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Gravitational shadow and emission spectrum of thin accretion disks in a plasma medium

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A thin thermal disk around a Schwarzschild black hole, seen through transparent plasma, produces frequency-dependent shadow images whose total-flux peak is set mainly by the observer's inclination angle.

desk verdict Useful new calculation of plasma-transported disk spectra, but the ngEHT diagnostic rests on an unexamined transparency assumption. read the letter →

arxiv 2505.07993 v2 pith:AONULQNC submitted 2025-05-12 gr-qc

Kirill Kobialko , Dmitri Gal'tsov , Alexey Molchanov This is my paper · ORCID
classification gr-qc MSC 83C5783C1085A25 PACS 04.70.Bw95.30.Jx98.62.Mw
keywords blackholeshadowthinaccretiondiskcoldplasmagravitationallensinginradiativetransferfrequency-dependentimagesmulti-frequencyimaging
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

The paper builds a unified model of black-hole shadow and disk emission in a plasma: a thin thermal accretion disk around a Schwarzschild black hole, immersed in cold, pressureless, transparent plasma that co-rotates with the disk. It derives a modified blackbody intensity formula for light that has travelled through the plasma, and shows that the observed image depends strongly on frequency, so the same disk looks different at different wavelengths. If the model holds, multi-frequency observations of black holes can read the inclination angle of the disk off the frequency at which the total received flux peaks, and can spot secondary and relativistic images that a single-frequency observation would miss. This is the kind of signal the next-generation horizon-resolving observations at 86, 230, and 345 GHz are being built to see.

What carries the argument

The carrying mechanism is the invariant distribution function of the radiation, $T=\omega^{-3}v_g^{-2}I(\omega)$, which the transport equation $dT/d\lambda=-\eta T+J$ keeps constant along a ray whenever the plasma neither absorbs nor emits ($\eta=0$, $J=0$). Inserting the equilibrium distribution of blackbody radiation in a plasma and using the identity $v_{ph}v_g=1$ that follows from the cold-plasma dispersion relation $k^2=\omega^2-\omega_p^2$, the plasma-frequency factors cancel and the transport law becomes the observed-intensity formula (17). The frequency-dependent ray paths themselves are governed by the effective potential $V=\beta^{-1}(\alpha^{-1}-\gamma^{-1}\rho'^2-\omega_p^2/\omega_\infty^2)$: it is the $\omega_o$-dependence entering through this potential that makes the shadow, the secondary images, and the flux spectra vary with wavelength. Around that core, the paper adds two analytic tools: coordinate rotations that reduce every photon orbit to an equatorial trajectory, and the equilibrium radius $r_e=2M(\sigma+1)/\sigma$ at which gravitational attraction and plasma repulsion balance, erasing the shadow.

What would settle it

Point one of the currently imaged supermassive black holes at the three planned radio bands (86, 230, and 345 GHz). The model predicts a specific frequency scaling of the shadow radius (for the $\sigma=2$ plasma profile, $R^2(\omega_o)=M^2(27-\omega_o^{-2})$), no shadow at all below a calculable equilibrium frequency, and a total-flux peak whose frequency tracks the viewing angle rather than the accretion rate; observing a shadow below the equilibrium frequency, or a flux peak that moves with the accretion rate, would break the claim. The cleanest numerical check is to rerun the same ray tracing with absorption and intrinsic emission switched on and see whether the peak-frequency diagnostic survives.

Watch

Extended reading notes

Core claim

The paper's central claim is that the specific intensity received from a blackbody thin accretion disk through transparent cold plasma is $$I_o(\omega_o)=\frac{\$omega_o^{3}$}{4\$pi^{3}$}\,\frac{1-\bar\$omega_p^{2}$/\$omega_o^{2}$}{$e^{{(1+z)\omega_o/T_D}}$-1},$$ with $\bar\omega_p$ the plasma frequency at the observer, $1+z$ the redshift accumulated along the ray, and $T_D$ the local disk temperature. The plasma density at the emission point cancels out of this formula, because the product of phase and group velocity in a cold plasma equals one ($v_{ph}v_g=1$), yet the observed spectrum is not a rescaled blackbody: rays of different frequencies move in different effective potentials, so the redshift, the source temperature, and even whether a ray hits the disk at all depend on $\omega_o$. Ray tracing in Schwarzschild spacetime then shows the shadow radius shrinking as frequency rises, the shadow vanishing completely below an equilibrium frequency at which the plasma's repulsive force balances gravity, and secondary images of the near disk edge appearing near that frequency; the computed flux at each frequency, normalized to the vacuum value, develops relative maxima that can exceed one, and the position of the dominant maximum is controlled mainly by the observer's inclination angle.

Load-bearing premise

Everything rests on assuming the plasma around the disk is perfectly transparent, absorbing no light and emitting none of its own, so that its only effect on the radiation is to bend rays and shift frequencies; once realistic absorption in the 86\u2013345 GHz band is switched on, the predicted images, secondary-image visibility, and flux-peak frequencies all change.

Editorial extensions

If this is right

  • Below an equilibrium frequency $\omega_e$, the gravitational shadow disappears entirely: plasma repulsion reflects every geodesic before it reaches the horizon, so a low-frequency observation shows disk light but no shadow.
  • Secondary images of the near edge of the disk become observable close to $\omega_e$, especially for steep plasma profiles ($\sigma=4,6$), whereas at higher frequencies the images approach their vacuum shapes.
  • The frequency position of the total-flux maximum is set mainly by the observer's inclination angle, giving a geometric diagnostic that does not depend on the poorly constrained mass accretion rate, which instead controls the peak's amplitude.
  • Normalized total intensity is independent of the accretion rate in vacuum but not in plasma, because dispersion makes the redshift and the source temperature frequency-dependent; the plasma spreads the same total energy over a larger image area, suppressing the peak intensity.
  • Because the shadow is frequency-dependent in plasma but frequency-independent in vacuum, multi-frequency imaging in the 86\u2013345 GHz band can separate plasma effects from spacetime-geometry effects on the shadow boundary.

Reading between the lines

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

  • Editorial inference: the same transport machinery should transfer to a rotating black hole, where the flux-maximum frequency would plausibly encode the spin as well as the inclination angle, giving multi-frequency campaigns a second clean observable.
  • Editorial inference: the factor $(1-\bar\omega_p^2/\omega_o^2)$ inside the intensity formula makes the low-frequency turnover of the observed spectrum a direct probe of the plasma frequency at the observer, so it could be used to estimate the line-of-sight electron density toward the source.
  • Editorial inference: the absorption-free predictions should be most trustworthy on the optically thin side of the band; near the frequencies where the source turns optically thick, rays linger in dense plasma, so the secondary-image and peak-frequency diagnostics would need to be recomputed with absorption included.
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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

3 major / 5 minor

Summary. This paper develops a ray-tracing framework for thermal radiation from a Novikov-Thorne thin accretion disk in Schwarzschild spacetime, surrounded by a cold, non-magnetized, pressureless, transparent plasma in stationary rotation. The central formal result is Eq. (17), an observed specific intensity that contains a plasma factor (1 - \bar{\omega}_p^2/\omega_o^2) and a redshifted Planck factor. The authors derive analytical shadow radii for power-law plasma profiles, compute frequency-resolved images, total integrated intensities, and total-flux spectra for different inclinations, accretion rates, and disk sizes, and propose that the frequency of the total-flux maximum can serve as an inclination diagnostic for ngEHT observations.

Significance. If the results hold, the paper provides a useful semi-analytical framework that connects plasma-modified ray propagation with thermal disk emission, and the proposed observables (secondary-image visibility near the plasma equilibrium frequency and flux-maximum frequency shifts) are interesting. The derivation of Eq. (17) from the invariant transport equation is internally coherent under the stated assumptions, and the sigma=2 shadow formula (84) is an elegant closed-form result. The numerical study covers a wide parameter space and the paper ships clearly presented figures. The main caveats are the assumed plasma transparency and the errors in two analytical displays; these affect the astrophysical interpretation and must be corrected before the ngEHT claims are accepted.

major comments (3)
  1. [Section V, Eq. (77)] The shadow radius is printed as R^2 = r^3(r^sigma - 2M(sigma+1)) / ((sigma-2)(r-2M)^2), but the correct algebra from Eq. (62) gives R^2 = r^3(sigma r - 2M(sigma+1)) / ((sigma-2)(r-2M)^2). The typo is not cosmetic: for sigma=0 the printed numerator is dimensionally inconsistent (r^sigma=1), and the allowed intervals (78)-(81) as well as Figure 3 are wrong for sigma values other than 1 and 2. Please correct the formula and recompute the affected analytical panels.
  2. [Section III, Eq. (55)] The displayed chain of inequalities is algebraically false. For alpha=gamma=1, rho=-5, and Omega_p=0.2, the second inequality in (55) states -5.76 <= -6.51, which is false. The intended conclusion (omega_p^2/omega^2 <= 1) is nevertheless correct and follows directly from (1-alpha gamma^{-1} rho^2)(1-gamma Omega_p^2/alpha) <= (1-Omega_p rho)^2, so the proof should be rewritten; as printed, the claim that the condition omega >= omega_p is automatically satisfied is not established.
  3. [Section II (after Eq. (16)) and Section V (Figs. 15-17)] The model sets the absorption and emission coefficients to zero (eta=0, J=0), yet the Introduction targets the 86-345 GHz band where Sgr A* and M87* are said to transit from optically thin to optically thick. Absorption would introduce a factor exp(-tau) into the secondary-image contributions that produce the F/F_Sch>1 peaks, and intrinsic plasma emission J would tend to fill the shadow. No estimate of the optical depth is given anywhere in the paper. The formal derivation is internally consistent, but the ngEHT diagnostic claim is not yet established for the targeted sources; please either include optical-depth estimates that justify transparency in the relevant regions or explicitly restrict the conclusions to optically thin configurations.
minor comments (5)
  1. [Section V, after Eq. (75)] The text reads 'at frequency omega'_o = h omega'_o'; this is a typo and should be 'omega'_o = h omega_o'.
  2. [Section V, after Eq. (75)] The sentence 'T'_D = T_D' conflicts with the rescaling F'_D = h^4 F_D; from Eq. (67) one obtains T'_D = h T_D. The ratios in Eq. (76) are consistent with the latter statement, so the sentence should be corrected.
  3. [Section IV, Eq. (69)] T_D is an intrinsic disk temperature, so writing T_D(omega_o) is misleading; the observed-frequency dependence enters through the redshift and through ray tracing, not through T_D itself. Please clarify the notation.
  4. [Section V] No convergence study is reported for the RK4 step size or for the angular resolution of the stereographic grid. Since the positions of flux maxima are quantitative claims, a resolution check should be added.
  5. [Section II, Eq. (10)] Since Eq. (17) inherits the validity of the blackbody-in-plasma distribution, a short derivation of Eq. (10), or at least a statement of its regime of validity, would make the paper more self-contained.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Eq. (17) is derived in-text from the transport equation and an externally cited Planck-in-plasma distribution, and the flux-peak diagnostic is an independent ray-tracing result.

full rationale

The paper's central observed-intensity formula (Eq. 17) is not an input in disguise: it follows from the invariant transport equation dT/dlambda = -eta*T + J (Eq. 12) with eta = J = 0, from the cited blackbody distribution (Eq. 10, Refs. [43,44]), and from the stated relation between T and specific intensity (Eq. 14). The algebra is shown in Eqs. (13)-(17), and the model assumptions (transparent, co-rotating plasma; negligible absorption and self-emission) are declared physical restrictions rather than fitted parameters. The shadow boundary (Eqs. 59 and 62) is derived from the Hamiltonian effective potential in this paper; the authors' own Ref. [54] is invoked only as a consistency check for the sigma = 0 vacuum limit, not to justify the central results. The total-flux peak-frequency diagnostic (Figs. 15-17) emerges from numerical ray tracing with chosen parameters (M = 1, Mdot = 0.1, etc.) and is normalized against an independently computed vacuum case; no parameter is fitted to the predicted quantity. The transparent-plasma assumption (eta = 0, J = 0) is the main physical weakness, but it is a modeling limitation and correctness risk, not a circular reduction of Eq. (17) to its inputs.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The paper's results rest on standard Hamiltonian plasma optics, the Novikov-Thorne disk model, and four explicitly stated physical idealizations (transparent plasma, co-rotation at the disk, static plasma at the observer, Schwarzschild spacetime). The blackbody-in-plasma distribution is imported from Refs. [43,44]. All model parameters (sigma, Mdot, inclination, disk size, observer distance, plasma amplitude) are chosen by hand for a parameter survey; none is fitted to observational data.

free parameters (6)
  • plasma density power sigma = sigma = 0, 2, 3, 4, 6 (illustrative)
    Sets the radial profile omega_p^2 = M^sigma/r^sigma in Eq. (74); not fitted to data, chosen to span shallow and steep profiles.
  • mass accretion rate Mdot = range 100 to 10^-8 (chosen, not fitted)
    Sets the disk temperature through the Novikov-Thorne flux Eq. (66); vacuum-normalized images are Mdot-independent in vacuum but Mdot-dependent in plasma.
  • observer inclination angle theta_bar = 0, 45, 84, 90 degrees
    Viewing angle of the observer; the paper's diagnostic is that the flux-peak frequency depends mainly on this parameter.
  • disk outer radius r_out = 10M, 15M, 20M, 25M, 30M
    Truncation radius of the thin disk in the ray tracer; affects the strength of plasma-induced flux peaks.
  • observer distance r_bar = 40M in all figures
    Static observer position; not the asymptotic infinity used in Eq. (62), so finite-distance effects are present.
  • plasma amplitude h = renormalized away via Eq. (75)
    A constant factor multiplying omega_p^2 can be absorbed by rescaling frequency and mass accretion rate, so it is not an independent parameter in the presented results.
assumptions (6)
  • domain assumption Hamiltonian for cold plasma in geometrical optics: H = 1/2(g^{alpha beta} pi_alpha pi_beta + omega_p^2)
    Standard plasma lensing model imported from Refs. [11,46]; it defines the effective photon trajectories and the potential V in Eq. (43).
  • domain assumption Blackbody distribution in a plasma is given by Eq. (10), yielding an invariant T_planck independent of omega_p (Eq. 15)
    Taken from Refs. [43,44]; Eq. (17) for observed intensity inherits this. It is not re-derived in the paper.
  • domain assumption Plasma is transparent: eta = 0 and J = 0
    Stated in Section II after Eq. (16); removes absorption and intrinsic emission. This is the main idealization relative to real ngEHT sources.
  • domain assumption Plasma co-rotates with the disk near the disk and is static at the observer
    Assumed in Section IV before Eq. (65); fixes the redshift factor (1+z) and the observed frequency mapping.
  • domain assumption Spacetime is static and spherically symmetric, Schwarzschild for all numerics
    Metric (19) and (73); makes trajectories planar and shadows circular. Spinning black holes are excluded.
  • domain assumption The plasma 4-velocity does not enter the Hamiltonian and affects only the redshift
    Taken from Refs. [18,48]; used in Eq. (52) and the proof of omega >= omega_p in Eq. (55).

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Cite this review

Pith. "Pith review of Gravitational shadow and emission spectrum of thin accretion disks in a plasma medium." pith.science (2026). https://pith.science/paper/AONULQNC

@misc{pith2026250507993,
  author       = {Pith},
  title        = {Pith review of: Gravitational shadow and emission spectrum of thin accretion disks in a plasma medium},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AONULQNC}},
  note         = {Machine review of arXiv:2505.07993}
}
read the original abstract

In anticipation of future multi-frequency observations of black hole with the Next Generation Event Horizon Telescope (ngEHT), we construct spectral images of a thin accretion disk around a spherically symmetric black hole immersed in cold, non-magnetized, pressureless plasma. The radiation from the disk is assumed to be thermal, and the surrounding plasma is entrained by its rotation. We use the general relativistic transport equation for the radiation in the plasma, accounting for both dispersion and plasma motion but neglecting absorption. Shadow images and intensity maps are computed across the full spectrum for an inverse power-law plasma density profile. The results show a strong dependence of the observed images on the radiation frequency, which looks promising for the possibility of extracting new information in future observations of the ngEHT.

Figures

Figures reproduced from arXiv: 2505.07993 by the authors.

Figure 1
Figure 1. FIG. 1: Strong gravitational lensing in a plasma medium. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Rotation of the coordinate system and corresponding transformations of the tetrad. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Gravitational shadow radius [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figures from the paper (15 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Observed specific intensity [PITH_FULL_IMAGE:figures/full_fig_p019_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Observed specific intensity [PITH_FULL_IMAGE:figures/full_fig_p020_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Observed specific intensity [PITH_FULL_IMAGE:figures/full_fig_p021_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Observed specific intensity [PITH_FULL_IMAGE:figures/full_fig_p022_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Observed specific intensity [PITH_FULL_IMAGE:figures/full_fig_p023_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Observed specific intensity [PITH_FULL_IMAGE:figures/full_fig_p024_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: Observed specific intensity [PITH_FULL_IMAGE:figures/full_fig_p025_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11: Observed intensity [PITH_FULL_IMAGE:figures/full_fig_p025_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12: Observed intensity [PITH_FULL_IMAGE:figures/full_fig_p026_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13: Observed intensity [PITH_FULL_IMAGE:figures/full_fig_p027_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14: Observed intensity [PITH_FULL_IMAGE:figures/full_fig_p028_14.png]
Figure 17
Figure 17. Figure 17: For small accretion disks, since most of the disk is immersed in high plasma densities, [PITH_FULL_IMAGE:figures/full_fig_p028_17.png]
Figure 15
Figure 15. Figure 15: FIG. 15: Observed radiation flux [PITH_FULL_IMAGE:figures/full_fig_p029_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16: Observed radiation flux [PITH_FULL_IMAGE:figures/full_fig_p030_16.png]
Figure 17
Figure 17. Figure 17: FIG. 17: Observed radiation flux [PITH_FULL_IMAGE:figures/full_fig_p031_17.png]

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Reference graph

Works this paper leans on

62 extracted references · 21 canonical work pages · cited by 3 Pith papers

  1. [1]

    Frequency independence (being an integral characteristic)

    work page

  2. [2]

    11 displays this normalized total intensity distribution for the plasma-free case

    Accretion-rate independence (in vacuum conditions) Fig. 11 displays this normalized total intensity distribution for the plasma-free case. Through 21 FIG. 7: Observed specific intensity I(ωo)/ISch max, % for plasma profile ω2 p =M 4r−4 at different frequenciesωo, mass accretion rate ˙M = 0.1, ADM mass M = 1 and inclination angle ¯θ = 84◦. careful normaliz...

    work page

  3. [3]

    Moscibrodzka and C

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

    arXiv 2018

  4. [4]

    Spectral line blurring occurs as different disk regions contribute to the same observed intensity through plasma dispersion effects

    work page

  5. [5]

    The table quantifies this suppression as percentage decreases rela- 22 FIG

    Systematic reduction of peak intensity emerges even without absorption processes, as evidenced in Table I. The table quantifies this suppression as percentage decreases rela- 22 FIG. 8: Observed specific intensity I(ωo)/ISch max, % for plasma profile ω2 p =M 4r−4 at different frequenciesωo, mass accretion rate ˙M = 0.1, ADM mass M = 1 and inclination angl...

    work page

  6. [6]

    Akiyama et al

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

    arXiv 2019

  7. [7]

    Akiyama et al

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

    2022

  8. [8]

    R¨ oder et al

    J. R¨ oder et al. (EHT), Astron. Astrophys. 695, A233 (2025), 2501.05518. 32

    arXiv 2025

Show all 62 references
  1. [9]

    Chael, S

    A. Chael, S. Issaoun, D. W. Pesce, M. D. Johnson, A. Ricarte, C. M. Fromm, and Y. Mizuno, Astrophys. J. 945, 40 (2023), 2210.12226

    2023 arXiv

  2. [10]

    Ricarte, M

    A. Ricarte, M. D. Johnson, Y. Y. Kovalev, D. C. M. Palumbo, and R. Emami, Galaxies 11, 5 (2023), 2211.03907

    2023 arXiv

  3. [11]

    M. D. Johnson et al., Galaxies 11, 61 (2023), 2304.11188

    2023 arXiv

  4. [12]

    Desire, A

    T. Desire, A. C´ ardenas-Avenda˜ no, and A. Chael, Astrophys. J.980, 262 (2025), 2411.17884

    2025 arXiv

  5. [13]

    Briozzo, E

    G. Briozzo, E. Gallo, and T. M¨ adler, Phys. Rev. D 107, 124004 (2023), 2211.05620

    2023 arXiv

  6. [14]

    Perlick, O

    V. Perlick, O. Y. Tsupko, and G. S. Bisnovatyi-Kogan, Phys. Rev. D 92, 104031 (2015), 1507.04217

    2015 arXiv

  7. [15]

    Perlick and O

    V. Perlick and O. Y. Tsupko, Phys. Rev. D 95, 104003 (2017), 1702.08768

    2017 arXiv

  8. [16]

    Perlick and O

    V. Perlick and O. Y. Tsupko, Phys. Rev. D 109, 064063 (2024), 2311.10615

    2024 arXiv

  9. [17]

    Bezdekova, V

    B. Bezdekova, V. Perlick, and J. Bicak, J. Math. Phys. 63, 092501 (2022), 2204.05593

    2022 arXiv

  10. [18]

    Bezdˇ ekov´ a, O

    B. Bezdˇ ekov´ a, O. Y. Tsupko, and C. Pfeifer, Phys. Rev. D109, 124024 (2024), 2403.16842

    2024 arXiv

  11. [19]

    Bogush, K

    I. Bogush, K. Kobialko, and D. Gal’tsov, Phys. Rev. D 108, 044070 (2023), 2306.12888

    2023 arXiv

  12. [20]

    Kobialko, I

    K. Kobialko, I. Bogush, and D. Gal’tsov, Phys. Rev. D 106, 084032 (2022), 2208.02690

    2022 arXiv

  13. [21]

    Song and C

    Y. Song and C. Zhang, Eur. Phys. J. C 83, 50 (2023), 2208.03661

    2023 arXiv

  14. [22]

    Kobialko, I

    K. Kobialko, I. Bogush, and D. Gal’tsov, Phys. Rev. D 109, 024060 (2024), 2312.07498

    2024 arXiv

  15. [23]

    J. I. McDonald and S. J. Witte, Phys. Rev. D 108, 103021 (2023), 2309.08655

    2023 arXiv

  16. [24]

    S´ aren´ y and V

    M. S´ aren´ y and V. Balek, Gen. Rel. Grav.51, 141 (2019), 1907.08525

    2019 arXiv

  17. [25]

    Balek, B

    V. Balek, B. Bezdˇ ekov´ a, and J. Biˇ c´ ak, J. Math. Phys.65, 082501 (2024), 2312.04451

    2024 arXiv

  18. [26]

    Rogers, Mon

    A. Rogers, Mon. Not. Roy. Astron. Soc. 465, 2151 (2017), 1611.01269

    2017 arXiv

  19. [27]

    Rogers, Universe 3, 3 (2017), 1701.05693

    A. Rogers, Universe 3, 3 (2017), 1701.05693

    2017 arXiv

  20. [28]

    Abdujabbarov, B

    A. Abdujabbarov, B. Toshmatov, Z. Stuchl´ ık, and B. Ahmedov, Int. J. Mod. Phys. D26, 1750051 (2016), 1512.05206

    2016 arXiv

  21. [29]

    Rogers, Class

    A. Rogers, Class. Quant. Grav. 41, 175007 (2024), 2407.20567

    2024 arXiv

  22. [30]

    Rogers, Mon

    A. Rogers, Mon. Not. Roy. Astron. Soc. 451, 17 (2015), 1505.06790

    2015 arXiv

  23. [31]

    Crisnejo, E

    G. Crisnejo, E. Gallo, E. F. Boero, and O. M. Moreschi, Phys. Rev. D 107, 084041 (2023), 2212.14297

    2023 arXiv

  24. [32]

    Atamurotov and B

    F. Atamurotov and B. Ahmedov, Phys. Rev. D 92, 084005 (2015), 1507.08131

    2015 arXiv

  25. [33]

    G. Z. Babar, A. Z. Babar, and F. Atamurotov, Eur. Phys. J. C 80, 761 (2020), [Erratum: Eur.Phys.J.C 82, 403 (2022)], 2008.05845

    2020 arXiv

  26. [34]

    Abdujabbarov, B

    A. Abdujabbarov, B. Juraev, B. Ahmedov, and Z. Stuchl´ ık, Astrophys. Space Sci. 361, 226 (2016)

    2016

  27. [35]

    Dastan, R

    S. Dastan, R. Saffari, and S. Soroushfar (2016), 1610.09477

    2016 arXiv

  28. [36]

    G. S. Bisnovatyi-Kogan and O. Y. Tsupko, Universe 3, 57 (2017), 1905.06615

    2017 arXiv

  29. [37]

    Huang, Y.-P

    Y. Huang, Y.-P. Dong, and D.-J. Liu, Int. J. Mod. Phys. D 27, 1850114 (2018), 1807.06268

    2018 arXiv

  30. [38]

    Gyulchev, P

    G. Gyulchev, P. Nedkova, T. Vetsov, and S. Yazadjiev, Phys. Rev. D 100, 024055 (2019), 1905.05273

    2019 arXiv

  31. [39]

    Chowdhuri and A

    A. Chowdhuri and A. Bhattacharyya, Phys. Rev. D 104, 064039 (2021), 2012.12914

    2021 arXiv

  32. [40]

    Zhang, H

    Z. Zhang, H. Yan, M. Guo, and B. Chen, Phys. Rev. D 107, 024027 (2023), 2206.04430

    2023 arXiv

  33. [41]

    Bogush, D

    I. Bogush, D. Gal’tsov, G. Gyulchev, K. Kobialko, P. Nedkova, and T. Vetsov, Phys. Rev. D 106, 024034 (2022), 2205.01919

    2022 arXiv

  34. [42]

    Gyulchev, P

    G. Gyulchev, P. Nedkova, T. Vetsov, and S. Yazadjiev, Eur. Phys. J. C81, 885 (2021), 2106.14697. 33

    2021 arXiv

  35. [43]

    K. D. Cole, Aust. J. Phys. 30, 671 (1977)

    1977

  36. [44]

    Igata, M

    T. Igata, M. Omamiuda, and Y. Takamori, Phys. Rev. D 111, 084062 (2025), 2502.11755

    2025 arXiv

  37. [45]

    Y. Hou, Z. Zhang, H. Yan, M. Guo, and B. Chen, Phys. Rev. D 106, 064058 (2022), 2206.13744

    2022 arXiv

  38. [46]

    D. N. Page and K. S. Thorne, Astrophys. J. 191, 499 (1974)

    1974

  39. [47]

    Bambi, Black Holes: A Laboratory for Testing Strong Gravity (Springer, 2017), ISBN 978- 981-10-4523-3, 978-981-13-5158-7, 978-981-10-4524-0

    C. Bambi, Black Holes: A Laboratory for Testing Strong Gravity (Springer, 2017), ISBN 978- 981-10-4523-3, 978-981-13-5158-7, 978-981-10-4524-0

    2017

  40. [48]

    Feleppa, V

    F. Feleppa, V. Bozza, and O. Y. Tsupko, Phys. Rev. D 110, 064031 (2024), 2406.07703

    2024 arXiv

  41. [49]

    S. V. Gaponenko, D. V. Novitsky, and D. V. Guzatov, Physica Scripta 98, 045614 (2023)

    2023

  42. [50]

    R. W. Lindquist, Annals Phys. 37, 487 (1966)

    1966

  43. [51]

    Kichenassamy and R

    S. Kichenassamy and R. A. Krikorian, Phys. Rev. D 32, 1866 (1985)

    1985

  44. [52]

    G. B. Rybicki, Radiative Processes in Astrophysics (Wiley-VCH, 2004), ISBN 978-0-471-82759-7, 978-3-527-61817-0

    2004

  45. [53]

    K. S. Virbhadra, Can. J. Phys. 102, 512 (2024), 2204.01792

    2024 arXiv

  46. [54]

    Grenzebach, V

    A. Grenzebach, V. Perlick, and C. L¨ ammerzahl, Phys. Rev. D 89, 124004 (2014), 1403.5234

    2014 arXiv

  47. [55]

    K. S. Virbhadra and G. F. R. Ellis, Phys. Rev. D 62, 084003 (2000), astro-ph/9904193

    2000 arXiv

  48. [56]

    Claudel, K

    C.-M. Claudel, K. S. Virbhadra, and G. F. R. Ellis, J. Math. Phys. 42, 818 (2001), gr-qc/0005050

    2001 arXiv

  49. [57]

    K. S. Virbhadra and G. F. R. Ellis, Phys. Rev. D 65, 103004 (2002)

    2002

  50. [59]

    Kobialko and D

    K. Kobialko and D. Gal’tsov, Phys. Rev. D 111, 044071 (2025), 2410.16127

    2025 arXiv

  51. [60]

    (68) Now we need to compare the characteristics of the radiation of the accretion disk in a vacuum and in the medium

    (67) The vacuum specific intensity of the radiation emitted by the disk is [42] ID(ωD) = ω3 D 4π3· 1 e ωD TD− 1 . (68) Now we need to compare the characteristics of the radiation of the accretion disk in a vacuum and in the medium. Our assumption is that in a plasma medium the...

  52. [61]

    Grenzebach, V

    A. Grenzebach, V. Perlick, and C. L¨ ammerzahl, Int. J. Mod. Phys. D 24, 1542024 (2015), 1503.03036

    2015 arXiv

  53. [62]

    K. S. Virbhadra, Phys. Rev. D 79, 083004 (2009), 0810.2109

    2009 arXiv

  54. [63]

    G. S. Bisnovatyi-Kogan and O. Y. Tsupko, Phys. Rev. D 105, 064040 (2022), 2201.01716. 34

    2022 arXiv

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