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Images of the thin accretion disk around Kerr black holes coupled to time periodic scalar fields

Galin N. Gyulchev1,2,*, Daniela D. Doneva3,4,†, Valentin O. Deliyski1,‡, Petya G. Nedkova1,§, and Stoytcho S. Yazadjiev1,5,∥

  • *Contact author: gyulchev@phys.uni-sofia.bg
  • †Contact author: daniela.doneva@uv.es
  • ‡Contact author: valentin.deliyski@phys.uni-sofia.bg
  • §Contact author: pnedkova@phys.uni-sofia.bg
  • ∥Contact author: yazad@phys.uni-sofia.bg
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Phys. Rev. D 114, 024074 – Published 27 July, 2026

DOI: https://doi.org/10.1103/3xwd-4p4w

Abstract

We investigate the orbital structure and observable appearance of rotating Kerr black holes endowed with synchronized scalar hair described by two time-periodic scalar fields with a flat target-space geometry. The presence of scalar hair enriches the geodesic structure of the spacetime relative to the Kerr case and significantly modifies the emission properties of geometrically thin Novikov-Thorne accretion disks. Combining an analysis of timelike circular orbits with backward ray tracing, we show that the normalized Noether charge governs the morphology and luminosity of both prograde and counterrotating disks. In the strongly scalarized regime, additional light rings and modified circular-orbit regions produce multiple inner emitting zones and strongly enhanced redshift patterns that depart markedly from the Kerr prediction. The most pronounced deviations occur in the counterrotating sector, where scalar hair generates inner retrograde radiative rings with substantially enhanced luminosity and distinctive frequency-shift signatures. Even when the spacetime approaches the Kerr geometry at weaker scalarization, the retrograde disk remains highly sensitive to the presence of scalar hair. Our results demonstrate that geometrically thin accretion disks can provide robust observational diagnostics of synchronized scalar hair and may offer a promising avenue for testing tensor-multiscalar gravity with future horizon-scale black-hole imaging observations.

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References (44)

  1. S. Hod, Stationary scalar clouds around rotating black holes, Phys. Rev. D 86, 104026 (2012).
  2. C. A. Herdeiro and E. Radu, Kerr black holes with scalar hair, Phys. Rev. Lett. 112, 221101 (2014).
  3. C. Herdeiro and E. Radu, Construction and physical properties of Kerr black holes with scalar hair, Classical Quantum Gravity 32, 144001 (2015).
  4. C. 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).
  5. Y. Brihaye, C. Herdeiro, and E. Radu, Inside black holes with synchronized hair, Phys. Lett. B 760, 279 (2016).
  6. J. F. Delgado, C. A. Herdeiro, E. Radu, and H. Rúnarsson, Kerr-Newman black holes with scalar hair, Phys. Lett. B 761, 234 (2016).
  7. T. Damour and G. Esposito-Farese, Tensor multiscalar theories of gravitation, Classical Quantum Gravity 9, 2093 (1992).
  8. M. Horbatsch, H. O. Silva, D. Gerosa, P. Pani, E. Berti, L. Gualtieri, and U. Sperhake, Tensor-multi-scalar theories: Relativistic stars and 3+1 decomposition, Classical Quantum Gravity 32, 204001 (2015).
  9. L. G. Collodel, D. D. Doneva, and S. S. Yazadjiev, Rotating tensor-multiscalar black holes with two scalars, Phys. Rev. D 102, 084032 (2020).
  10. The Event Horizon Telescope Collaboration, First M87 Event Horizon Telescope results. IV. Imaging the central supermassive black hole, Astrophys. J. Lett. 875, L4 (2019).
  11. The Event Horizon Telescope Collaboration, First Sagittarius a* Event Horizon Telescope results. II. EHT and multiwavelength observations, data processing, and calibration, Astrophys. J. Lett. 930, L13 (2022).
  12. J. Nicoules, J. Ferreira, C. A. R. Herdeiro, E. Radu, and M. Zilhão, Splitting the gravitational atom: Instabilities of black holes with synchronized/resonant hair, Phys. Rev. D 113, L061507 (2026).
  13. P. V. Cunha, C. A. Herdeiro, E. Radu, and H. F. Rúnarsson, Shadows of Kerr black holes with scalar hair, Phys. Rev. Lett. 115, 211102 (2015).
  14. P. V. Cunha, C. A. Herdeiro, E. Radu, and H. F. Runarsson, Shadows of Kerr black holes with and without scalar hair, Int. J. Mod. Phys. D 25, 1641021 (2016).
  15. 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).
  16. I. D. Novikov and K. S. Thorne, Astrophysics of black holes, in Black Holes (Les Astres Occlus), edited by C. DeWitt and B. DeWitt (Gordon and Breach, New York, 1973), pp. 343–450.
  17. D. N. Page and K. S. Thorne, Disk-accretion onto a black hole. time-averaged structure of accretion disk, Astrophys. J. 191, 499 (1974).
  18. J. M. Bardeen and J. A. Petterson, The lense-thirring effect and accretion disks around Kerr black holes, Astrophys. J. Lett. 195, L65 (1975).
  19. P. A. G. Scheuer and R. Feiler, On the bardeen–petterson effect, Mon. Not. R. Astron. Soc. 282, 291 (1996).
  20. A. R. King and J. E. Pringle, Growing supermassive black holes by chaotic accretion, Mon. Not. R. Astron. Soc. 373, L90 (2006).
  21. C. Nixon, A. King, and D. Price, Tearing up the disc: Misaligned accretion on to a binary, Mon. Not. R. Astron. Soc. 422, 2547 (2012).
  22. N. C. Stone and B. D. Metzger, Rates of stellar tidal disruption as probes of the supermassive black hole mass function, Mon. Not. R. Astron. Soc. 455, 859 (2016).
  23. J. P. Luminet, Image of a spherical black hole with thin accretion disk, Astron. Astrophys. 75, 228 (1979), https://ui.adsabs.harvard.edu/abs/1979A&A....75..228L.
  24. C. T. Cunningham and J. M. Bardeen, The optical appearance of a star orbiting an extreme Kerr black hole, Astrophys. J. 173, L137 (1972).
  25. C. T. Cunningham, The effects of redshifts and focusing on the spectrum of an accretion disk around a Kerr black hole, Astrophys. J. 202, 788 (1975).
  26. C. Fanton, M. Calvani, F. de Felice, and A. Cadez, Detecting accretion disks in active galactic nuclei, Publ. Astron. Soc. Pac. 109, 706 (1997).
  27. L. G. Collodel, D. D. Doneva, and S. S. Yazadjiev, Circular orbit structure and thin accretion disks around Kerr black holes with scalar hair, Astrophys. J. 910, 52 (2021).
  28. M. Heydari-Fard, M. Heydari-Fard, and N. Riazi, Thin accretion disk images of rotating hairy Horndeski black holes, Astrophys. Space Sci. 369, 96 (2024).
  29. 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).
  30. Z. Li and X.-K. Guo, Thin accretion disk around rotating hairy black hole: Radiative property and optical appearance, Eur. Phys. J. C 85, 679 (2025).
  31. Q. Wan, Y. Hou, Y. Huang, P.-C. Li, M. Guo, and B. Chen, Distorting Kerr images with parity-odd scalar hair, arXiv:2605.28376.
  32. G.-P. Li, M.-Q. Wu, K.-J. He, and Q.-Q. Jiang, Observational features of massive boson stars with thin disk accretion, Phys. Rev. D 113, 043009 (2026).
  33. V. A. Ishkaeva and S. V. Sushkov, Image of an accreting general Ellis–Bronnikov wormhole, Phys. Rev. D 108, 084054 (2023).
  34. C.-H. Hao, X. Su, and Y.-Q. Wang, AdS Ellis wormholes with scalar field, Eur. Phys. J. C 85, 348 (2025).
  35. 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).
  36. F. Lora-Clavijo, O. Pimentel et al., Osiris: A new code for ray tracing around compact objects, Eur. Phys. J. C 82, 103 (2022).
  37. S. S. Yazadjiev and D. D. Doneva, Dark compact objects in massive tensor-multi-scalar theories of gravity, Phys. Rev. D 99, 084011 (2019).
  38. L. G. Collodel, D. D. Doneva, and S. S. Yazadjiev, Rotating tensor-multiscalar solitons, Phys. Rev. D 101, 044021 (2020).
  39. G. N. Gyulchev, V. O. Deliyski, P. G. Nedkova, S. S. Yazadjiev, and D. D. Doneva, Gaussian curvature effects in hairy Kerr black hole imaging, J. Phys. Conf. Ser. 3239, 012014 (2026).
  40. J. F. M. Delgado, C. A. R. Herdeiro, and E. Radu, Equatorial timelike circular orbits around generic ultracompact objects, Phys. Rev. D 105, 064026 (2022).
  41. M. E. Pessah and C.-K. Chan, On angular momentum transport in boundary layers, Astrophys. J. 751, 48 (2012).
  42. N. Marshall, M. J. Avara, and J. C. McKinney, Angular momentum transport in thin magnetically arrested discs, Mon. Not. R. Astron. Soc. 478, 1837 (2018).
  43. I. Sengo, P. V. Cunha, C. A. Herdeiro, and E. Radu, The imitation game reloaded: Effective shadows of dynamically robust spinning proca stars, J. Cosmol. Astropart. Phys. 05 (2024) 054.
  44. P. V. P. Cunha, C. A. R. Herdeiro, B. Kleihaus, J. Kunz, and E. Radu, Shadows of Einstein-dilaton-Gauss-Bonnet black holes, Phys. Lett. B 768, 373 (2017).

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Phys. Rev. D 114, 024074– Published 27 July, 2026
  • Received 13 April 2026
  • Accepted 29 June 2026
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