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arxiv: 2607.01017 · v1 · pith:KEXW7DXBnew · submitted 2026-07-01 · 🌀 gr-qc · astro-ph.HE

Horizon-scale intensity and polarization images of rotating Konoplya-Zhidenko black holes with thick accretion flows

Bing-Bing Chen , Chen-Yu Yang , Guo-Ping Li , Xin-Yun Hu This is my paper

Pith reviewed 2026-07-02 08:23 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords Konoplya-Zhidenko black holethick accretion flowblack hole shadowpolarization imagesnon-Kerr spacetimehorizon-scale imaginggeneral relativity tests
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The pith

Thick accretion flows around rotating non-Kerr black holes produce distinct intensity and polarization image features.

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

The authors model the shadow and polarization images of a rotating Konoplya-Zhidenko black hole with a thick, optically thin accretion flow described by a ballistic approximation. The resulting images feature an outer bright ring from higher-order light paths and an inner dark region cast by the event horizon. Increasing the deformation parameter enlarges the higher-order images, while higher spin and inclination make them more asymmetric due to relativistic effects. Linear polarization is reduced in the higher-order regions with vectors covering the entire plane, providing signatures distinct from thin-disk models that can test the black hole geometry.

Core claim

The thick disk model produces features in both intensity and polarization images that differ markedly from those in thin disk models. Within the framework used in this work, the observed intensity and polarization signatures can serve as effective probes of the underlying spacetime geometry and near horizon accretion dynamics.

What carries the argument

Analytical ballistic approximation accretion flow model for the Konoplya-Zhidenko rotating black hole spacetime with deformation parameter η.

If this is right

  • Increasing the deformation parameter η enlarges the size of higher order images without significantly changing their shape.
  • Increasing the spin parameter a and observer inclination angle θ_o enhances asymmetry of the higher order images with much larger intensity on the left side.
  • The degree of linear polarization is much smaller in the higher-order image region than in other regions.
  • Polarization vectors extend over the whole image plane.

Where Pith is reading between the lines

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

  • These image differences could allow future very-long-baseline interferometry to constrain the deformation parameter for observed black hole candidates.
  • The modeling approach could be extended to other non-Kerr metrics to identify whether each produces unique polarization signatures.
  • Validation against full magnetohydrodynamic simulations would be needed to confirm whether the ballistic flow approximation captures the actual near-horizon gas behavior.

Load-bearing premise

The accretion flow around the black hole is described by an analytical ballistic approximation model.

What would settle it

Observation of black hole images showing polarization degrees and patterns matching thin disk models rather than the reduced polarization in higher-order regions predicted for thick flows would falsify the claim.

Figures

Figures reproduced from arXiv: 2607.01017 by Bing-Bing Chen, Chen-Yu Yang, Guo-Ping Li, Xin-Yun Hu.

Figure 1
Figure 1. Figure 1: Effects of the deformation parameter η and the observer inclination angle θo on the black hole shadow in the BAAF model. The spin parameter is fixed at a = 0.3. 10 [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Intensity cuts along the x and y directions. The fixed parameters are η = −0.9 and a = 0.3, and the red, green, and blue curves correspond to θo = 0◦ , 17◦ , 75◦ , respectively [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Intensity cuts along the x and y directions. The fixed parameters are a = 0.3 and θo = 75◦ , and the red, green, and blue curves correspond to η = −0.9, 0.1, 0.9, respectively. -8 -4 0 4 8 -8 -4 0 4 8 x y 0.2 0.4 0.6 0.8 1.0 (a) a = 0.1 -8 -4 0 4 8 -8 -4 0 4 8 x y 0.2 0.4 0.6 0.8 1.0 (b) a = 0.7 -8 -4 0 4 8 -8 -4 0 4 8 x y 0.2 0.4 0.6 0.8 1.0 (c) a = 1.2 [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Effect of the spin parameter a on the black hole shadow in the BAAF model. The deformation parameter and observer inclination angle are fixed at η = 0.5 and θo = 75◦ , respectively. (a) a = 0.1 (b) a = 0.7 (c) a = 1.2 [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Blurred images processed with a Gaussian filter, where the standard deviation is set to 1 [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Distributions of the Stokes parameters Q˜ o,U˜ o, V˜ o. The fixed parameters are η = −0.9, a = 0.3, θo = 0◦ . Figs. 7 and 8 show the effects of the black hole parameters η, θo, and a on the Stokes parameter ˜Io and the linear polarization vector ⃗f. In these figures, ˜Io denotes the intensity distribution. The arrows represent the linear polarization vector, and their colors and directions correspond to th… view at source ↗
Figure 7
Figure 7. Figure 7: Effects of the deformation parameter η and the observer inclination angle θo on the polar￾ization images. The spin parameter is fixed at a = 0.3. 14 [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Effect of the spin parameter a on the polarization images. The deformation parameter and observer inclination angle are fixed at η = 0.5 and θo = 75◦ , respectively. 6 Conclusion and Discussion In recent years, many studies have focused on simulations of black hole shadow images illuminated by thin accretion disks. In more realistic physical scenarios, however, the geometrical thickness of the accretion di… view at source ↗
read the original abstract

We investigate the shadow and polarization images of a Konoplya-Zhidenko rotating non-Kerr black hole surrounded by a geometrically thick and optically thin accretion flow. The accretion flow is described by an analytical ballistic approximation accretion flow model. The numerical results show that the shadow image exhibits two main features, an outer bright ring and an inner dark region. The former corresponds to higher order images, while the latter is produced by the black hole event horizon. Increasing the deformation parameter $\eta$ does not significantly change the overall shape of the higher order images, but it enlarges their size. Increasing the spin parameter $a$ and the observer inclination angle $\theta_o$ enhances the asymmetry of the higher order images and makes the intensity on the left side much larger than that on the right side. This behavior is associated with frame dragging and the relativistic Doppler effect. In the polarization images, the degree of linear polarization is much smaller in the higher-order image region than in other regions, and the polarization vectors extend over the whole image plane. These results indicate that the thick disk model produces features in both intensity and polarization images that differ markedly from those in thin disk models. Within the framework used in this work, the observed intensity and polarization signatures can serve as effective probes of the underlying spacetime geometry and near horizon accretion dynamics.

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 manuscript numerically investigates shadow and polarization images of rotating Konoplya-Zhidenko black holes with a geometrically thick, optically thin accretion flow modeled via an analytical ballistic approximation. It reports an outer bright ring (higher-order images) and inner dark region (event horizon) in intensity maps, with left-right asymmetry increasing with spin a and inclination θ_o due to frame-dragging and Doppler boosting. Polarization maps show reduced linear polarization degree in higher-order regions and vectors spanning the image plane. The authors conclude that these features differ markedly from thin-disk cases and can probe the underlying spacetime geometry and near-horizon dynamics within the adopted framework.

Significance. If the reported trends hold, the work contributes to the literature on non-Kerr metrics and thick-disk imaging by extending ray-tracing calculations to the Konoplya-Zhidenko spacetime and highlighting polarization signatures. The parameter study of deformation η, spin a, and observer angle provides concrete trends that could inform EHT-like observations. No machine-checked proofs or fully reproducible code are mentioned, but the forward simulations of intensity and polarization constitute a clear, falsifiable set of predictions within the model.

major comments (2)
  1. [Abstract] Abstract: The central claim that 'the thick disk model produces features in both intensity and polarization images that differ markedly from those in thin disk models' is load-bearing for the paper's significance, yet no direct side-by-side comparison, quantitative difference metric, or reference to equivalent thin-disk ray-tracing runs (same metric, same code) is supplied; without this the magnitude and robustness of the distinction cannot be assessed.
  2. [Abstract] Abstract: All image features and their reported dependence on a, θ_o, and η rest on the specific analytical ballistic approximation for the flow (velocity, density, and emissivity profiles), but the manuscript supplies neither the explicit functional forms, the choice of free parameters in the approximation, nor any sensitivity tests or comparison to MHD simulations; this assumption is load-bearing for the interpretation that the signatures probe spacetime geometry.
minor comments (1)
  1. The abstract would be clearer if it stated the specific ranges or fiducial values explored for the deformation parameter η, spin a, and inclination θ_o.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and will incorporate revisions to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that 'the thick disk model produces features in both intensity and polarization images that differ markedly from those in thin disk models' is load-bearing for the paper's significance, yet no direct side-by-side comparison, quantitative difference metric, or reference to equivalent thin-disk ray-tracing runs (same metric, same code) is supplied; without this the magnitude and robustness of the distinction cannot be assessed.

    Authors: We agree that a direct comparison would better substantiate the central claim. In the revised manuscript we will add a new figure (or appendix) showing side-by-side intensity and polarization images computed with the identical ray-tracing code for both the thick ballistic flow and a standard thin-disk model in the same Konoplya-Zhidenko spacetime. We will also report quantitative metrics, such as the fractional difference in bright-ring radius and mean linear polarization fraction, to allow readers to assess the magnitude of the reported distinctions. revision: yes

  2. Referee: [Abstract] Abstract: All image features and their reported dependence on a, θ_o, and η rest on the specific analytical ballistic approximation for the flow (velocity, density, and emissivity profiles), but the manuscript supplies neither the explicit functional forms, the choice of free parameters in the approximation, nor any sensitivity tests or comparison to MHD simulations; this assumption is load-bearing for the interpretation that the signatures probe spacetime geometry.

    Authors: The explicit functional forms of the velocity, density and emissivity profiles together with the chosen parameter values are already stated in Section II (Eqs. 5–8). To address the referee’s concern we will expand that section with the complete expressions, tabulate the adopted free-parameter values, and add a short sensitivity study showing how modest variations in those parameters affect the reported image features. A full MHD comparison lies outside the scope of the present analytical-model study; we will nevertheless add a paragraph discussing the model’s limitations and citing relevant MHD literature. revision: partial

Circularity Check

0 steps flagged

No circularity; forward simulations from specified flow model

full rationale

The paper computes shadow and polarization images via numerical ray-tracing on a Konoplya-Zhidenko metric with an analytical ballistic accretion flow. Reported features (outer bright ring, left-right asymmetry, low polarization degree in higher-order images) are direct numerical outputs of this setup. No equation reduces a claimed prediction to a fitted parameter or self-defined quantity by construction, and no load-bearing step relies on a self-citation chain that itself assumes the target result. The ballistic model is an input assumption whose validity is external to the derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the Konoplya-Zhidenko metric as a valid non-Kerr spacetime and on the ballistic approximation as an adequate description of the thick flow; both are domain assumptions imported from prior literature without new derivation here.

axioms (2)
  • domain assumption Konoplya-Zhidenko metric correctly describes the spacetime of a rotating non-Kerr black hole
    Used as the background metric for all ray tracing (abstract).
  • domain assumption Analytical ballistic approximation adequately models the geometrically thick, optically thin accretion flow
    Explicitly adopted to generate the emission (abstract).

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discussion (0)

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Reference graph

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