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arxiv: 2501.07029 · v2 · submitted 2025-01-13 · 🌀 gr-qc · hep-th

Shadow of the Scalar Hairy Black Hole with Inverted Higgs Potential

Kok-Geng Lim , Xiao Yan Chew This is my paper

Pith reviewed 2026-05-23 06:05 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords hairy black holeblack hole shadowaccretion diskscalar fieldray tracingM87Sgr A*no-hair theorem
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0 comments X

The pith

A hairy black hole with scalar field at the horizon produces a larger shadow and accretion disk than a Schwarzschild black hole of equal horizon radius, while ring brightness stays nearly the same.

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

The paper investigates the appearance of a black hole carrying scalar hair that arises when Einstein gravity couples to a scalar field with an inverted Higgs potential. Ray-tracing calculations classify light paths into direct, lensed, and photon-ring contributions and compare three thin-disk models against the Schwarzschild case at matched horizon radius. The calculations show that both shadow diameter and disk extent grow with the horizon scalar value while the brightness of the rings changes little. This near-invariance in brightness allows the hairy solution to reproduce Schwarzschild-like images once the horizon radius is permitted to vary. The same framework yields upper limits on the potential coefficient from existing images of M87 and Sgr A*.

Core claim

In the Einstein-Klein-Gordon theory with potential V(φ) = -Λ φ⁴ + μ φ², a hairy black hole carrying nonzero scalar field φ_H at the horizon has a shadow and accretion disk whose sizes increase with φ_H; the brightness of the direct, lensed, and photon-ring emissions remains nearly unaffected, so that the hairy black hole can reproduce the optical appearance of a Schwarzschild black hole when its horizon radius is adjusted accordingly; the model also supplies observational bounds on Λ from M87 and Sgr A* data.

What carries the argument

Ray-tracing classification of photon trajectories into direct, lensed, and photon-ring classes around the hairy black hole metric derived from the Einstein-Klein-Gordon action.

If this is right

  • Shadow and accretion-disk sizes increase with the horizon scalar value φ_H at fixed horizon radius.
  • Brightness of the direct, lensed, and photon-ring features remains nearly independent of φ_H.
  • The hairy black hole can reproduce Schwarzschild-like images by suitable choice of horizon radius.
  • The coefficient Λ in the scalar potential is bounded by existing images of M87 and Sgr A*.

Where Pith is reading between the lines

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

  • Independent measurement of horizon radius would turn the reported size difference into a practical test for scalar hair.
  • Current Event Horizon Telescope data may already be consistent with a range of hairy solutions once horizon radius is allowed to vary.
  • The same ray-tracing setup could be applied to other scalar potentials to map which ones produce observable deviations.

Load-bearing premise

The three chosen models of optically and geometrically thin accretion disks capture the essential differences in optical appearance between the hairy black hole and Schwarzschild without further adjustments when horizon radius is held fixed.

What would settle it

A measurement showing that shadow diameter stays constant rather than increasing with horizon scalar value φ_H at fixed horizon radius would disprove the reported size dependence.

Figures

Figures reproduced from arXiv: 2501.07029 by Kok-Geng Lim, Xiao Yan Chew.

Figure 1
Figure 1. Figure 1: FIG. 1: (a) Two basic properties of the HBH: The reduced area of horizon [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (a) The trajectories of light rays are presented in the two-dimensional Cartesian coordinate ( [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (a) The three models of emitted intensity profiles: [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: (a) The location of ISCO, [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The fractional number of orbits, [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The trajectories of light rays are presented in the two-dimensional Cartesian coordinate ( [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: The three transfer functions [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Three models of emitted intensity profiles: [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Three models of observed intensity profiles: [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: The optical appearance of Model I for (a) the Schwarzschild black hole; HBHs with [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: The optical appearance of Model II for (a) the Schwarzschild black hole; HBHs with [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: The optical appearance of Model III for (a) the Schwarzschild black hole; HBHs with [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: The constraints imposed on [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
read the original abstract

We study the imaging of a hairy black hole (HBH) in the Einstein-Klein-Gordon theory, where Einstein gravity is minimally coupled to a scalar potential $V(\phi)=-\Lambda \phi^4 + \mu \phi^2$ with $\Lambda$ and $\mu$ are constants. As a consequence, a nontrivial scalar field at the event horizon $\phi_H$ allows the HBH to evade the no-hair theorem, bifurcate from the Schwarzschild black hole by acquiring some new properties, which can affect the shadow of the HBH received by a distant observer. The framework of ray-tracing is adopted to investigate the optical appearance of the HBH, thus the trajectories of light rays around the HBH can be classified into three emissions: direct, lensed and photon ring. Employing three models of optically and geometrically thin accretion disk, we compare the differences between the Schwarzschild black hole and HBH with same horizon radius in a specific model, and find that the size of the shadow and accretion disk increases as $\phi_H$ increases, but the brightness of the rings remain nearly unaffected, this implies our HBH can potentially mimic the Schwarzschild black hole if we vary the horizon radius of the HBH. Finally, we also constraint the parameter $\Lambda$ from the observations of supermassive black holes in the galactic center of M87 and Sgr A$^{*}$, which could offer new insights for imaging of black holes and astrophysical observations.

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 paper examines the shadow and optical appearance of a scalar hairy black hole (HBH) in Einstein-Klein-Gordon theory with inverted Higgs potential V(ϕ) = −Λϕ⁴ + μϕ². Employing ray-tracing to classify photon trajectories into direct, lensed, and photon-ring emissions, and applying three standard models of optically and geometrically thin accretion disks, the authors compare the HBH to Schwarzschild at fixed horizon radius. They report that shadow and accretion-disk sizes increase with ϕ_H while ring brightness remains nearly constant, suggesting that the HBH can mimic Schwarzschild by suitable choice of horizon radius, and derive an observational constraint on Λ from M87* and Sgr A* data.

Significance. If the numerical results and parameter constraint hold, the work supplies a concrete example of how scalar hair can alter shadow size while preserving apparent ring brightness, offering a potential route to test the no-hair theorem with EHT-style imaging and to bound the inverted-Higgs parameters.

major comments (2)
  1. [Abstract] The mimicry claim (shadow and disk size grow with ϕ_H at fixed r_h while brightness is unaffected) rests on freely varying the horizon radius after ϕ_H is fixed; the abstract presents the Λ constraint as an independent observational limit, yet the derivation details and independence from the r_h choice are not supplied, leaving open whether the constraint is circular with the fit.
  2. [Comparison of accretion-disk models] The three thin-disk models are applied directly to the HBH metric; the non-trivial scalar hair modifies the lapse and redshift factors relative to Schwarzschild, yet no explicit check is given that the emission profiles and ray-tracing intensities require no metric-specific rescaling before the brightness comparison at fixed r_h can be drawn.
minor comments (2)
  1. [Abstract] The abstract states that 'the brightness of the rings remain nearly unaffected' but supplies neither quantitative error estimates nor the precise intensity ratios used to reach this conclusion.
  2. [Abstract] Notation for the potential parameters (Λ, μ) and the horizon value ϕ_H is introduced without an explicit statement of the ranges explored or the numerical method used to solve the Einstein-Klein-Gordon system.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We appreciate the referee's detailed review and valuable suggestions. Below we provide point-by-point responses to the major comments. We will make revisions to address the concerns raised.

read point-by-point responses

  1. Referee: [Abstract] The mimicry claim (shadow and disk size grow with ϕ_H at fixed r_h while brightness is unaffected) rests on freely varying the horizon radius after ϕ_H is fixed; the abstract presents the Λ constraint as an independent observational limit, yet the derivation details and independence from the r_h choice are not supplied, leaving open whether the constraint is circular with the fit.

    Authors: We thank the referee for pointing this out. In the manuscript, the mimicry is demonstrated by comparing HBH and Schwarzschild at the same horizon radius r_h, showing that shadow and disk sizes increase with ϕ_H while ring brightness stays nearly constant. To mimic the Schwarzschild case, one can adjust r_h for a given ϕ_H to match the observed shadow size. The constraint on Λ is obtained by requiring that the HBH shadow size matches the observed values for M87* and Sgr A* for various ϕ_H, which determines the allowed range for Λ independent of a specific r_h choice, as r_h is adjusted accordingly. However, we agree that the abstract and the relevant section lack sufficient detail on this procedure. We will revise the abstract and add explicit steps in the text explaining how the Λ constraint is derived and why it is not circular. revision: yes

  2. Referee: [Comparison of accretion-disk models] The three thin-disk models are applied directly to the HBH metric; the non-trivial scalar hair modifies the lapse and redshift factors relative to Schwarzschild, yet no explicit check is given that the emission profiles and ray-tracing intensities require no metric-specific rescaling before the brightness comparison at fixed r_h can be drawn.

    Authors: The ray-tracing code computes the photon trajectories and intensities using the specific metric of the HBH, incorporating the modified lapse and redshift factors through the geodesic equations and the redshift factor in the intensity calculation. The thin-disk models provide the emission profile in the rest frame of the disk, and the observed intensity is obtained by integrating along the null geodesics without additional rescaling, as the metric effects are already included in the ray-tracing. Nevertheless, we acknowledge that an explicit verification or comparison of the redshift factors between the two metrics at fixed r_h would strengthen the presentation. We will add a paragraph or appendix providing this check in the revised version. revision: yes

Circularity Check

0 steps flagged

No circularity: metric, ray-tracing, and observational bounds are independent of target claims

full rationale

The derivation proceeds from the Einstein-Klein-Gordon action with the stated inverted-Higgs potential to obtain the HBH metric, then applies standard ray-tracing and three thin-disk emission models (direct/lensed/photon-ring classification) to compute images at fixed horizon radius. The reported trends (shadow/disk size growth with ϕ_H, near-constant ring brightness) and the subsequent statement that r_h variation can produce mimicry are direct numerical outputs of that pipeline, not reductions of the output to the input by definition or by a fitted parameter renamed as prediction. The Λ bound is extracted from external EHT shadow-diameter data on M87* and Sgr A*, which lie outside the model’s fitted quantities. No self-citation chain, ansatz smuggling, or uniqueness theorem imported from the authors’ prior work is load-bearing for the central claims. The calculation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 1 invented entities

The central claim rests on the existence of a nontrivial scalar solution at the horizon for the given potential, the validity of ray-tracing in this spacetime, and the appropriateness of the three thin-disk models; Lambda and mu are free constants whose values are later constrained or left unspecified.

free parameters (3)
  • Lambda
    Coefficient of the negative quartic term in the scalar potential; its value is constrained from M87 and Sgr A* data but the fitting procedure is not shown.
  • mu
    Coefficient of the quadratic term in the scalar potential; treated as a free constant.
  • phi_H
    Scalar field value at the event horizon; varied parametrically to study shadow changes.
axioms (2)
  • domain assumption Einstein gravity is minimally coupled to a real scalar field with potential V(ϕ) = −Λϕ⁴ + μϕ²
    Stated in the abstract as the theory framework that permits a hairy solution.
  • domain assumption Ray-tracing accurately classifies light trajectories into direct, lensed, and photon-ring emissions for the purpose of imaging
    Adopted without further justification in the abstract.
invented entities (1)
  • Scalar hairy black hole with inverted Higgs potential no independent evidence
    purpose: To produce a nontrivial scalar field at the horizon that evades the no-hair theorem and alters the shadow
    Introduced via the choice of potential and the assumption of a nontrivial ϕ_H

pith-pipeline@v0.9.0 · 5797 in / 1693 out tokens · 45296 ms · 2026-05-23T06:05:51.354629+00:00 · methodology

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Reference graph

Works this paper leans on

101 extracted references · 101 canonical work pages · 20 internal anchors

  1. [1]

    Israel, Event horizons in static vacuum space-times, Phys

    W. Israel, Event horizons in static vacuum space-times, Phys. Rev. 164, 1776 (1967)

    work page 1967

  2. [2]

    Carter, Axisymmetric Black Hole Has Only Two Degrees of Freedom, Phys

    B. Carter, Axisymmetric Black Hole Has Only Two Degrees of Freedom, Phys. Rev. Lett. 26, 331 (1971)

    work page 1971

  3. [3]

    Ruffini and J

    R. Ruffini and J. A. Wheeler, Introducing the black hole, Phys. Today 24, 30 (1971)

    work page 1971

  4. [4]

    Scalar hairy black holes and scalarons in the isolated horizons formalism

    A. Corichi, U. Nucamendi, and M. Salgado, Scalar hairy black holes and scalarons in the isolated horizons formalism, Phys. Rev. D 73, 084002 (2006), arXiv:gr-qc/0504126

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  5. [5]

    X. Y. Chew, D.-h. Yeom, and J. L. Bl´ azquez-Salcedo, Properties of scalar hairy black holes and scalarons with asymmetric potential, Phys. Rev. D 108, 044020 (2023), arXiv:2210.01313 [gr-qc]

    work page arXiv 2023

  6. [6]

    X. Y. Chew and D.-h. Yeom, Hairy Reissner-Nordstr¨ om black holes with asymmetric vacua, Phys. Rev. D 110, 044036 (2024), arXiv:2401.09039 [gr-qc]. 18

    work page arXiv 2024

  7. [7]

    S. R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys. Rev. D 21, 3305 (1980)

    work page 1980

  8. [8]

    S. S. Gubser, Phase transitions near black hole horizons, Class. Quant. Grav. 22, 5121 (2005), arXiv:hep-th/0505189

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  9. [9]

    X. Y. Chew and K.-G. Lim, Scalar hairy black holes with an inverted Mexican-hat potential, Phys. Rev. D 109, 064039 (2024), arXiv:2307.13972 [gr-qc]

    work page arXiv 2024

  10. [10]

    X. Y. Chew and Y. S. Myung, Simplest model of a scalarized black hole in the Einstein-Klein-Gordon theory, Phys. Rev. D 110, 044011 (2024), arXiv:2405.04921 [gr-qc]

    work page arXiv 2024

  11. [11]

    Exact Black-Hole Solution With Self-Interacting Scalar Field

    O. Bechmann and O. Lechtenfeld, Exact black hole solution with selfinteracting scalar field, Class. Quant. Grav. 12, 1473 (1995), arXiv:gr-qc/9502011

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  12. [12]

    Scalar Deformations of Schwarzschild Holes and Their Stability

    H. Dennhardt and O. Lechtenfeld, Scalar deformations of Schwarzschild holes and their stability, Int. J. Mod. Phys. A 13, 741 (1998), arXiv:gr-qc/9612062

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  13. [13]

    K. A. Bronnikov and G. N. Shikin, Spherically symmetric scalar vacuum: No go theorems, black holes and solitons, Grav. Cosmol. 8, 107 (2002), arXiv:gr-qc/0109027

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  14. [14]

    Exact black hole solution with a minimally coupled scalar field

    C. Martinez, R. Troncoso, and J. Zanelli, Exact black hole solution with a minimally coupled scalar field, Phys. Rev. D 70, 084035 (2004), arXiv:hep-th/0406111

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  15. [15]

    V. V. Nikonov, J. V. Tchemarina, and A. N. Tsirulev, A two-parameter family of exact asymptotically flat solutions to the Einstein-scalar field equations, Class. Quant. Grav. 25, 138001 (2008)

    work page 2008

  16. [16]

    Exact Hairy Black Holes and their Modification to the Universal Law of Gravitation

    A. Anabalon and J. Oliva, Exact Hairy Black Holes and their Modification to the Universal Law of Gravitation, Phys. Rev. D 86, 107501 (2012), arXiv:1205.6012 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  17. [17]

    O. S. Stashko and V. I. Zhdanov, Spherically symmetric configurations of General Relativity in presence of scalar field: separation of test body circular orbits, Gen. Rel. Grav. 50, 105 (2018), arXiv:1702.02800 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  18. [18]

    Gao and J

    C. Gao and J. Qiu, On black holes with scalar hairs, Gen. Rel. Grav. 54, 158 (2022), arXiv:2111.11582 [gr-qc]

    work page arXiv 2022

  19. [19]

    Karakasis, G

    T. Karakasis, G. Koutsoumbas, and E. Papantonopoulos, Black holes with scalar hair in three dimensions, Phys. Rev. D 107, 124047 (2023), arXiv:2305.00686 [gr-qc]

    work page arXiv 2023

  20. [20]

    A. N. Atmaja, Bogomol’nyi-like equations in gravity theories, Eur. Phys. J. C 84, 456 (2024), arXiv:2310.12476 [gr-qc]

    work page arXiv 2024

  21. [21]

    Li and J

    X. Li and J. Ren, Probing light scalars with not quite black holes, Phys. Rev. D 109, 104061 (2024), arXiv:2312.12894 [gr-qc]

    work page arXiv 2024

  22. [22]

    X.-P. Rao, H. Huang, and J. Yang, Hairy Black Holes with Arbitrary Small Areas, arXiv preprint (2024), arXiv:2403.11770 [gr-qc]

    work page arXiv 2024

  23. [23]

    M. P. Wijayanto, E. S. Fadhilla, F. T. Akbar, and B. E. Gunara, Global existence of classical static solutions of four dimensional Einstein–Klein–Gordon system, Gen. Rel. Grav. 55, 19 (2023), arXiv:2208.14361 [math-ph]

    work page arXiv 2023

  24. [24]

    M. P. Wijayanto, F. T. Akbar, and B. E. Gunara, Global existence and completeness of classical solutions in higher dimensional Einstein–Klein–Gordon system, Gen. Rel. Grav. 56, 22 (2024), arXiv:2304.09449 [gr-qc]

    work page arXiv 2024

  25. [25]

    Kunz and Y

    J. Kunz and Y. Shnir, Charged hairy black holes in the gauged Einstein-Friedberg-Lee-Sirlin model, Phys. Rev. D 107, 104062 (2023), arXiv:2303.16562 [hep-th]

    work page arXiv 2023

  26. [26]

    J. Kunz, V. Loiko, and Y. Shnir, Hairy dyonic Reissner-Nordstr¨ om black holes in an Einstein-Maxwell-Friedberg-Lee-Sirlin type model, Phys. Rev. D 110, 125020 (2024), arXiv:2407.21463 [hep-th]

    work page arXiv 2024

  27. [27]

    Brihaye, F

    Y. Brihaye, F. Buisseret, B. Hartmann, and O. Layfield, Boson stars and black holes with (complex and) real scalar hair, arXiv preprint (2024), arXiv:2410.22231 [gr-qc]

    work page arXiv 2024

  28. [28]

    Herdeiro, E

    C. Herdeiro, E. Radu, and E. dos Santos Costa Filho, Spinning Proca-Higgs balls, stars and hairy black holes, JCAP 07, 081, arXiv:2406.03552 [gr-qc]

    work page arXiv

  29. [29]

    Kocherlakota et al

    P. Kocherlakota et al. (Event Horizon Telescope), Constraints on black-hole charges with the 2017 EHT observations of M87*, Phys. Rev. D 103, 104047 (2021), arXiv:2105.09343 [gr-qc]

    work page arXiv 2017

  30. [30]

    First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way

    K. Akiyama et al. (Event Horizon Telescope), First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way, Astrophys. J. Lett. 930, L12 (2022), arXiv:2311.08680 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  31. [31]

    Akiyama et al

    K. Akiyama et al. (Event Horizon Telescope), First Sagittarius A* Event Horizon Telescope Results. VI. Testing the Black Hole Metric, Astrophys. J. Lett. 930, L17 (2022), arXiv:2311.09484 [astro-ph.HE]

    work page arXiv 2022

  32. [32]

    Testing the No-Hair Theorem with Observations of Black Holes in the Electromagnetic Spectrum

    T. Johannsen, Testing the No-Hair Theorem with Observations of Black Holes in the Electromagnetic Spectrum, Class. Quant. Grav. 33, 124001 (2016), arXiv:1602.07694 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  33. [33]

    The Current Ability to Test Theories of Gravity with Black Hole Shadows

    Y. Mizuno, Z. Younsi, C. M. Fromm, O. Porth, M. De Laurentis, H. Olivares, H. Falcke, M. Kramer, and L. Rezzolla, The Current Ability to Test Theories of Gravity with Black Hole Shadows, Nature Astron. 2, 585 (2018), arXiv:1804.05812 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  34. [34]

    Younsi, D

    Z. Younsi, D. Psaltis, and F. ¨Ozel, Black Hole Images as Tests of General Relativity: Effects of Spacetime Geometry, Astrophys. J. 942, 47 (2023), arXiv:2111.01752 [astro-ph.HE]

    work page arXiv 2023

  35. [35]

    S. Chen, J. Jing, W.-L. Qian, and B. Wang, Black hole images: A review, Sci. China Phys. Mech. Astron. 66, 260401 (2023), arXiv:2301.00113 [astro-ph.HE]

    work page arXiv 2023

  36. [36]

    Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A$^*$

    S. Vagnozzi et al., Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A, Class. Quant. Grav. 40, 165007 (2023), arXiv:2205.07787 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  37. [37]

    Experimental studies of black holes: status and fu- ture prospects,

    R. Genzel, F. Eisenhauer, and S. Gillessen, Experimental studies of black holes: status and future prospects, Astron. Astrophys. Rev. 32, 3 (2024), arXiv:2404.03522 [astro-ph.GA]

    work page arXiv 2024

  38. [38]

    Ayzenberg et al., Fundamental Physics Opportunities with the Next-Generation Event Horizon Telescope, arXiv preprint (2023), arXiv:2312.02130 [astro-ph.HE]

    D. Ayzenberg et al., Fundamental Physics Opportunities with the Next-Generation Event Horizon Telescope, arXiv preprint (2023), arXiv:2312.02130 [astro-ph.HE]. 19

    work page arXiv 2023

  39. [39]

    Afshordi et al., Black Holes Inside and Out 2024: visions for the future of black hole physics (2024) arXiv:2410.14414 [gr-qc]

    N. Afshordi et al., Black Holes Inside and Out 2024: visions for the future of black hole physics (2024) arXiv:2410.14414 [gr-qc]

    work page arXiv 2024

  40. [40]

    J. C. McKinney, A. Tchekhovskoy, and R. D. Blandford, General Relativistic Magnetohydrodynamic Simulations of Magnetically Choked Accretion Flows around Black Holes, Mon. Not. Roy. Astron. Soc. 423, 3083 (2012), arXiv:1201.4163 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  41. [41]

    General relativistic magnetohydrodynamical simulations of the jet in M87

    M. Moscibrodzka, H. Falcke, and H. Shiokawa, General relativistic magnetohydrodynamical simulations of the jet in M 87, Astron. Astrophys. 586, A38 (2016), arXiv:1510.07243 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  42. [42]

    Chatterjee, Z

    K. Chatterjee, Z. Younsi, M. Liska, A. Tchekhovskoy, S. B. Markoff, D. Yoon, D. van Eijnatten, C. Hesp, A. Ingram, and M. van der Klis, Observational signatures of disc and jet misalignment in images of accreting black holes, Mon. Not. Roy. Astron. Soc. 499, 362 (2020), arXiv:2002.08386 [astro-ph.GA]

    work page arXiv 2020

  43. [43]

    S. M. Ressler, C. J. White, E. Quataert, and J. M. Stone, Ab Initio Horizon-Scale Simulations of Magnetically Arrested Accretion in Sagittarius A* Fed by Stellar Winds, Astrophys. J. Lett. 896, L6 (2020), arXiv:2006.00005 [astro-ph.HE]

    work page arXiv 2020

  44. [44]

    S. E. Gralla, D. E. Holz, and R. M. Wald, Black Hole Shadows, Photon Rings, and Lensing Rings, Phys. Rev. D 100, 024018 (2019), arXiv:1906.00873 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  45. [45]

    C. A. R. Herdeiro, A. M. Pombo, E. Radu, P. V. P. Cunha, and N. Sanchis-Gual, The imitation game: Proca stars that can mimic the Schwarzschild shadow, JCAP 04, 051, arXiv:2102.01703 [gr-qc]

    work page arXiv

  46. [46]

    P. L. B. de S´ a, H. C. D. Lima, Jr., C. A. R. Herdeiro, and L. C. B. Crispino, Static boson stars in the Einstein-Friedberg- Lee-Sirlin theory and their astrophysical images, Phys. Rev. D 110, 104047 (2024), arXiv:2406.02695 [gr-qc]

    work page arXiv 2024

  47. [47]

    Vagnozzi and L

    S. Vagnozzi and L. Visinelli, Hunting for extra dimensions in the shadow of M87*, Phys. Rev. D 100, 024020 (2019), arXiv:1905.12421 [gr-qc]

    work page arXiv 2019

  48. [48]

    Banerjee, S

    I. Banerjee, S. Chakraborty, and S. SenGupta, Silhouette of M87*: A New Window to Peek into the World of Hidden Dimensions, Phys. Rev. D 101, 041301 (2020), arXiv:1909.09385 [gr-qc]

    work page arXiv 2020

  49. [49]

    P. V. P. Cunha, C. A. R. Herdeiro, and E. Radu, EHT constraint on the ultralight scalar hair of the M87 supermassive black hole, Universe 5, 220 (2019), arXiv:1909.08039 [gr-qc]

    work page arXiv 2019

  50. [50]

    R. A. Konoplya, Shadow of a black hole surrounded by dark matter, Phys. Lett. B 795, 1 (2019), arXiv:1905.00064 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  51. [51]

    J. Peng, M. Guo, and X.-H. Feng, Influence of quantum correction on black hole shadows, photon rings, and lensing rings, Chin. Phys. C 45, 085103 (2021), arXiv:2008.00657 [gr-qc]

    work page arXiv 2021

  52. [52]

    Zeng and H.-Q

    X.-X. Zeng and H.-Q. Zhang, Influence of quintessence dark energy on the shadow of black hole, Eur. Phys. J. C 80, 1058 (2020), arXiv:2007.06333 [gr-qc]

    work page arXiv 2020

  53. [53]

    Kumar and S

    R. Kumar and S. G. Ghosh, Rotating black holes in 4 D Einstein-Gauss-Bonnet gravity and its shadow, JCAP 07, 053, arXiv:2003.08927 [gr-qc]

    work page arXiv 2003

  54. [54]

    Innermost stable circular orbit and shadow of the 4 D Einstein–Gauss–Bonnet black hole,

    M. Guo and P.-C. Li, Innermost stable circular orbit and shadow of the 4 D Einstein–Gauss–Bonnet black hole, Eur. Phys. J. C 80, 588 (2020), arXiv:2003.02523 [gr-qc]

    work page arXiv 2020

  55. [55]

    Zeng, H.-Q

    X.-X. Zeng, H.-Q. Zhang, and H. Zhang, Shadows and photon spheres with spherical accretions in the four-dimensional Gauss–Bonnet black hole, Eur. Phys. J. C 80, 872 (2020), arXiv:2004.12074 [gr-qc]

    work page arXiv 2020

  56. [56]

    Li and K.-J

    G.-P. Li and K.-J. He, Shadows and rings of the Kehagias-Sfetsos black hole surrounded by thin disk accretion, JCAP 06, 037, arXiv:2105.08521 [gr-qc]

    work page arXiv

  57. [57]

    Guerrero, G

    M. Guerrero, G. J. Olmo, D. Rubiera-Garcia, and D. S.-C. G´ omez, Shadows and optical appearance of black bounces illuminated by a thin accretion disk, JCAP 08, 036, arXiv:2105.15073 [gr-qc]

    work page arXiv

  58. [58]

    Khodadi, G

    M. Khodadi, G. Lambiase, and D. F. Mota, No-hair theorem in the wake of Event Horizon Telescope, JCAP 09, 028, arXiv:2107.00834 [gr-qc]

    work page arXiv

  59. [59]

    J. Yang, C. Zhang, and Y. Ma, Shadow and stability of quantum-corrected black holes, Eur. Phys. J. C 83, 619 (2023), arXiv:2211.04263 [gr-qc]

    work page arXiv 2023

  60. [60]

    B.-H. Lee, W. Lee, and Y. S. Myung, Shadow cast by a rotating black hole with anisotropic matter, Phys. Rev. D 103, 064026 (2021), arXiv:2101.04862 [gr-qc]

    work page arXiv 2021

  61. [61]

    Li and X.-M

    Y.-Z. Li and X.-M. Kuang, Precession of bounded orbits and shadow in quantum black hole spacetime, Phys. Rev. D 107, 064052 (2023)

    work page 2023

  62. [62]

    Li, Observational Features of Thin Accretion Disk Around Rotating Regular Black Hole, arXiv preprint (2024), arXiv:2412.08447 [gr-qc]

    Z. Li, Observational Features of Thin Accretion Disk Around Rotating Regular Black Hole, arXiv preprint (2024), arXiv:2412.08447 [gr-qc]

    work page arXiv 2024

  63. [63]

    M. Guerrero, The optical appearance of compact stars: Shadows and luminous rings, in Gravity, Cosmology, and Astrophysics: A Journey of Exploration and Discovery with Female Pioneers , edited by B. Hartmann and J. Kunz (Springer Nature Switzerland, 2023) pp. 101–121

    work page 2023

  64. [64]

    X.-J. Wang, Y. Meng, X.-M. Kuang, and K. Liao, Distinguishing black holes with and without spontaneous scalarization in Einstein-scalar-Gauss–Bonnet theories via optical features, Eur. Phys. J. C 84, 1243 (2024), arXiv:2409.20200 [gr-qc]

    work page arXiv 2024

  65. [65]

    Sui, Z.-L

    T.-T. Sui, Z.-L. Wang, and W.-D. Guo, The effect of scalar hair on the charged black hole with the images from accretions disk, Eur. Phys. J. C 84, 441 (2024), arXiv:2311.10946 [gr-qc]

    work page arXiv 2024

  66. [66]

    Y. Xu, H. Huang, M.-Y. Lai, and D.-C. Zou, Identifying doppelgange Black Holes through Shadow Images, arXiv preprint (2024), arXiv:2407.06562 [gr-qc]

    work page arXiv 2024

  67. [67]

    Huang, J

    H. Huang, J. Kunz, and D. Mitra, Shadow images of compact objects in beyond Horndeski theory, JCAP 05, 007, arXiv:2401.15249 [gr-qc]

    work page arXiv

  68. [68]

    Y. Hou, J. Huang, Y. Mizuno, M. Guo, and B. Chen, Unique Imprint of Black Hole Spin on the Polarization of Near-Horizon Images, arXiv preprint (2024), arXiv:2409.07248 [gr-qc]

    work page arXiv 2024

  69. [69]

    Meng, X.-M

    Y. Meng, X.-M. Kuang, X.-J. Wang, B. Wang, and J.-P. Wu, Images from disk and spherical accretions of hairy Schwarzschild black holes, Phys. Rev. D 108, 064013 (2023), arXiv:2306.10459 [gr-qc]. 20

    work page arXiv 2023

  70. [70]

    Zeng, K.-J

    X.-X. Zeng, K.-J. He, J. Pu, G.-p. Li, and Q.-Q. Jiang, Holographic Einstein rings of a Gauss–Bonnet AdS black hole, Eur. Phys. J. C 83, 897 (2023), arXiv:2302.03692 [gr-qc]

    work page arXiv 2023

  71. [71]

    Z. Tu, M. Tang, and Z. Xu, Short-hair black holes and the strong cosmic censorship conjecture, Eur. Phys. J. C 84, 1275 (2024), arXiv:2410.03327 [gr-qc]

    work page arXiv 2024

  72. [72]

    C. Chen, Q. Pan, and J. Jing, Precessions of spherical orbits in the rotating Melvin black hole spacetime and its constraints from the jet of M87*, arXiv preprint (2024), arXiv:2410.09022 [gr-qc]

    work page arXiv 2024

  73. [73]

    Y. Chen, L. Cheng, P. Wang, and H. Yang, Polarized Image of a Synchrotron-emitting Ring in Einstein-Maxwell-scalar Theory, arXiv preprint (2024), arXiv:2409.05304 [gr-qc]

    work page arXiv 2024

  74. [74]

    Wei, Y.-C

    S.-W. Wei, Y.-C. Zou, Y.-P. Zhang, and Y.-X. Liu, Constraining black hole parameters with the precessing jet nozzle of M87*, Phys. Rev. D 110, 064006 (2024), arXiv:2401.17689 [gr-qc]

    work page arXiv 2024

  75. [75]

    Y. S. Myung, Photon ring bounds of scalar hairy charged black holes, Gen. Rel. Grav. 56, 60 (2024), arXiv:2401.08200 [gr-qc]

    work page arXiv 2024

  76. [76]

    Kumar Walia, S

    R. Kumar Walia, S. G. Ghosh, and S. D. Maharaj, Testing Rotating Regular Metrics with EHT Results of Sgr A*, Astrophys. J. 939, 77 (2022), arXiv:2207.00078 [gr-qc]

    work page arXiv 2022

  77. [77]

    Zheng, M.-Q

    H.-B. Zheng, M.-Q. Wu, G.-P. Li, and Q.-Q. Jiang, Shadow and accretion disk images of Kerr-Newman black hole in modified gravity theory, arXiv preprint (2024), arXiv:2411.10315 [gr-qc]

    work page arXiv 2024

  78. [78]

    Wang, Shadows and rings of a de Sitter–Schwarzschild black hole, Eur

    Z.-L. Wang, Shadows and rings of a de Sitter–Schwarzschild black hole, Eur. Phys. J. Plus138, 1131 (2023), arXiv:2307.12361 [gr-qc]

    work page arXiv 2023

  79. [79]

    M. A. Raza, M. Zubair, F. Atamurotov, and A. Abdujabbarov, Probing Loop Quantum Gravity via Kerr Black Hole and EHT Results, arXiv preprint (2025), arXiv:2501.01308 [gr-qc]

    work page arXiv 2025

  80. [80]

    Wu, E.-W

    B. Wu, E.-W. Liang, and X. Zhang, Algorithms for generating and analyzing black hole images based on the analytical equations of lightlike geodesics, arXiv preprint (2024), arXiv:2501.00361 [gr-qc]

    work page arXiv 2024

Showing first 80 references.