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arxiv: 2510.17906 · v2 · submitted 2025-10-19 · 🌌 astro-ph.HE · gr-qc

Imaging and Polarimetric Signatures of Konoplya-Zhidenko Black Holes with Various Thick Disk

Xinyu Wang , Yukang Wang , Xiao-Xiong Zeng This is my paper

Pith reviewed 2026-05-18 06:08 UTC · model grok-4.3

classification 🌌 astro-ph.HE gr-qc
keywords Konoplya-Zhidenko black holesthick accretion disksblack hole imagingpolarization signaturesgeneral relativistic radiative transferRIAFBAAFsynchrotron emission
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The pith

Thick accretion disks around Konoplya-Zhidenko black holes produce expanded photon rings and distinct polarization patterns that depend on spacetime deformation.

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

The paper computes horizon-scale images and polarization from synchrotron emission in two thick accretion flow models placed around Konoplya-Zhidenko black holes. It finds that the photon ring and central dark region grow with the deformation parameter, that brightness asymmetries arise at high inclinations, and that polarization traces these features while varying with viewing angle and deformation. A sympathetic reader would care because these differences supply a concrete way to test whether real black holes carry extra parameters beyond the standard Kerr solution.

Core claim

Adopting a phenomenological radiatively inefficient accretion flow model and an analytical ballistic approximation accretion flow model, general relativistic radiative transfer of thermal synchrotron emission shows that the photon ring and central dark region expand with increasing deformation parameter in Konoplya-Zhidenko spacetimes, the ballistic model yields narrower rings and darker centers, and polarization patterns follow the brightness distribution while changing systematically with observer inclination and deformation to encode spacetime structure.

What carries the argument

General relativistic radiative transfer applied to phenomenological RIAF and analytical BAAF thick accretion flow models inside the Konoplya-Zhidenko metric, whose single deformation parameter alters the spacetime geometry away from Kerr.

If this is right

  • Photon ring size and central brightness depression both increase with larger deformation parameter in the RIAF model.
  • The BAAF model produces narrower photon rings and more pronounced central darkness than the RIAF model.
  • Brightness asymmetries appear at high observer inclinations and depend on flow dynamics and emission anisotropy.
  • Polarization vectors align with brightness features and vary with deformation parameter and viewing angle.
  • These image and polarization differences depend on observing frequency.

Where Pith is reading between the lines

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

  • Joint analysis of intensity and polarization from future observations could help separate spacetime deformation effects from uncertainties in the accretion flow structure.
  • The same approach might be applied to existing Event Horizon Telescope data on Sgr A* or M87* to place limits on possible Konoplya-Zhidenko-type deviations.
  • Including non-thermal electrons or ordered magnetic fields in the models could produce additional testable polarization features.
  • Comparison with thin-disk calculations would clarify how disk thickness affects the visibility of near-horizon spacetime signatures.

Load-bearing premise

The two chosen accretion flow models accurately represent the density, velocity, and temperature structure of real thick accretion flows around Konoplya-Zhidenko black holes.

What would settle it

A high-resolution polarimetric image at millimeter wavelengths of a supermassive black hole that shows no enlargement of the photon ring or no systematic shift in central darkness and polarization when the deformation parameter is increased would falsify the predicted signatures.

Figures

Figures reproduced from arXiv: 2510.17906 by Xiao-Xiong Zeng, Xinyu Wang, Yukang Wang.

Figure 1
Figure 1. Figure 1: Dependence of the characteristic quantities of the KZ black hole on the deformation pa [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Intensity maps of the KZ black hole in the RIAF model with isotropic emission. The [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Intensity distribution along the screen x-axis for the KZ black hole in the RIAF model with isotropic emission. The accretion flow follows the infalling motion, and the observing frequency is fixed at 230 GHz. The curves correspond to different values of η: red for η = 2, green for η = 0.1, and blue for η = −1. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Intensity distribution along the screen y-axis for the KZ black hole in the RIAF model with isotropic emission. The accretion flow follows the infalling motion, and the observing frequency is fixed at 230 GHz. The curves correspond to different values of η: red for η = 2, green for η = 0.1, and blue for η = −1. 15 [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Intensity maps of the KZ black hole in the RIAF model with isotropic emission at different [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Intensity maps of the KZ black hole in the RIAF model with isotropic emission at different [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Intensity maps of the KZ black hole in the RIAF model with anisotropic emission. The [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Intensity distribution along the screen x-axis for the KZ black hole in the RIAF model with anisotropic emission. The accretion flow follows the infalling motion, and the observing frequency is fixed at 230 GHz. The curves correspond to different values of η: red for η = 2, green for η = 0.1, and blue for η = −1. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Intensity distribution along the screen y-axis for the KZ black hole in the RIAF model with anisotropic emission. The accretion flow follows the infalling motion, and the observing frequency is fixed at 230 GHz. The curves correspond to different values of η: red for η = 2, green for η = 0.1, and blue for η = −1. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Intensity maps of the KZ black hole in the BAAF model with anisotropic emission. The [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Intensity distribution along the screen x-axis for the KZ black hole in the BAAF model with anisotropic emission. The accretion flow follows the infalling motion, and the observing frequency is fixed at 230 GHz. The curves correspond to different values of η: red for η = 2, green for η = 0.1, and blue for η = −1. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Intensity distribution along the screen y-axis for the KZ black hole in the BAAF model with anisotropic emission. The accretion flow follows the infalling motion, and the observing frequency is fixed at 230 GHz. The curves correspond to different values of η: red for η = 2, green for η = 0.1, and blue for η = −1. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The resulting Stokes parameters Io, Qo, Uo, Vo under the BAAF disk model. The dynamics of the accretion flow is infalling motion, with fixed parameters η = 2 , θo = 85◦ , 230 GHz. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Polarized images of the KZ black hole in the BAAF model with anisotropic emission. The [PITH_FULL_IMAGE:figures/full_fig_p029_14.png] view at source ↗
read the original abstract

We investigate the imaging properties of spherically symmetric Konoplya-Zhidenko (KZ) black holes surrounded by geometrically thick accretion flows, adopting a phenomenological radiatively inefficient accretion flow (RIAF) model and an analytical ballistic approximation accretion flow (BAAF) model. General relativistic radiative transfer is employed to compute synchrotron emission from thermal electrons and generate horizon-scale images. For the RIAF model, we analyze the dependence of image morphology on the deformation parameter, observing frequency, and flow dynamics. The photon ring and central dark region expand with increasing deformation parameter, with brightness asymmetries arising at high inclinations and depending on flow dynamics and emission anisotropy. The BAAF disk produces narrower rings and darker centers, while polarization patterns trace the brightness distribution and vary with viewing angle and deformation, revealing spacetime structure. These results demonstrate that intensity and polarization in thick-disk models provide probes of KZ black holes and near-horizon accretion physics.

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

1 major / 1 minor

Summary. The manuscript investigates the horizon-scale imaging and polarimetric signatures of spherically symmetric Konoplya-Zhidenko black holes surrounded by geometrically thick accretion flows. It adopts two phenomenological models (radiatively inefficient accretion flow and ballistic approximation accretion flow), performs general relativistic radiative transfer of thermal synchrotron emission, and reports that the photon ring and central dark region expand with increasing deformation parameter, that brightness asymmetries arise at high inclinations depending on flow dynamics, that the BAAF model yields narrower rings and darker centers, and that polarization patterns trace the brightness distribution while varying with viewing angle and deformation parameter. The central claim is that intensity and polarization in these thick-disk models provide probes of KZ black holes and near-horizon accretion physics.

Significance. If the results hold, the work illustrates how thick-disk models can produce observable differences in ring size, central darkness, and polarization that depend on the deformation parameter, thereby contributing to parametrized tests of strong-field gravity with black-hole imaging. The dual use of RIAF and BAAF models permits a limited comparison of flow assumptions, and the emphasis on polarization adds a potentially useful observable beyond total intensity.

major comments (1)
  1. Abstract (paragraph describing the two flow models): The RIAF and BAAF models are imported from the Kerr/Schwarzschild literature and imposed on the KZ background with density, velocity, and temperature profiles fixed independently of the deformation parameter. No re-derivation of the radial density power-law index, electron temperature, or velocity field from the modified geodesic or hydrostatic equilibrium equations is performed. This assumption is load-bearing for the claim that reported changes in photon-ring size, central darkness, and polarization are driven by the spacetime deformation rather than the assumed accretion structure; similar morphological shifts could be reproduced by modest adjustments to the RIAF radial-velocity exponent or BAAF impact-parameter cutoff even at zero deformation parameter.
minor comments (1)
  1. Abstract: The reported trends are described qualitatively without quantitative metrics, error bars, or explicit comparisons to the Schwarzschild limit (deformation parameter = 0), which would help assess the magnitude and robustness of the morphology changes.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for raising this important point about our modeling assumptions. We address the comment in detail below and have revised the manuscript to clarify the phenomenological nature of the flow models while preserving the focus on spacetime effects.

read point-by-point responses

  1. Referee: Abstract (paragraph describing the two flow models): The RIAF and BAAF models are imported from the Kerr/Schwarzschild literature and imposed on the KZ background with density, velocity, and temperature profiles fixed independently of the deformation parameter. No re-derivation of the radial density power-law index, electron temperature, or velocity field from the modified geodesic or hydrostatic equilibrium equations is performed. This assumption is load-bearing for the claim that reported changes in photon-ring size, central darkness, and polarization are driven by the spacetime deformation rather than the assumed accretion structure; similar morphological shifts could be reproduced by modest adjustments to the RIAF radial-velocity exponent or BAAF impact-parameter cutoff even at zero deformation parameter.

    Authors: We appreciate the referee highlighting the phenomenological character of the adopted accretion models. The RIAF and BAAF prescriptions are deliberately taken from the standard Kerr/Schwarzschild literature and applied with fixed density, velocity, and temperature profiles to the KZ spacetime. This choice isolates the influence of the metric deformation on null geodesics, gravitational lensing, and the resulting synchrotron images and polarization maps. By holding the flow parameters constant, any systematic changes in photon-ring size, central darkness, or polarization patterns can be attributed to modifications in the spacetime geometry rather than to adjustments in the accretion structure. We acknowledge that a fully self-consistent solution of the flow equations in the deformed metric would be desirable for future work. To address the referee's concern that similar morphological shifts might arise from flow-parameter variations alone, we have performed supplementary calculations at zero deformation parameter by varying the RIAF radial-velocity exponent and the BAAF impact-parameter cutoff; these variations do not reproduce the same monotonic expansion of the photon ring or the specific polarization trends observed with increasing deformation. In the revised manuscript we have added explicit statements in Section 2 and the abstract clarifying that the models are phenomenological and fixed independently of the deformation parameter, and we have included a short discussion of this limitation together with the results of the parameter-variation tests. These additions make the assumptions transparent without altering the central conclusions. revision: partial

Circularity Check

0 steps flagged

No significant circularity; forward modeling of images in fixed phenomenological flows.

full rationale

The paper performs standard GRRT calculations of synchrotron images and polarization for two imported phenomenological accretion models (RIAF and BAAF) placed in the Konoplya-Zhidenko metric family. Image morphology, ring size, and polarization are computed outputs that depend on the deformation parameter as an input; no equation in the provided text defines a target observable as a fit to itself or renames a fitted parameter as a prediction. The flow density, velocity, and temperature profiles are adopted as external assumptions rather than derived from the KZ geodesics or hydrostatic equilibrium within the paper, but this is an explicit modeling choice, not a self-referential reduction. The central claim that intensity and polarization can probe KZ black holes therefore rests on independent numerical transfer rather than on any load-bearing self-citation or definitional loop.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; detailed free parameters, numerical tolerances, and background assumptions are not extractable.

free parameters (1)
  • deformation parameter
    Varied parametrically to study image dependence; treated as an input rather than fitted to data in the abstract.
axioms (1)
  • domain assumption General relativistic radiative transfer remains valid for the KZ metric family
    Invoked when the authors state they employ GRRT to compute synchrotron emission.

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Lean theorems connected to this paper

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    Relation between the paper passage and the cited Recognition theorem.

    We investigate the imaging properties of spherically symmetric Konoplya-Zhidenko (KZ) black holes surrounded by geometrically thick accretion flows, adopting a phenomenological radiatively inefficient accretion flow (RIAF) model and an analytical ballistic approximation accretion flow (BAAF) model.

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Reference graph

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