- Access by Xinjiang University
Distorting Kerr images with parity-odd scalar hair
Phys. Rev. D 114, 084012 – Published 5 October, 2026
DOI: https://doi.org/10.1103/f3wb-bv6m
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 scalar energy density is concentrated in two reflection-symmetric, off-equatorial toroidal regions surrounding the black hole core. We study the dependence of the images on hair strength and viewing angle, identifying a weak-hair regime close to the Kerr limit. With increasing hair fraction, 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 ringlike patterns. These results highlight possible geometric signatures of black holes with excited scalar hair.
Physics Subject Headings (PhySH)
Article Text
References (62)
- K. Akiyama et al. (Event Horizon Telescope Collaboration), First M87 event horizon telescope results. I. The shadow of the supermassive black hole, Astrophys. J. Lett. 875, L1 (2019).
- K. Akiyama et al. (Event Horizon Telescope Collaboration), 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).
- M. D. Johnson et al., Key science goals for the next-generation event horizon telescope, Galaxies 11, 61 (2023).
- D. Ayzenberg et al., Fundamental physics opportunities with future ground-based mm/sub-mm VLBI arrays, Living Rev. Relativity 28, 4 (2025); 28, 7(E) (2025).
- M. D. Johnson et al., The Black Hole explorer: Motivation and vision, Proc. SPIE Int. Soc. Opt. Eng. 13092, 130922D (2024).
- Carlos A. R. Herdeiro and E. Radu, Kerr black holes with scalar hair, Phys. Rev. Lett. 112, 221101 (2014).
- C. Herdeiro and E. Radu, Construction and physical properties of Kerr black holes with scalar hair, Classical Quantum Gravity 32, 144001 (2015).
- C. A. R. Herdeiro and E. Radu, A new spin on black hole hair, Int. J. Mod. Phys. D 23, 1442014 (2014).
- B. Kleihaus, J. Kunz, and S. Yazadjiev, Scalarized hairy black holes, Phys. Lett. B 744, 406 (2015).
- Carlos A. R. Herdeiro, E. Radu, and H. Rúnarsson, Kerr black holes with self-interacting scalar hair: Hairier but not heavier, Phys. Rev. D 92, 084059 (2015).
- S. Hod, Extremal Kerr–Newman black holes with extremely short charged scalar hair, Phys. Lett. B 751, 177 (2015).
- C. Herdeiro, E. Radu, and H. Rúnarsson, Kerr black holes with Proca hair, Classical Quantum Gravity 33, 154001 (2016).
- J. F. M. Delgado, C. A. R. Herdeiro, and E. Radu, Kerr black holes with synchronised scalar hair and higher azimuthal harmonic index, Phys. Lett. B 792, 436 (2019).
- S. Hod, Stationary scalar clouds around rotating black holes, Phys. Rev. D 86, 104026 (2012); 86, 129902(E) (2012).
- S. Hod, Kerr-Newman black holes with stationary charged scalar clouds, Phys. Rev. D 90, 024051 (2014).
- C. L. Benone, Luis C. B. Crispino, C. Herdeiro, and E. Radu, Kerr-Newman scalar clouds, Phys. Rev. D 90, 104024 (2014).
- B. Ganchev and J. E. Santos, Scalar hairy black holes in four dimensions are unstable, Phys. Rev. Lett. 120, 171101 (2018).
- W. E. East, Massive boson superradiant instability of black holes: Nonlinear growth, saturation, and gravitational radiation, Phys. Rev. Lett. 121, 131104 (2018).
- 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).
- J. A. Carretero, P. Grandclément, C. Palenzuela, and M. Salgado, Nonlinear stability of rotating hairy black holes, Phys. Rev. D 113, 064059 (2026).
- J. Nicoules, J. Ferreira, Carlos A. R. Herdeiro, E. Radu, and M. Zilhão, Splitting the gravitational atom: Instabilities of black holes with synchronized or resonant hair, Phys. Rev. D 113, L061507 (2026).
- Pedro V. P. Cunha, Carlos A. R. Herdeiro, E. Radu, and H. F. Runarsson, Shadows of Kerr black holes with scalar hair, Phys. Rev. Lett. 115, 211102 (2015).
- F. H. Vincent, E. Gourgoulhon, C. Herdeiro, and E. Radu, Astrophysical imaging of Kerr black holes with scalar hair, Phys. Rev. D 94, 084045 (2016).
- P. V. P. Cunha, J. Grover, C. Herdeiro, E. Radu, H. Runarsson, and A. Wittig, Chaotic lensing around boson stars and Kerr black holes with scalar hair, Phys. Rev. D 94, 104023 (2016).
- G. N. Gyulchev, L. G. Collodel, S. S. Yazadjiev, D. D. Doneva, and P. G. Nedkova, Images of a thin accretion disk around Kerr Black Hole with synchronized scalar hair, J. Phys. Conf. Ser. 3002, 012002 (2025).
- G. N. Gyulchev, D. D. Doneva, V. O. Deliyski, P. G. Nedkova, and S. S. Yazadjiev, Images of the thin accretion disk around Kerr black holes coupled to time periodic scalar fields, Phys. Rev. D 114, 024074 (2026).
- V. O. Deliyski, G. N. Gyulchev, D. D. Doneva, P. G. Nedkova, and S. S. Yazadjiev, Polarized equatorial emission around Kerr black holes with synchronized scalar hair. I. Direct images, Eur. Phys. J. C 86, 908 (2026).
- M. Afrin, R. Kumar, and S. G. Ghosh, Parameter estimation of hairy Kerr black holes from its shadow and constraints from M87*, Mon. Not. R. Astron. Soc. 504, 5927 (2021).
- G. N. Gyulchev, A. Roy, L. G. Collodel, P. G. Nedkova, S. S. Yazadjiev, and D. D. Doneva, Shadows of rotating hairy Kerr black holes coupled to time periodic scalar fields with a nonflat target space, Phys. Rev. D 109, 104051 (2024).
- Y. Chen, L. Li, and P. Wang, Optical appearance of scalarized Kerr-Newman black holes with multiple light rings, arXiv:2604.11652.
- Y.-Q. Wang, Y.-X. Liu, and S.-W. Wei, Excited Kerr black holes with scalar hair, Phys. Rev. D 99, 064036 (2019).
- J. Kunz, I. Perapechka, and Y. Shnir, Kerr black holes with parity-odd scalar hair, Phys. Rev. D 100, 064032 (2019).
- Y. Huang, D.-J. Liu, and H. Zhang, Dynamics of photons and shadows for black holes haired with parity-odd fields, J. High Energy Phys. 11 (2025) 027.
- W. H. Press and S. A. Teukolsky, Floating orbits, superradiant scattering and the black-hole bomb, Nature (London) 238, 211 (1972).
- R. Brito, V. Cardoso, and P. Pani, Superradiance: New frontiers in black hole physics, Lect. Notes Phys. 906, 1 (2015).
- Y. Huang, D.-J. Liu, and H. Zhang, Lensing and light rings of parity-odd rotating boson stars, Sci. China Phys. Mech. Astron. 68, 280411 (2025).
- D. J. Kaup, Klein-Gordon Geon, Phys. Rev. 172, 1331 (1968).
- R. Ruffini and S. Bonazzola, Systems of selfgravitating particles in general relativity and the concept of an equation of state, Phys. Rev. 187, 1767 (1969).
- S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford University Press, New York, 1983).
- R. W. Lindquist, Relativistic transport theory, Ann. Phys. (N.Y.) 37, 487 (1966).
- S. E. Gralla, D. E. Holz, and R. M. Wald, Black hole shadows, photon rings, and lensing rings, Phys. Rev. D 100, 024018 (2019).
- A. Chael, M. D. Johnson, and A. Lupsasca, Observing the inner shadow of a black hole: A direct view of the event horizon, Astrophys. J. 918, 6 (2021).
- Y. Hou, Z. Zhang, H. Yan, M. Guo, and B. Chen, Image of a Kerr-Melvin black hole with a thin accretion disk, Phys. Rev. D 106, 064058 (2022).
- Z. Zhang, Y. Hou, and M. Guo, Observational signatures of rotating black holes in the semiclassical gravity with trace anomaly*, Chin. Phys. C 48, 085106 (2024).
- Y. Meng, X.-J. Wang, Y.-Z. Li, and X.-M. Kuang, Effects of hair on the image of a rotating black hole illuminated by a thin accretion disk, Eur. Phys. J. C 85, 627 (2025).
- K.-J. He, C.-Y. Yang, X.-X. Zeng, and Z.-X. Chang, Shadow images of a rotating black hole in Kalb-Ramond gravity surrounded by the thin accretion disk*, Chin. Phys. C 50, 035102 (2026).
- Q. Ou, Z.-B. Wu, Q. Wan, and P.-C. Li, Probing lorentz-violating effects via precession and accretion disk images of a rotating bumblebee black hole, J. Cosmol. Astropart. Phys. 08 (2026) 080.
- Y. Hou, Z. Zhang, M. Guo, and B. Chen, Dark matter from primordial black holes would hold charge, J. Cosmol. Astropart. Phys. 02 (2023) 030.
- Z. Zhang, Y. Hou, M. Guo, and B. Chen, Imaging thick accretion disks and jets surrounding black holes, J. Cosmol. Astropart. Phys. 05 (2024) 032.
- F. Zhou, J. Huang, Y. Li, Z. Zhang, Y. Hou, M. Guo, and B. Chen, Nonthermal synchrotron emission and polarization signatures during black hole flux eruptions, Astrophys. J. 1002, 152 (2026).
- Q. Wan, Y. Hou, and M. Guo, Probing the scalar hair of rotating Horndeski black holes through thick disk images, Phys. Rev. D 113, 083023 (2026).
- T. Johannsen, Photon Rings around Kerr and Kerr-like Black Holes, Astrophys. J. 777, 170 (2013).
- H. Olivares, Z. Younsi, C. M. Fromm, M. De Laurentis, O. Porth, Y. Mizuno, H. Falcke, M. Kramer, and L. Rezzolla, How to tell an accreting boson star from a black hole, Mon. Not. R. Astron. Soc. 497, 521 (2020).
- J. L. Rosa, Caio F. B. Macedo, and D. Rubiera-Garcia, Imaging compact boson stars with hot spots and thin accretion disks, Phys. Rev. D 108, 044021 (2023).
- M. Wang, S. Chen, and J. Jing, Chaotic shadows of black holes: a short review, Commun. Theor. Phys. 74, 097401 (2022).
- R. Berens, P. Galison, T. Gravely, A. Lupsasca, and L. C. Stein, Chaos and fractals of the black hole photon ring, arXiv:2603.08790.
- J. Shipley and S. R. Dolan, Binary black hole shadows, chaotic scattering and the Cantor set, Classical Quantum Gravity 33, 175001 (2016).
- F. Bacchini, D. R. Mayerson, B. Ripperda, J. Davelaar, H. Olivares, T. Hertog, and B. Vercnocke, Fuzzball shadows: Emergent horizons from microstructure, Phys. Rev. Lett. 127, 171601 (2021).
- Y. Huang, Y.-P. Dong, and D.-J. Liu, Revisiting the shadow of a black hole in the presence of a plasma, Int. J. Mod. Phys. D 27, 1850114 (2018).
- H.-X. Jiang, I. K. Dihingia, C. Liu, Y. Mizuno, and T. Zhu, Enhanced Blandford Znajek jet in loop quantum black hole, J. Cosmol. Astropart. Phys. 05 (2024) 101.
- A. Uniyal, I. K. Dihingia, Y. Mizuno, and L. Rezzolla, The future ability to test theories of gravity with black-hole shadows, Nat. Astron. 1, 8 (2025).
- J.-z. Xia, H.-x. Jiang, C. Liu, and Y. Mizuno, Evidence for dynamical filtering: High binary fraction, hard-binary excess, and unresolved triples in the surviving core of NGC 6791, Astrophys. J. 1003, 203 (2026).