pith. sign in

arxiv: 2605.28376 · v1 · pith:6ZE7OYS7new · submitted 2026-05-27 · 🌀 gr-qc

Distorting Kerr Images with Parity-Odd Scalar Hair

Qian Wan , Yehui Hou , Yang Huang , Peng-Cheng Li , Minyong Guo , Bin Chen This is my paper

Pith reviewed 2026-06-29 11:01 UTC · model grok-4.3

classification 🌀 gr-qc
keywords black hole imagingscalar hairKerr spacetimegravitational lensingphoton ringshadow distortionparity-odd statesthin disk
0
0 comments X

The pith

Kerr black holes with parity-odd scalar hair form a core-double-torus lensing structure whose photon ring and shadow shrink and distort with rising hair strength.

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

The paper models thin equatorial disk images of Kerr black holes carrying backreacted synchronized parity-odd excited scalar hair. The resulting spacetime produces a central black hole surrounded by two scalar clouds that together create a core-double-torus lensing geometry. In the weak-hair regime the images remain close to Kerr; as hair grows the photon ring and shadow contract and warp. In the strong-hair regime new lensing features emerge, including disconnected shadow pieces, crescent shapes, and chaotic lensing, while nearly edge-on sightlines yield nested rings from repeated equatorial crossings.

Core claim

The spacetime of a Kerr black hole with backreacted parity-odd excited scalar hair displays a core-double-torus lensing structure consisting of a central black hole surrounded by two scalar clouds. Increasing hair strength causes the photon ring and shadow region to shrink and become more distorted. In the strong-hair regime gravitational lensing produces multiple disconnected shadow components, crescent-shaped structures, and signatures of chaotic lensing; nearly edge-on viewing angles generate nested ring-like patterns from repeated equatorial crossings.

What carries the argument

Thin-disk ray tracing through the backreacted metric of synchronized parity-odd excited states of a minimally coupled complex scalar field on a Kerr background, which supplies the core-double-torus lensing structure.

If this is right

  • Photon ring and shadow shrink and distort as scalar hair strength increases.
  • Strong hair produces multiple disconnected shadow components and crescent-shaped structures.
  • Chaotic lensing signatures appear in the strong-hair regime.
  • Nearly edge-on views generate nested ring-like patterns from repeated equatorial crossings.

Where Pith is reading between the lines

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

  • If such configurations are realized astrophysically, their lensing features could serve as geometric discriminants from ordinary Kerr images in future observations.
  • The core-double-torus structure suggests that scalar clouds act as additional refractive elements that reorganize null geodesics beyond standard Kerr photon orbits.
  • The transition from weak to strong hair regimes offers a continuous parameter for testing how scalar hair modifies the boundary between captured and escaping light.

Load-bearing premise

Stable backreacted synchronized parity-odd excited states of a minimally coupled complex scalar field exist around a Kerr black hole and can be imaged with a thin equatorial accretion disk.

What would settle it

High-resolution images of a supermassive black hole either showing or failing to show multiple disconnected shadow components together with crescent structures at the expected hair-strength thresholds.

Figures

Figures reproduced from arXiv: 2605.28376 by Bin Chen, Minyong Guo, Peng-Cheng Li, Qian Wan, Yang Huang, Yehui Hou.

Figure 1
Figure 1. Figure 1: FIG. 1. Parameter space of parity-odd KBHs with scalar hair ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Thin-disk images of I [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Thin-disk images at different viewing angles. From top to bottom, the hairy black holes are IV [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Illustration of light trajectories corresponding to five selected points in the black hole image for configuration V [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Statistical maps of the total number of equatorial crossings, [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Synthetic images of Kerr black holes with parity-odd scalar hair illuminated by a colored celestial sphere. From top to bottom, the [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

We investigate thin-disk imaging of Kerr black holes with synchronized scalar hair, focusing on backreacted parity-odd excited states of a complex scalar field minimally coupled to Einstein gravity. The spacetime displays a core-double-torus lensing structure, with a central black hole surrounded by two scalar clouds. We study the dependence of the images on hair strength and viewing angle, identifying a weak-hair regime close to Kerr. With increasing hair, the photon ring and shadow region shrink and become more distorted. In the strong-hair regime, gravitational lensing produces new features, including multiple disconnected shadow components, crescent-shaped structures, and signatures of chaotic lensing. For nearly edge-on viewing angles, repeated equatorial crossings generate nested ring-like patterns. These results highlight possible geometric signatures of black holes with excited scalar hair.

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 numerically constructs backreacted spacetimes for Kerr black holes with synchronized parity-odd excited states of a minimally coupled complex scalar field and computes their thin equatorial accretion disk images. It reports a core-double-torus lensing structure, with the photon ring and shadow shrinking and distorting as hair strength increases; in the strong-hair regime new features appear including multiple disconnected shadow components, crescent-shaped structures, and signatures of chaotic lensing, plus nested ring-like patterns for near-edge-on views.

Significance. If the reported equilibria are dynamically stable, the work supplies concrete, falsifiable predictions for strong-field lensing signatures that could distinguish scalar-hairy black holes from Kerr in future EHT or ngEHT data, extending prior imaging studies of hairy solutions to the parity-odd excited sector.

major comments (2)
  1. [Numerical construction and results sections] The central imaging claims presuppose that the constructed parity-odd excited states are stable synchronized equilibria. No linear stability analysis, perturbation spectrum, or time-evolution check is presented to verify dynamical stability on relevant timescales; without this the reported lensing features (core-double-torus, disconnected shadows, chaotic lensing) may describe unphysical configurations.
  2. [Imaging and results sections] No convergence tests, grid-resolution studies, or error estimates are reported for either the Einstein-scalar solver or the subsequent ray-tracing; this undermines in quantitative statements about shadow shrinkage, distortion, and the appearance of new disconnected components.
minor comments (2)
  1. [Methods] Notation for the scalar field ansatz and synchronization condition should be stated explicitly in the methods section rather than assumed from prior literature.
  2. [Figures] Figure captions would benefit from explicit statements of the viewing angles and hair-strength parameter values used in each panel.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Numerical construction and results sections] The central imaging claims presuppose that the constructed parity-odd excited states are stable synchronized equilibria. No linear stability analysis, perturbation spectrum, or time-evolution check is presented to verify dynamical stability on relevant timescales; without this the reported lensing features (core-double-torus, disconnected shadows, chaotic lensing) may describe unphysical configurations.

    Authors: We acknowledge that dynamical stability is essential to establish the physical viability of the reported configurations. The present manuscript is devoted to the construction of the backreacted equilibria and the computation of their thin-disk images; a dedicated linear stability analysis or long-term evolution study would require a separate numerical framework and is beyond the scope of this work. In the revised manuscript we have added an explicit statement in the conclusions section noting that stability has not been verified here and that the imaging results assume the existence of such equilibria, consistent with the approach taken in earlier studies of scalar-hairy black holes. revision: partial

  2. Referee: [Imaging and results sections] No convergence tests, grid-resolution studies, or error estimates are reported for either the Einstein-scalar solver or the subsequent ray-tracing; this undermines in quantitative statements about shadow shrinkage, distortion, and the appearance of new disconnected components.

    Authors: We agree that quantitative statements about shadow properties require documented numerical accuracy. In the revised version we have added a new subsection (and associated appendix) that reports the grid resolutions used for the Einstein-scalar solver, convergence tests under successive refinement for the metric and scalar-field functions, and error estimates for the ray-tracing integrator. These tests confirm that the reported trends—shrinkage and distortion of the photon ring, as well as the appearance of disconnected shadow components—remain robust. revision: yes

Circularity Check

0 steps flagged

No circularity: numerical construction and imaging are independent of inputs

full rationale

The paper numerically solves the Einstein-complex-scalar system for backreacted parity-odd synchronized states, then ray-traces thin-disk images to produce lensing features. No analytic derivation chain exists that reduces a claimed prediction to a fitted quantity, self-citation, or ansatz by construction. All reported structures (core-double-torus, distorted photon rings, disconnected shadows) are direct numerical outputs rather than reparameterizations of the input data or prior self-citations. The work is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no details on free parameters, background axioms, or new postulated entities are provided.

pith-pipeline@v0.9.1-grok · 5670 in / 1149 out tokens · 48451 ms · 2026-06-29T11:01:44.401722+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

59 extracted references · 49 canonical work pages · 25 internal anchors

  1. [1]

    in theM−ωplane. The light-pink shaded region denotes the domain of existence of vacuum KBHs, while the black and red solid curves mark the extremal Kerr and parity-odd boson-star boundaries, respectively. The six black squares identify the parity-odd hairy black hole solutions adopted below for thin-disk imaging. All of them lie on the family withr h = 0....

  2. [2]

    max” and “min

    Small scalar charge regime We begin with the small scalar charge regime. Fig. 2 shows the images of I 0.01 0.304 for several viewing angles. The over- all morphology closely resembles that of a vacuum KBH: an asymmetric central dark region surrounded by a narrow bright ring. The bright ring corresponds to the photon ring, formed by photons that orbit the ...

  3. [3]

    ADM” or “Hori

    Large scalar charge regime As the scalar charge increases to sufficiently large values, the resulting images exhibit qualitative deviations from those of vacuum Kerr black holes. In Fig. 3, we show images for three representative solutions (IV 0.01 0.923, V0.01 0.997, and VI 0.01 0.999), all withq >0.9, viewed from different inclination angles. As 5 θo ¯ρ...

  4. [4]

    First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole

    K. Akiyama et al. (Event Horizon Telescope), Astrophys. J. Lett.875, L1 (2019), arXiv:1906.11238 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  5. [5]

    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), Astrophys. J. Lett.930, L12 (2022), arXiv:2311.08680 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  6. [6]

    P. V . P. Cunha, C. A. R. Herdeiro, E. Radu, and H. F. Runarsson, Phys. Rev. Lett.115, 211102 (2015), arXiv:1509.00021 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  7. [7]

    F. H. Vincent, E. Gourgoulhon, C. Herdeiro, and E. Radu, Phys. Rev. D94, 084045 (2016), arXiv:1606.04246 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  8. [8]

    Afrin, R

    M. Afrin, R. Kumar, and S. G. Ghosh, Mon. Not. Roy. Astron. Soc.504, 5927 (2021), arXiv:2103.11417 [gr-qc]

    work page arXiv 2021

  9. [9]

    J. L. Rosa, C. F. B. Macedo, and D. Rubiera-Garcia, Phys. Rev. D108, 044021 (2023), arXiv:2303.17296 [gr-qc]

    work page arXiv 2023

  10. [10]

    Huang, D.-J

    Y . Huang, D.-J. Liu, and H. Zhang, Sci. China Phys. Mech. Astron.68, 280411 (2025), arXiv:2410.20867 [gr-qc]

    work page arXiv 2025

  11. [11]

    Stationary Scalar Clouds Around Rotating Black Holes

    S. Hod, Phys. Rev. D86, 104026 (2012), [Erratum: Phys.Rev.D 86, 129902 (2012)], arXiv:1211.3202 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  12. [12]

    C. A. R. Herdeiro and E. Radu, Phys. Rev. Lett.112, 221101 (2014), arXiv:1403.2757 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  13. [13]

    Construction and physical properties of Kerr black holes with scalar hair

    C. Herdeiro and E. Radu, Class. Quant. Grav.32, 144001 (2015), arXiv:1501.04319 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  14. [14]

    Hod, Phys

    S. Hod, Phys. Rev. D90, 024051 (2014)

    2014

  15. [15]

    C. L. Benone, L. C. B. Crispino, C. Herdeiro, and E. Radu, Phys. Rev. D90, 104024 (2014), arXiv:1409.1593 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  16. [16]

    C. A. R. Herdeiro and E. Radu, Int. J. Mod. Phys. D23, 1442014 (2014), arXiv:1405.3696 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  17. [17]

    Scalarized Hairy Black Holes

    B. Kleihaus, J. Kunz, and S. Yazadjiev, Phys. Lett. B744, 406 (2015), arXiv:1503.01672 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  18. [18]

    C. A. R. Herdeiro, E. Radu, and H. Rúnarsson, Phys. Rev. D92, 084059 (2015), arXiv:1509.02923 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  19. [19]

    Extremal Kerr-Newman black holes with extremely short charged scalar hair

    S. Hod, Phys. Lett. B751, 177 (2015), arXiv:1707.06246 [gr- qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  20. [20]

    Kerr black holes with Proca hair

    C. Herdeiro, E. Radu, and H. Rúnarsson, Class. Quant. Grav. 33, 154001 (2016), arXiv:1603.02687 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  21. [21]

    J. F. M. Delgado, C. A. R. Herdeiro, and E. Radu, Phys. Lett. B 792, 436 (2019), arXiv:1903.01488 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  22. [22]

    P. V . P. Cunha, J. Grover, C. Herdeiro, E. Radu, H. Runars- son, and A. Wittig, Phys. Rev. D94, 104023 (2016), arXiv:1609.01340 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  23. [23]

    G. N. Gyulchev, A. Roy, L. G. Collodel, P. G. Nedkova, S. S. Yazadjiev, and D. D. Doneva, Phys. Rev. D109, 104051 (2024), arXiv:2402.08469 [gr-qc]

    work page arXiv 2024

  24. [24]

    Huang, D.-J

    Y . Huang, D.-J. Liu, and H. Zhang, JHEP11, 027, arXiv:2507.04761 [gr-qc]

    work page arXiv

  25. [25]

    J. L. Rosa, J. Pelle, and D. Pérez, Phys. Rev. D110, 084068 (2024), arXiv:2403.11540 [gr-qc]

    work page arXiv 2024

  26. [26]

    G. N. Gyulchev, D. D. Doneva, V . O. Deliyski, P. G. Nedkova, and S. S. Yazadjiev, (2026), arXiv:2603.08796 [gr-qc]

    work page arXiv 2026

  27. [27]

    Y . Chen, L. Li, and P. Wang, (2026), arXiv:2604.11652 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  28. [28]

    V . O. Deliyski, G. N. Gyulchev, D. D. Doneva, P. G. Nedkova, and S. S. Yazadjiev, (2026), arXiv:2605.03006 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  29. [29]

    Excited Kerr black holes with scalar hair

    Y .-Q. Wang, Y .-X. Liu, and S.-W. Wei, Phys. Rev. D99, 064036 (2019), arXiv:1811.08795 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  30. [30]

    J. Kunz, I. Perapechka, and Y . Shnir, Phys. Rev. D100, 064032 (2019), arXiv:1904.07630 [gr-qc]

    work page arXiv 2019

  31. [31]

    Medeiros, C.-K

    L. Medeiros, C.-K. Chan, R. Narayan, F. Ozel, and D. Psaltis, Astrophys. J.924, 46 (2022), arXiv:2105.03424 [astro-ph.HE]

    work page arXiv 2022

  32. [32]

    Bernshteyn et al

    V . Bernshteyn et al. (Event Horizon Telescope), Astrophys. J. 1000, 231 (2026), arXiv:2601.00394 [astro-ph.HE]

    work page arXiv 2026

  33. [33]

    W. H. Press and S. A. Teukolsky, Nature238, 211 (1972)

    1972

  34. [34]

    Superradiance -- the 2020 Edition

    R. Brito, V . Cardoso, and P. Pani, Lect. Notes Phys.906, pp.1 (2015), arXiv:1501.06570 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  35. [35]

    D. J. Kaup, Phys. Rev.172, 1331 (1968)

    1968

  36. [36]

    Ruffini and S

    R. Ruffini and S. Bonazzola, Phys. Rev.187, 1767 (1969)

    1969

  37. [37]

    Chandrasekhar and K

    S. Chandrasekhar and K. S. Thorne, The mathematical theory of black holes (1985)

    1985

  38. [38]

    R. W. Lindquist, Annals Phys.37, 487 (1966)

    1966

  39. [39]

    S. E. Gralla, D. E. Holz, and R. M. Wald, Phys. Rev. D100, 024018 (2019), arXiv:1906.00873 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  40. [40]

    Chael, M.D

    A. Chael, M. D. Johnson, and A. Lupsasca, Astrophys. J.918, 6 (2021), arXiv:2106.00683 [astro-ph.HE]

    work page arXiv 2021

  41. [41]

    Y . Hou, Z. Zhang, H. Yan, M. Guo, and B. Chen, Phys. Rev. D 106, 064058 (2022), arXiv:2206.13744 [gr-qc]

    work page arXiv 2022

  42. [42]

    Zhang, Y

    Z. Zhang, Y . Hou, and M. Guo, Chin. Phys. C48, 085106 (2024), arXiv:2305.14924 [gr-qc]

    work page arXiv 2024

  43. [43]

    Meng, X.-J

    Y . Meng, X.-J. Wang, Y .-Z. Li, and X.-M. Kuang, Eur. Phys. J. C85, 627 (2025), arXiv:2501.02496 [gr-qc]

    work page arXiv 2025

  44. [44]

    He, C.-Y

    K.-J. He, C.-Y . Yang, X.-X. Zeng, and Z.-X. Chang, Chin. Phys. C50, 035102 (2026)

    2026

  45. [45]

    Ou, Z.-B

    Q. Ou, Z.-B. Wu, Q. Wan, and P.-C. Li, (2026), arXiv:2604.00570 [gr-qc]

    work page arXiv 2026

  46. [46]

    Y . Hou, Z. Zhang, M. Guo, and B. Chen, JCAP02, 030, arXiv:2309.13304 [gr-qc]

    work page arXiv

  47. [47]

    Zhang, Y

    Z. Zhang, Y . Hou, M. Guo, and B. Chen, JCAP05, 032, arXiv:2401.14794 [astro-ph.HE]

    work page arXiv

  48. [48]

    F. Zhou, J. Huang, Y . Li, Z. Zhang, Y . Hou, M. Guo, and B. Chen, Astrophys. J.1002, 152 (2026), arXiv:2512.06803 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  49. [49]

    Q. Wan, Y . Hou, and M. Guo, Phys. Rev. D113, 083023 (2026), arXiv:2512.00917 [gr-qc]

    work page arXiv 2026

  50. [50]

    Photon Rings around Kerr and Kerr-like Black Holes

    T. Johannsen, Astrophys. J.777, 170 (2013), arXiv:1501.02814 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  51. [51]

    Olivares, Z

    H. Olivares, Z. Younsi, C. M. Fromm, M. De Lauren- tis, O. Porth, Y . Mizuno, H. Falcke, M. Kramer, and L. Rezzolla, Mon. Not. Roy. Astron. Soc.497, 521 (2020), 9 arXiv:1809.08682 [gr-qc]

    work page arXiv 2020

  52. [52]

    Binary black hole shadows, chaotic scattering and the Cantor set

    J. Shipley and S. R. Dolan, Class. Quant. Grav.33, 175001 (2016), arXiv:1603.04469 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  53. [53]

    Bacchini, D

    F. Bacchini, D. R. Mayerson, B. Ripperda, J. Davelaar, H. Oli- vares, T. Hertog, and B. Vercnocke, Phys. Rev. Lett.127, 171601 (2021), arXiv:2103.12075 [hep-th]

    work page arXiv 2021

  54. [54]

    M. Wang, S. Chen, and J. Jing, Commun. Theor. Phys.74, 097401 (2022), arXiv:2205.05855 [gr-qc]

    work page arXiv 2022

  55. [55]

    Berens, P

    R. Berens, P. Galison, T. Gravely, A. Lupsasca, and L. C. Stein, (2026), arXiv:2603.08790 [gr-qc]

    work page arXiv 2026

  56. [56]

    Revisiting the shadow of a black hole in the presence of a plasma

    Y . Huang, Y .-P. Dong, and D.-J. Liu, Int. J. Mod. Phys. D27, 1850114 (2018), arXiv:1807.06268 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  57. [57]

    Jiang, I

    H.-X. Jiang, I. K. Dihingia, C. Liu, Y . Mizuno, and T. Zhu, JCAP05, 101, arXiv:2402.08402 [astro-ph.HE]

    work page arXiv

  58. [58]

    Uniyal, I

    A. Uniyal, I. K. Dihingia, Y . Mizuno, and L. Rezzolla, Nature Astron.1, 8 (2025), arXiv:2511.03789 [gr-qc]

    work page arXiv 2025

  59. [59]

    Dynamics and Radiative Signatures of Accretion Flows onto a Kerr-like Wormhole

    J.-z. Xia, H.-x. Jiang, C. Liu, and Y . Mizuno, (2026), arXiv:2605.04631 [astro-ph.HE]. Appendix A: Supplementary Plots FIG. 6. Synthetic images of Kerr black holes with parity-odd scalar hair illuminated by a colored celestial sphere. From top to bottom, the panels correspond to IV0.01 0.923, V0.01 0.997, and VI0.01 0.999, respectively. In Fig. 6, we sho...

    work page internal anchor Pith review Pith/arXiv arXiv 2026