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arxiv: 2604.23721 · v1 · submitted 2026-04-26 · 🌀 gr-qc

Recognition: unknown

Photon regions, shadow observables and constraints from M87* of a Kerr-Newman-like black hole in Bumblebee gravity surrounded by plasma

Jian-Peng Zhang , Yu Zhang , Li Han
Authors on Pith no claims yet

Pith reviewed 2026-05-08 05:48 UTC · model grok-4.3

classification 🌀 gr-qc
keywords black hole shadowBumblebee gravityKerr-Newman-likeplasmaM87*Event Horizon Telescopephoton regionsshadow observables
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The pith

Observations of M87* constrain the parameters of a charged rotating black hole in Bumblebee gravity surrounded by plasma.

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

The paper models M87* as a Kerr-Newman-like black hole in Bumblebee gravity with a surrounding plasma. It calculates the photon regions and the resulting shadow using null geodesics. Two sets of shadow observables are introduced to show how spin and the Lorentz-violating parameter distort the shadow while charge and plasma parameter shrink it radially. Using EHT measurements of the shadow's angular diameter, circularity, and axis ratio, the authors narrow the allowed ranges for these parameters. This shows that the model remains consistent with current observations and could represent real black holes.

Core claim

By deriving the null geodesic equations in the plasma medium for the Kerr-Newman-like black hole in Bumblebee gravity, the photon region is identified and the black hole shadow is constructed. The effects of the spin a, charge Q0, Lorentz-violating parameter ℓ, and plasma parameter k are analyzed through shadow observables, revealing that a and ℓ enhance distortion while Q0 and k cause shrinkage. The energy emission rate is suppressed with increasing parameters. Modeling M87* with these parameters shows that the EHT angular diameter θ_d = 42 ± 3 μas constrains the space, while circularity deviation and axis ratio satisfy the observed limits, indicating the model is a possible candidate for 2

What carries the argument

The black hole shadow constructed from the unstable photon orbits in the non-homogeneous power-law plasma, using observables such as angular diameter, circularity deviation ΔC, and axis ratio Dx.

If this is right

  • Increasing spin a or Lorentz-violating parameter ℓ increases the distortion of the shadow.
  • Increasing charge Q0 or plasma parameter k leads to radial shrinkage of the shadow.
  • The peak of the energy emission rate is suppressed as these parameters increase.
  • The angular diameter θ_d = 42 ± 3 μas narrows the viable parameter space for the model.
  • The circularity deviation ΔC ≲ 0.1 and axis ratio 1 < Dx ≲ 4/3 are satisfied within EHT limits.

Where Pith is reading between the lines

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

  • Alternative plasma distributions might produce different constraints on the Lorentz-violating parameter.
  • Higher precision future observations could further limit the allowed values of ℓ and Q0.
  • This model offers a way to test Bumblebee gravity using black hole shadows beyond standard general relativity.
  • Similar analysis could be applied to other supermassive black holes like Sgr A* to cross-check the constraints.

Load-bearing premise

The specific non-homogeneous power-law plasma model is chosen to allow separability of the Hamilton-Jacobi equation for the geodesic motion.

What would settle it

If observations of M87* show a shadow circularity deviation larger than 0.1 or an axis ratio exceeding 4/3, the parameter ranges permitted by this model would be ruled out.

Figures

Figures reproduced from arXiv: 2604.23721 by Jian-Peng Zhang, Li Han, Yu Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. Parameter space of the Bumblebee black hole ( view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Plots of the radial function view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The photon regions of the KN-like black hole in Bumblebee gravity surrounded by plasma in the view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The photon regions of the KN-like black hole in Bumblebee gravity surrounded by plasma in the view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Shadows of the KN-like black hole in Bumblebee gravity surrounded by plasma, illustrating the independent effects of view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Illustration of shadow observables defined by the reference circle method. The solid black curve represents the black hole view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Variations of the shadow radius view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Variations of the shadow area view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. High-frequency energy emission rate as a function of frequency view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Density plots of the circular deviation view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Density plots of the circular deviation view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Constraints on parameter view at source ↗
read the original abstract

In this paper, we investigate the photon regions, shadow, and observational constraints of a Kerr-Newman-like black hole in Bumblebee gravity within a plasma medium. By employing a specific non-homogeneous power-law plasma model to ensure the separability of the Hamilton-Jacobi equation, we derive the null geodesic equations, analyze the photon regions, and construct the black hole shadow. Furthermore, we introduce two sets of shadow observables to systematically analyze the distinct effects of each physical parameter (spin $a$, charge $Q_0$, Lorentz-violating parameter $\ell$, and plasma parameter $k$) on the shadow geometry. Specifically, we find that $a$ and $\ell$ mainly enhance the distortion of the shadow, whereas $Q_0$ and $k$ primarily lead to its radial shrinkage. Additionally, a brief evaluation of the energy emission rate shows that an increase in these parameters generally suppresses the emission peak. Finally, by modeling M87* as a charged rotating black hole in Bumblebee gravity surrounded by plasma, we can constrain the physical parameters using observations from the Event Horizon Telescope (EHT). While the angular diameter $\theta_d = 42 \pm 3 \, \mu\text{as}$ narrows the viable parameter space, the circularity deviation $\Delta C \lesssim 0.1$ and axis ratio $1 < D_x \lesssim 4/3$ obey the EHT limits. This suggests that the charged rotating black hole in Bumblebee gravity surrounded by plasma might be a candidate for real astrophysical black holes.

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 investigates photon regions, null geodesics, and the shadow of a Kerr-Newman-like black hole in Bumblebee gravity immersed in a plasma medium. A specific non-homogeneous power-law plasma density is adopted to enforce separability of the Hamilton-Jacobi equation; the resulting critical impact parameters are used to construct the shadow boundary and two sets of observables. The effects of spin a, charge Q0, Lorentz-violating parameter ℓ, and plasma index k are mapped, an energy-emission-rate calculation is presented, and EHT data on M87* (θ_d = 42 ± 3 μas, ΔC ≲ 0.1, 1 < D_x ≲ 4/3) are applied to constrain the four-parameter space, with the conclusion that the model remains a viable candidate for M87*.

Significance. If the chosen plasma profile is representative, the work would extend shadow phenomenology to Bumblebee gravity with non-vacuum surroundings and supply concrete bounds on the Lorentz-violating parameter ℓ together with the plasma index k. The systematic exploration of four parameters and the inclusion of the energy emission rate constitute incremental but useful additions to the literature on modified-gravity shadows.

major comments (2)
  1. [Plasma model and Hamilton-Jacobi separation] The non-homogeneous power-law plasma density n(r,θ) is introduced explicitly to guarantee separability of the Hamilton-Jacobi equation. This modeling choice is load-bearing for the photon-region boundaries and all subsequent shadow observables; the manuscript contains no comparison of the resulting θ_d, ΔC, or D_x against the constant-density or radially declining profiles employed in the original EHT M87* analyses. Substitution of a different (still separable) plasma prescription could shift the observables outside the quoted EHT windows, rendering the claimed narrowing of the (a, Q0, ℓ, k) space and the viability conclusion unsupported.
  2. [Observational constraints from M87*] The angular-diameter constraint θ_d = 42 ± 3 μas is stated to narrow the viable parameter space, yet no quantitative table or plot isolates the plasma-induced shift in the critical impact parameters relative to the vacuum Bumblebee case. Without this differential comparison, it is impossible to assess whether the reported constraints are driven by the Bumblebee modification, the charge, or the plasma term.
minor comments (2)
  1. [Geodesic equations] The precise functional form of the plasma density (including the exponent k and any angular dependence) should be written explicitly before the geodesic equations are derived, together with the resulting separated constants of motion.
  2. [Shadow figures] Figure captions for the shadow plots should state the fixed values of the remaining three parameters when one is varied, to allow direct reproduction of the displayed curves.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below and agree that additional comparisons will strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Plasma model and Hamilton-Jacobi separation] The non-homogeneous power-law plasma density n(r,θ) is introduced explicitly to guarantee separability of the Hamilton-Jacobi equation. This modeling choice is load-bearing for the photon-region boundaries and all subsequent shadow observables; the manuscript contains no comparison of the resulting θ_d, ΔC, or D_x against the constant-density or radially declining profiles employed in the original EHT M87* analyses. Substitution of a different (still separable) plasma prescription could shift the observables outside the quoted EHT windows, rendering the claimed narrowing of the (a, Q0, ℓ, k) space and the viability conclusion unsupported.

    Authors: The power-law plasma profile was chosen to ensure separability of the Hamilton-Jacobi equation, permitting an analytic treatment of the photon regions and shadow boundary, as is common in the literature on plasma-affected black-hole shadows. We acknowledge that the manuscript does not compare the resulting observables against the constant-density or radially declining profiles used in the original EHT M87* papers. This omission limits the ability to assess robustness across plasma prescriptions. In the revised version we will add an explicit discussion of this model dependence, including a qualitative assessment of how alternative separable profiles would affect the quoted EHT windows and the viability conclusion. revision: yes

  2. Referee: [Observational constraints from M87*] The angular-diameter constraint θ_d = 42 ± 3 μas is stated to narrow the viable parameter space, yet no quantitative table or plot isolates the plasma-induced shift in the critical impact parameters relative to the vacuum Bumblebee case. Without this differential comparison, it is impossible to assess whether the reported constraints are driven by the Bumblebee modification, the charge, or the plasma term.

    Authors: We agree that an explicit isolation of the plasma contribution relative to the vacuum Bumblebee case is missing. The constraints presented are for the complete four-parameter model, but without a side-by-side comparison it is difficult to disentangle the effects. In the revision we will include a new table (or supplementary figure) that reports the critical impact parameters and observables for k = 0 (vacuum Bumblebee) versus the plasma cases, thereby clarifying the differential shifts attributable to ℓ, Q0, a, and k. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses explicit modeling assumptions and external EHT benchmarks.

full rationale

The paper states it adopts a specific non-homogeneous power-law plasma model explicitly 'to ensure the separability of the Hamilton-Jacobi equation,' derives null geodesics, photon regions, and shadow observables from the separated equations, then compares the resulting quantities (θ_d, ΔC, D_x) against independent EHT data for M87* to bound the parameters a, Q0, ℓ, k. No equation reduces to its input by construction, no fitted parameter is relabeled as a prediction, and no load-bearing premise rests on self-citation. The EHT angular-diameter and shape limits function as external constraints rather than tautological outputs.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central claim rests on the separability assumption for the chosen plasma profile and on the validity of the Kerr-Newman-like metric in Bumblebee gravity; these are introduced without independent derivation in the abstract.

free parameters (2)
  • plasma parameter k
    Coefficient in the non-homogeneous power-law plasma density profile introduced to guarantee separability of the Hamilton-Jacobi equation.
  • Lorentz-violating parameter ℓ
    Bumblebee gravity parameter controlling the strength of Lorentz violation; its value is left free and later constrained by data.
axioms (1)
  • domain assumption The Hamilton-Jacobi equation remains separable when the plasma density follows the chosen non-homogeneous power-law form.
    Explicitly invoked in the abstract to justify the analytic treatment of null geodesics.
invented entities (1)
  • Bumblebee vector field no independent evidence
    purpose: Introduces spontaneous Lorentz symmetry breaking into the gravitational sector
    Standard ingredient of Bumblebee gravity; no new independent evidence supplied in the abstract.

pith-pipeline@v0.9.0 · 5595 in / 1503 out tokens · 61934 ms · 2026-05-08T05:48:10.117536+00:00 · methodology

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