-transfer codes, is transparent about the distinction between actual and projected limits for intensity and circular polarization, and clearly labels its Green's-function treatment as exploratory. However, several load-bearing approximations, especially the plasma-frame transformation of the screened electric field and the normalization of Eq. (4), are not yet established. The specific exclusion curves in Fig. 1 should therefore be viewed as provisional until the plasma-response calculation and the numerical coefficients are supplied.

major comments (4)
  1. [DARK PHOTON POLARIMETRY AND BLACK HOLES, Eq. (5)] The plasma-frame signal calculation appears internally inconsistent. The text argues that the DP-induced electric field is Debye-screened in the plasma and can be neglected, but then uses the unscreened vacuum E_A' from Eq. (4) in the Lorentz transformation to obtain B'_A' ≈ beta_p E_A'. If the plasma enforces E'_A' ≈ 0, the transverse Lorentz transformation instead gives B'_A' ≈ B_A' (up to O(beta_p^2) corrections). From Eq. (4), B_A'/E_A' ≈ (2/3) alpha^2, so the two prescriptions differ by a factor of order beta_p/alpha^2; for alpha = 0.1 and beta_p = 0.1 this is roughly 10-15, and for alpha = 0.03 it is about 100. Since the claimed limits scale inversely with the signal amplitude, the quoted reach and the quoted mass scaling would both change, with the scaling following from B_A' ∝ alpha^{11/2} rather than E_A' ∝ alpha^{7/2}. The appeal to Ref. [47] is not specific enough to resolve the issue. The paper should provide the plasma-response calculation or an explicit MHD-motivated expression for the plasma-frame B'_A'.
  2. [Eq. (4)] The numerical coefficients 0.2 and 0.3 in Eq. (4) are quoted without derivation, and no details are given for the evaluation of the Green's-function integrals that produce them. The text also states that the flat-spacetime Green's function is a leading-order approximation because the Kerr metric differs from flat spacetime by O(1) factors. Both issues directly affect the normalization of the signal and therefore the epsilon limits in Fig. 1. The authors should show how the coefficients are obtained, e.g., by providing the explicit integrals, a small-alpha expansion, or a numerical evaluation code, and should estimate the error from the flat-spacetime approximation rather than only asserting that it is O(1).
  3. [Abstract and Fig. 1, alpha < 0.3 restriction] The abstract states that the M87* analysis reaches a best limit near mu = 10^-20 eV. For M87* with M ≈ 6.5e9 M_sun, one has r_g = GM/c^2 ≈ 9.6e14 cm, so alpha = G M mu/(hbar c) ≈ 0.49 at mu = 10^-20 eV. This exceeds the stated restriction alpha < 0.3 imposed for the superradiance condition of the (1,1,0,1) mode. The M87* exclusion curve should therefore terminate near mu ≈ 6e-21 eV rather than extending to 10^-20 eV, which would move the claimed best reach. Please clarify the alpha definition used in the analysis or correct the stated mass window.
  4. [POLARIMETRIC CONSTRAINTS ON PHOTON-DARK PHOTON KINETIC MIXING, Eqs. (8)-(11)] The posterior in Eq. (8) and the resulting 95% CL limits depend directly on the assumed variances sigma_q, but the paper only states sigma_q ∼ O(10 degrees). For M87*, the text refers to bins that are 'approximately Gaussian' but gives no explicit sigma per bin; for Sgr A*, the noise floor phi^n_PA is marginalized with a uniform prior, but no value or derivation is given. Without the actual variance assignments and a discussion of correlations between bins or time samples, the limits in Fig. 1 are not reproducible. Please provide the specific sigma_q values and justify their independence.
minor comments (5)
  1. [Eq. (5)] The signs ± and ∓ in Eq. (5) are not defined relative to the boost direction; please specify the convention.
  2. [Eq. (8)] The exponent in Eq. (8) appears to contain an extra minus sign: 'exp[− −(O_q−O~_q)^2/(2σ_q^2)]' should be 'exp[−(O_q−O~_q)^2/(2σ_q^2)]'.
  3. [Fig. 1 caption] The caption contains garbled characters in the labels for the blue/red shaded regions and the hatched region; these labels should be rendered cleanly.
  4. [After Eq. (2)] The statement that 'r represents r−r+ in the Boyer-Lindquist coordinate system' should define r_+ explicitly and state the sign convention clearly.
  5. [DARK PHOTON POLARIMETRY AND BLACK HOLES] In the sentence describing the Stokes parameter V, 'contributes through f radiation' appears to be a typo; it should refer to synchrotron radiation or the relevant emission/absorption coefficient.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the DP-induced signal is computed from the kinetic-mixing Lagrangian and literature cloud profiles, and the EHT data only enter as compared observables, not as fitted inputs to the predicted signal.

full rationale

The derivation chain for the central claim is self-contained with respect to the data it constrains. The DP-induced electromagnetic fields in Eq. (4) are computed from the effective current J'^nu = -epsilon mu^2 A'^nu and the hydrogenic cloud profile in Eq. (2), both of which are stated inputs taken from the DP superradiance literature (Refs. [43,44]), not from the EHT polarimetric data. The posterior in Eq. (8) compares EHT PA observables to IPOLE predictions with the DP-induced oscillating component added linearly; epsilon is not fitted but excluded via a uniform prior and marginalization over the random phase phi_0. The only data-fitted quantities are the background electron density parameters n0_e and H in Eq. (7), chosen to match the total image intensity with the DP cloud turned off; these calibrate the astrophysical background and do not determine the epsilon-dependence of the DP signal amplitude. The paper's own scaling BA' proportional to epsilon alpha^{7/2} is derived from the input Lagrangian and cloud profile, not from the EHT measurements. Although the treatment of the DP electric field in the plasma frame is physically debatable (the paper uses the unscreened vacuum EA' to drive BA' in Eq. (5) while also arguing the electrostatic component is Debye-screened), that is a modeling/correctness concern rather than a circularity because the prediction still follows from the stated equations and inputs rather than from the target data. The self-citation to Ref. [32] concerns axion cosmic birefringence methodology and is not load-bearing for the DP polarimetric limits. No step in the paper reduces, by its own equations or by a self-citation chain, to the EHT measurements or to a previously fitted value.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The central claim rests on literature-provided superradiance cloud profiles, a flat-spacetime approximation for the induced fields, plasma screening assumptions, and four fitted or nuisance parameters (n0_e, H, phi0, sigma_q). No new particles or entities are introduced beyond the established dark photon model.

free parameters (4)
  • n0_e = 3.4e5 /cm3 for M87*, 3.0e7 /cm3 for Sgr A*
    Electron density normalization in the RIAF model; set so the IPOLE image intensity matches EHT observations with DP effects off.
  • H = 0.3
    Disk scale height in the RIAF model; chosen to match EHT image intensity.
  • phi0 = marginalized over [0, 2 pi]
    Random phase of the DP cloud; integrated out with a uniform prior in the posterior.
  • sigma_q = O(10 deg)
    Assumed Gaussian noise variance for the PA observables; estimated from the EHT data without detailed per-bin derivation.
assumptions (7)
  • domain assumption DP cloud profile for the (n,j,l,m)=(1,1,0,1) superradiance mode is given by Eq. (2) from [43,44].
    The fastest-growing mode is assumed to dominate; taken from prior literature without re-derivation.
  • domain assumption Flat-spacetime Green's function is a leading-order approximation for the EM fields in the Kerr metric for rg < r << rc.
    Authors state the Kerr metric differs from flat by O(1) in this region; the error is unquantified.
  • domain assumption The DP-induced electric field EA' is fully screened by the BH plasma and can be neglected.
    Based on Debye length estimates for M87* and Sgr A* plasma; if screening is incomplete, additional effects appear.
  • domain assumption Radiative transfer coefficients from SYMPHONY are valid for nu >> nu_B.
    The analysis restricts to this regime, with a hatched region where the assumption breaks down.
  • domain assumption The EHT PA observables are Gaussian-distributed with known variance sigma_q.
    By assumption in the posterior; bins are selected to be approximately Gaussian.
  • domain assumption Superradiance cloud saturates to mass M_c ~ 0.1 alpha M within cosmic age in the considered region.
    Used to set the turning point at low masses; no detailed growth-rate calculation is shown.
  • standard math Uniform prior distributions on log10 epsilon and phi0.
    Posterior construction assumes uniform priors for the mixing parameter and the cloud phase.

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Cite this review

Pith. "Pith review of Dark Photon Polarimetry." pith.science (2026). https://pith.science/paper/YGE6PM34

@misc{pith2026250113849,
  author       = {Pith},
  title        = {Pith review of: Dark Photon Polarimetry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YGE6PM34}},
  note         = {Machine review of arXiv:2501.13849}
}
abstract

We propose detecting dark photons (DP), a major candidate for wave dark matter, through polarimetry. The DP can modify Maxwell's equations due to its kinetic mixing with regular photons, inducing an oscillating component in the electromagnetic field. This may leave an imprint on polarimetric light signals, such as Faraday rotation, characterized by a distinctive wave pattern in spacetime. We then apply this method to investigate ultralight DPs produced through the superradiance of supermassive black holes for demonstration. Using the polarimetric measurements of radiation from the M87$^\ast$ and Sgr A$^\ast$ at the Event Horizon Telescope, we show that novel limits on the photon-DP mixing parameter can be set for the rarely-explored DP mass ranges: explicitly $10^{-22} - 10^{-20}\,$eV with the best reach of $\sim 10^{-8}$ achieved at $\sim 10^{-20}$eV, and $10^{-19} - 10^{-17}\,$eV with the best reach of $\sim 10^{-11}$ achieved at $\sim 10^{-17}$eV. Given the universality of its underlying physics, we expect DP polarimetry to be broadly applicable for DP detection in laboratory experiments and astronomical observations.

Figures

Figures reproduced from arXiv: 2501.13849 by the authors.

Figure 1
Figure 1. FIG. 1: 95% confidence level (CL) exclusion limits on the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

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Works this paper leans on

66 extracted references · 19 canonical work pages

  1. [47]

    Xin and E

    S. Xin and E. R. Most (2024), 2406.02992

    arXiv 2024

  2. [1]

    Zwicky, Helv

    F. Zwicky, Helv. Phys. Acta 6, 110 (1933)

    work page 1933

  3. [2]

    Aghanim et al

    N. Aghanim et al. (Planck), Astron. Astrophys. 641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], 1807.06209

    arXiv 2020

  4. [3]

    Markevitch, A

    M. Markevitch, A. H. Gonzalez, D. Clowe, A. Vikhlinin, L. David, W. Forman, C. Jones, S. Murray, and W. Tucker, Astrophys. J. 606, 819 (2004), astro- ph/0309303

    arXiv 2004

  5. [4]

    Aprile et al

    E. Aprile et al. (XENON), Phys. Rev. Lett. 131, 041003 (2023), 2303.14729

    arXiv 2023

  6. [5]

    Meng et al

    Y. Meng et al. (PandaX-4T), Phys. Rev. Lett. 127, 261802 (2021), 2107.13438

    arXiv 2021

  7. [6]

    Aalbers et al

    J. Aalbers et al. (LZ), Phys. Rev. Lett. 131, 041002 (2023), 2207.03764

    arXiv 2023

  8. [7]

    Hui, Ann

    L. Hui, Ann. Rev. Astron. Astrophys. 59, 247 (2021), 2101.11735

    arXiv 2021

Show all 66 references
  1. [8]

    Redondo and G

    J. Redondo and G. Raffelt, JCAP 08, 034 (2013), 1305.2920

    2013 arXiv

  2. [9]

    N. Bar, K. Blum, J. Eby, and R. Sato, Phys. Rev. D 99, 103020 (2019), 1903.03402

    2019 arXiv

  3. [10]

    Schive, T

    H.-Y. Schive, T. Chiueh, and T. Broadhurst, Nature Physics 10, 496–499 (2014), ISSN 1745-2481, URL http: //dx.doi.org/10.1038/nphys2996

    2014 doi

  4. [11]

    W. Hu, R. Barkana, and A. Gruzinov, Phys. Rev. Lett. 85, 1158 (2000), astro-ph/0003365

    2000 arXiv

  5. [12]

    Hlozek, D

    R. Hlozek, D. J. E. Marsh, and D. Grin, Mon. Not. Roy. Astron. Soc. 476, 3063 (2018), 1708.05681

    2018 arXiv

  6. [13]

    M. Nori, R. Murgia, V. Irˇ siˇ c, M. Baldi, and M. Viel, Mon. Not. Roy. Astron. Soc. 482, 3227 (2019), 1809.09619

    2019 arXiv

  7. [14]

    Braaten, A

    E. Braaten, A. Mohapatra, and H. Zhang, Phys. Rev. Lett. 117, 121801 (2016), 1512.00108

    2016 arXiv

  8. [15]

    Holdom, Phys

    B. Holdom, Phys. Lett. B 166, 196 (1986)

    1986

  9. [16]

    B¨ ahre et al., JINST8, T09001 (2013), 1302.5647

    R. B¨ ahre et al., JINST8, T09001 (2013), 1302.5647

    2013 arXiv

  10. [17]

    Agnes et al

    P. Agnes et al. (DarkSide), Phys. Rev. Lett. 130, 101002 (2023), 2207.11968

    2023

  11. [18]

    Aprile et al

    E. Aprile et al. (XENON), Phys. Rev. D 106, 022001 (2022), [Erratum: Phys.Rev.D 110, 109903 (2024)], 2112.12116

    2022 arXiv

  12. [19]

    Cervantes et al., Phys

    R. Cervantes et al., Phys. Rev. D 106, 102002 (2022), 2204.09475

    2022 arXiv

  13. [20]

    H. An, S. Ge, W.-Q. Guo, X. Huang, J. Liu, and Z. Lu, Phys. Rev. Lett. 130, 181001 (2023), 2207.05767

    2023 arXiv

  14. [21]

    Caputo, H

    A. Caputo, H. Liu, S. Mishra-Sharma, and J. T. Ruder- man, Phys. Rev. Lett. 125, 221303 (2020), 2002.05165. 6

    2020 arXiv

  15. [22]

    Wadekar and G

    D. Wadekar and G. R. Farrar, Phys. Rev. D 103, 123028 (2021), 1903.12190

    2021 arXiv

  16. [23]

    S. Yan, L. Li, and J. Fan, JHEP 06, 028 (2024), 2312.06746

    2024 arXiv

  17. [24]

    Caputo, A

    A. Caputo, A. J. Millar, C. A. J. O’Hare, and E. Vitagliano, Phys. Rev. D 104, 095029 (2021), 2105.04565

    2021 arXiv

  18. [25]

    D. J. E. Marsh, Phys. Rept. 643, 1 (2016), 1510.07633

    2016 arXiv

  19. [26]

    L. Hui, J. P. Ostriker, S. Tremaine, and E. Witten, Phys- ical Review D 95, 043541 (2017)

    2017

  20. [27]

    S. M. Carroll, G. B. Field, and R. Jackiw, Phys. Rev. D 41, 1231 (1990)

    1990

  21. [28]

    S. M. Carroll and G. B. Field, Phys. Rev. D 43, 3789 (1991)

    1991

  22. [29]

    Lue, L.-M

    A. Lue, L.-M. Wang, and M. Kamionkowski, Phys. Rev. Lett. 83, 1506 (1999), astro-ph/9812088

    1999 arXiv

  23. [30]

    B. Feng, M. Li, J.-Q. Xia, X. Chen, and X. Zhang, Phys. Rev. Lett. 96, 221302 (2006), astro-ph/0601095

    2006 arXiv

  24. [31]

    M. A. Fedderke, P. W. Graham, and S. Rajendran, Phys. Rev. D 100, 015040 (2019), 1903.02666

    2019 arXiv

  25. [32]

    T. Liu, X. Lou, and J. Ren, Phys. Rev. Lett. 130, 121401 (2023), 2111.10615

    2023 arXiv

  26. [33]

    Xue et al

    X. Xue et al. (2024), 2412.02229

    2024

  27. [34]

    Y. Chen, Y. Liu, R.-S. Lu, Y. Mizuno, J. Shu, X. Xue, Q. Yuan, and Y. Zhao, Nature Astronomy 6, 592–598 (2022), ISSN 2397-3366, URL http://dx.doi.org/10. 1038/s41550-022-01620-3

    2022

  28. [35]

    Yuan, Z.-Q

    G.-W. Yuan, Z.-Q. Xia, C. Tang, Y. Zhao, Y.-F. Cai, Y. Chen, J. Shu, and Q. Yuan, Journal of Cosmology and Astroparticle Physics 2021, 018 (2021)

    2021

  29. [36]

    Y. Chen, C. Li, Y. Mizuno, J. Shu, X. Xue, Q. Yuan, Y. Zhao, and Z. Zhou, Journal of Cosmology and As- troparticle Physics 2022, 073 (2022)

    2022

  30. [37]

    Gan, L.-T

    X. Gan, L.-T. Wang, and H. Xiao, Phys. Rev. D 110, 063039 (2024), 2311.02149

    2024 arXiv

  31. [38]

    Castillo, J

    A. Castillo, J. Martin-Camalich, J. Terol-Calvo, D. Blas, A. Caputo, R. T. G. Santos, L. Sberna, M. Peel, and J. A. Rubi˜ no Mart ´ ın, JCAP06, 014 (2022), 2201.03422

    2022 arXiv

  32. [39]

    Adachi et al

    S. Adachi et al. (POLARBEAR) (2024), 2403.02096

    2024 arXiv

  33. [40]

    S. L. Detweiler, Phys. Rev. D 22, 2323 (1980)

    1980

  34. [41]

    Akiyama et al

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

    2019 arXiv

  35. [42]

    Akiyama et al

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

    2022 arXiv

  36. [43]

    Baryakhtar, R

    M. Baryakhtar, R. Lasenby, and M. Teo, Physical Review D 96, 035019 (2017)

    2017

  37. [44]

    Siemonsen, C

    N. Siemonsen, C. Mondino, D. Egana-Ugrinovic, J. Huang, M. Baryakhtar, and W. E. East, Phys. Rev. D 107, 075025 (2023), 2212.09772

    2023 arXiv

  38. [45]

    S. A. Teukolsky, Phys. Rev. Lett. 29, 1114 (1972)

    1972

  39. [46]

    Chatterjee et al., Galaxies 11, 38 (2023), 2212.01804

    K. Chatterjee et al., Galaxies 11, 38 (2023), 2212.01804

    2023 arXiv

  40. [48]

    P. K. Leung, C. F. Gammie, and S. C. Noble, Astrophys. J. 737, 21 (2011)

    2011

  41. [49]

    Marszewski, B

    A. Marszewski, B. S. Prather, A. V. Joshi, A. Pandya, and C. F. Gammie, The Astrophysical Journal 921, 17 (2021)

    2021

  42. [50]

    Dexter, Mon

    J. Dexter, Mon. Not. Roy. Astron. Soc. 462, 115 (2016), 1602.03184

    2016 arXiv

  43. [51]

    Pandya, Z

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

    2016 arXiv

  44. [52]

    Moscibrodzka and C

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

    2018 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]

    https://github.com/AFD-Illinois/ipole

  47. [55]

    Pu and A

    H.-Y. Pu and A. E. Broderick, The Astrophysical Journal 863, 148 (2018)

    2018

  48. [56]

    Akiyama et al

    K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 910, L13 (2021), 2105.01173

    2021 arXiv

  49. [57]

    Akiyama et al

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

    2024

  50. [58]

    Akiyama et al

    K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett. 910, L12 (2021), 2105.01169

    2021 arXiv

  51. [59]

    M. D. Johnson, V. L. Fish, S. S. Doeleman, D. P. Marrone, R. L. Plambeck, J. F. Wardle, K. Akiyama, K. Asada, C. Beaudoin, L. Blackburn, et al., Science350, 1242 (2015)

    2015

  52. [60]

    M. A. Fedderke, P. W. Graham, D. F. Jackson Kim- ball, and S. Kalia, Phys. Rev. D 104, 095032 (2021), 2108.08852

    2021 arXiv

  53. [61]

    S. R. Dolan, Phys. Rev. D 76, 084001 (2007), 0705.2880

    2007 arXiv

  54. [62]

    Akiyama et al

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

    2019 arXiv

  55. [63]

    Akiyama, A

    K. Akiyama, A. Alberdi, W. Alef, J. C. Algaba, R. Anan- tua, K. Asada, R. Azulay, U. Bach, A.-K. Baczko, D. Ball, et al., The Astrophysical Journal Letters 957, L20 (2023)

    2023

  56. [64]

    D. B. Melrose and R. C. McPhedran, Electromagnetic Processes in Dispersive Media (1991)

    1991

  57. [65]

    J. F. Acevedo, A. Bhoonah, and K. Cheng (2025), 2501.01489

    2025 arXiv

  58. [66]

    Center for High Throughput Computing, Center for high throughput computing (2006), URL https://chtc.cs.wisc.edu/

    2006

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