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arxiv: 2508.20910 · v2 · submitted 2025-08-28 · 🌀 gr-qc

Images of the accretion disk in Hybrid metric-Palatini gravity

P.I. Dyadina , N.A. Avdeev This is my paper

Pith reviewed 2026-05-18 20:42 UTC · model grok-4.3

classification 🌀 gr-qc
keywords accretion diskhybrid metric-Palatini gravityblack hole imagesray-tracingscalar fieldNovikov-Thorne modelredshift mapsintensity maps
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The pith

Scalar field parameters reshape direct and secondary images of accretion disks around black holes in hybrid metric-Palatini gravity.

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

The paper computes images of thin accretion disks around static spherically symmetric black holes in hybrid metric-Palatini gravity. It applies the Novikov-Thorne model together with semi-analytic ray-tracing to produce redshift and intensity maps across different scalar field configurations, including Higgs-type potentials and cases with no potential. A sympathetic reader would care because the resulting maps show that scalar field parameters control the temperature, brightness, and ring structure of the images, with extreme values producing cooler and dimmer disks than those predicted by general relativity. The work also reports that the secondary ring deviates in size and appearance from the general-relativity case, suggesting a possible observational test. This constitutes an early exploration of how modified-gravity effects might appear in realistic black-hole environments.

Core claim

In hybrid metric-Palatini gravity, static spherically symmetric black holes host accretion disks whose direct and secondary images, generated with the Novikov-Thorne thin-disk model and semi-analytic ray-tracing, depend significantly on the scalar field parameters. Configurations with extreme scalar field values produce cooler and dimmer disks than in general relativity, while the inclination angle mainly controls asymmetry and brightness distribution. The structure and angular size of the secondary ring also deviate noticeably from general-relativity predictions, offering a potential observational signature.

What carries the argument

Semi-analytic ray-tracing through the curved spacetime of hybrid metric-Palatini black holes for varying scalar field configurations with and without potentials

If this is right

  • Scalar field parameters control the temperature and brightness of both direct and secondary disk images.
  • Extreme scalar field values produce cooler and dimmer disks than those in general relativity.
  • The secondary ring exhibits deviations in structure and angular size from general-relativity predictions.
  • Inclination angle governs asymmetry and brightness distribution across the images.

Where Pith is reading between the lines

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

  • Future high-resolution radio or X-ray observations could place bounds on allowed scalar field values by measuring secondary ring properties.
  • The same ray-tracing approach could be applied to rotating black holes or thick-disk models to check whether the deviations persist.
  • If confirmed, such signatures would link black-hole imaging data directly to constraints on scalar-tensor modifications of gravity.

Load-bearing premise

The Novikov-Thorne thin-disk model and the semi-analytic ray-tracing procedure remain valid without additional corrections in spacetimes sourced by the hybrid metric-Palatini scalar field.

What would settle it

A high-resolution observation of the angular size or intensity of the secondary ring around a supermassive black hole that matches general-relativity expectations for all scalar field parameter choices would falsify the reported deviations.

Figures

Figures reproduced from arXiv: 2508.20910 by N.A. Avdeev, P.I. Dyadina.

Figure 1
Figure 1. Figure 1: The coordinate system of the disk studies: we follow the classical convention, measuring the angle counterclockwise from the x-axis to the line connecting point m with point O′ . In this setup, the angle y ′Oy′′ is equal to η −π. Thus, light emitted from point M with coordinates (r, ϕ) reaches point m on the screen of the distant observer, where its coordinates are (b, η). Exploiting spherical symmetry, th… view at source ↗
Figure 2
Figure 2. Figure 2: Continuous distributions of redshift z in the direct (odd rows) and secondary [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The complete apparent images of the thin accretion disk for different values [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The critical ring diameter Sd = 42µas of HMPG BHs in the two-dimensional space of parameter ϕ0 and mass M. Here the observational angle and BH distance are fixed at 17◦ and 16.8 Mpc, respectively. The scale corresponding to ϕ0 is logarithmic for convenience ages. Currently, the best and only images of BHs have been obtained by EHT [2–11]. This telescope has an angular resolution of approximately 20µas at 1… view at source ↗
read the original abstract

In this paper we obtain and study images of accretion disks around static spherically symmetric black holes in hybrid metric-Palatini gravity. We use Novikov-Thorne thin-disk model. Semi-analytic ray-tracing methods in curved spacetime are employed to generate the images of the disk for different scalar field configurations, including both Higgs-type potentials and cases without a potential. The resulting images, including both redshift and intensity maps, are analyzed. The results show that the scalar field parameters play a significant role in shaping both the direct and secondary images of the disk, while the inclination angle primarily affects the asymmetry and brightness distribution. In particular, configurations with extreme scalar field values lead to cooler and dimmer disk compared to General Relativity. Furthermore, the structure and angular size of the secondary ring exhibit noticeable deviations from General Relativity, offering a potential observational signature. This work should be regarded as a first step toward modeling realistic accretion disks within the hybrid metric-Palatini gravity framework, and toward assessing their potential observational distinguishability from General Relativity predictions.

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 / 2 minor

Summary. The manuscript computes images of thin accretion disks around static spherically symmetric black holes in hybrid metric-Palatini gravity. It employs the standard Novikov-Thorne thin-disk model together with semi-analytic ray-tracing to produce redshift and intensity maps for different scalar-field configurations (Higgs-type potentials and potential-free cases). The central claims are that scalar-field parameters strongly shape both direct and secondary images, that extreme scalar values yield cooler and dimmer disks relative to General Relativity, and that the secondary ring exhibits observable structural and angular-size deviations that could serve as a distinguishing signature.

Significance. If the central claims are substantiated, the work supplies a concrete, potentially falsifiable prediction for how hybrid metric-Palatini gravity could be distinguished from GR via high-resolution accretion-disk imaging, particularly through the secondary ring. The study is presented as an initial exploration, which appropriately tempers expectations while opening a new modeling direction in modified gravity.

major comments (2)
  1. [Abstract] Abstract (methods paragraph): The manuscript substitutes the hybrid metric-Palatini functions into the standard Novikov-Thorne radial flux formula without deriving or citing a proof that the scalar-field stress-energy leaves the specific-energy, angular-momentum, and local energy-conservation relations unchanged. Because the spacetime is explicitly sourced by the hybrid scalar, an unexamined effective modification to the disk stress-energy tensor could alter the temperature profile and intensity maps independently of the metric change; this assumption is load-bearing for the claims of cooler/dimmer disks.
  2. [Results] Results (image analysis): The reported deviations in secondary-ring structure and angular size are stated qualitatively but without quantitative metrics (e.g., fractional change in ring radius or peak-intensity ratio) or error estimates. No comparison table or plot against the GR limit is described, and the abstract supplies no information on how the ray-tracing code was validated (convergence tests, reproduction of known GR images, or analytic limits). These omissions prevent assessment of whether the claimed observational signatures are robust.
minor comments (2)
  1. [Abstract] The abstract should explicitly state the numerical ranges or representative values of the scalar-field parameters that were explored.
  2. Notation for the metric functions and scalar-field potential should be introduced once in a dedicated section and used consistently thereafter.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and describe the revisions that will be incorporated to improve the manuscript.

read point-by-point responses

  1. Referee: The manuscript substitutes the hybrid metric-Palatini functions into the standard Novikov-Thorne radial flux formula without deriving or citing a proof that the scalar-field stress-energy leaves the specific-energy, angular-momentum, and local energy-conservation relations unchanged. Because the spacetime is explicitly sourced by the hybrid scalar, an unexamined effective modification to the disk stress-energy tensor could alter the temperature profile and intensity maps independently of the metric change.

    Authors: We agree that this point requires clarification. In hybrid metric-Palatini gravity the scalar field enters the gravitational sector and modifies the metric functions, but the thin-disk matter is assumed to be minimally coupled and pressureless. Consequently, the orbital motion remains geodesic with respect to the effective metric, and the specific energy, angular momentum, and radial flux retain the standard Novikov-Thorne expressions evaluated on the modified metric. In the revised manuscript we will add a short paragraph in Section 2 that recalls the Killing-vector conserved quantities for the static spherically symmetric line element and shows that the flux formula is unchanged in form. revision: yes

  2. Referee: The reported deviations in secondary-ring structure and angular size are stated qualitatively but without quantitative metrics (e.g., fractional change in ring radius or peak-intensity ratio) or error estimates. No comparison table or plot against the GR limit is described, and the abstract supplies no information on how the ray-tracing code was validated.

    Authors: We accept that quantitative support and validation details will strengthen the results. The revised version will include a new table listing the angular radius of the secondary ring, the peak intensity ratio relative to the direct image, and the effective temperature at the ISCO for representative scalar-field values, together with the corresponding GR numbers. Fractional deviations will be reported with estimated numerical uncertainties obtained from convergence tests. The methods section will be expanded to describe the ray-tracing algorithm, including the number of rays, integration tolerances, and explicit checks that the code recovers published GR images when the scalar-field parameters are set to zero. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation of disk images

full rationale

The paper solves the static spherically symmetric metric in hybrid metric-Palatini gravity, then applies the standard Novikov-Thorne thin-disk flux formula and semi-analytic ray-tracing to that fixed metric to produce redshift and intensity maps. No parameters are fitted to the generated images or secondary-ring properties; the outputs are direct numerical evaluations of the metric functions under the unmodified Novikov-Thorne assumptions. No self-definitional steps, fitted-input predictions, or load-bearing self-citations appear in the derivation chain. The central claims follow from straightforward substitution of the new metric into existing, externally validated methods, rendering the computation self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central results rest on the applicability of the standard thin-disk model and ray-tracing in the modified spacetime; scalar-field parameters are treated as free inputs whose specific values are chosen by the authors.

free parameters (1)
  • scalar field parameters
    Values controlling the strength and potential of the scalar field that are varied to produce different disk images.
axioms (1)
  • domain assumption Novikov-Thorne thin-disk model applies unchanged in hybrid metric-Palatini gravity
    Used to set the disk structure and emissivity before ray-tracing.

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