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Cosmological properties of black-hole hair in the linearly coupled scalar-Gauss-Bonnet theory

Dražen Glavan1,* and Darío Jaramillo-Garrido2,†

  • *Contact author: glavan@fzu.cz
  • †Contact author: djaramil@ucm.es
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Phys. Rev. D 114, 044020 – Published 7 August, 2026

DOI: https://doi.org/10.1103/q3nv-ccwn

Abstract

We investigate the superhorizon behavior of scalar hair sourced by black holes in de Sitter spacetime in the linearly coupled shift-symmetric scalar-Gauss-Bonnet theory. Working in the test-field regime, we show that this hair exhibits both temporal and spatial growth on superhorizon scales. This growth is not a special consequence of the black hole, but instead follows from the dynamics of a minimally coupled massless scalar field in expanding de Sitter spacetime. Moreover, it is not even specific to black holes, but also arises for a point scalar charge in de Sitter, indicating that a scalarized black hole acts effectively as a localized subhorizon source of scalar perturbations. Backreaction, when important, first arises on subhorizon scales and does not by itself eliminate the superhorizon profile. The time-dependent scalar hair also carries a steady outward energy flux, which frames the test-field regime as a transient, and helps explain the difficulties encountered in attempts to construct self-consistent static solutions.

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References (30)

  1. J. D. Bekenstein, Novel “no-scalar-hair” theorem for black holes, Phys. Rev. D 51, R6608 (1995).
  2. L. Hui and A. Nicolis, No-hair theorem for the Galileon, Phys. Rev. Lett. 110, 241104 (2013).
  3. T. P. Sotiriou and S. Y. Zhou, Black hole hair in generalized scalar-tensor gravity, Phys. Rev. Lett. 112, 251102 (2014).
  4. G. Antoniou, A. Bakopoulos, and P. Kanti, Evasion of no-hair theorems and novel black-hole solutions in Gauss-Bonnet theories, Phys. Rev. Lett. 120, 131102 (2018).
  5. T. P. Sotiriou and S. Y. Zhou, Black hole hair in generalized scalar-tensor gravity: An explicit example, Phys. Rev. D 90, 124063 (2014).
  6. S. R. Coleman, J. Preskill, and F. Wilczek, Growing hair on black holes, Phys. Rev. Lett. 67, 1975 (1991).
  7. S. R. Coleman, J. Preskill, and F. Wilczek, Quantum hair on black holes, Nucl. Phys. B378, 175 (1992).
  8. H. Ogawa, T. Kobayashi, and T. Suyama, Instability of hairy black holes in shift-symmetric Horndeski theories, Phys. Rev. D 93, 064078 (2016).
  9. R. Benkel, T. P. Sotiriou, and H. Witek, Black hole hair formation in shift-symmetric generalised scalar-tensor gravity, Classical Quantum Gravity 34, 064001 (2017).
  10. J. F. M. Delgado, C. A. R. Herdeiro, and E. Radu, Spinning black holes in shift-symmetric Horndeski theory, J. High Energy Phys. 04 (2020) 180.
  11. Y. Brihaye, B. Hartmann, and J. Urrestilla, Solitons and black hole in shift symmetric scalar-tensor gravity with cosmological constant, J. High Energy Phys. 06 (2018) 074.
  12. A. Bakopoulos, G. Antoniou, and P. Kanti, Novel black-hole solutions in Einstein-Scalar-Gauss-Bonnet theories with a cosmological constant, Phys. Rev. D 99, 064003 (2019).
  13. Y. Brihaye, C. Herdeiro, and E. Radu, Black hole spontaneous scalarisation with a positive cosmological constant, Phys. Lett. B 802, 135269 (2020).
  14. E. Babichev, I. Sawicki, and L. G. Trombetta, Black-hole hair in scalar-Gauss-Bonnet gravity is altered by cosmology, Phys. Rev. D 111, L041502 (2025).
  15. L. Parker, Particle creation in expanding universes, Phys. Rev. Lett. 21, 562 (1968).
  16. L. M. Burko, A. I. Harte, and E. Poisson, Mass loss by a scalar charge in an expanding universe, Phys. Rev. D 65, 124006 (2002).
  17. E. T. Akhmedov, A. Roura, and A. Sadofyev, Classical radiation by free-falling charges in de Sitter spacetime, Phys. Rev. D 82, 044035 (2010).
  18. D. Glavan, S. P. Miao, T. Prokopec, and R. P. Woodard, Breaking of scaling symmetry by massless scalar on de Sitter, Phys. Lett. B 798, 134944 (2019).
  19. R. Gaur and M. Visser, Cosmology in Painlevé-Gullstrand coordinates, J. Cosmol. Astropart. Phys. 09 (2022) 030.
  20. D. Glavan, S. P. Miao, T. Prokopec, and R. P. Woodard, Large logarithms from quantum gravitational corrections to a massless, minimally coupled scalar on de Sitter, J. High Energy Phys. 03 (2022) 088.
  21. E. Babichev, G. Esposito-Farèse, I. Sawicki, and L. G. Trombetta, Large black-hole scalar charges induced by cosmology in Horndeski theories, Phys. Rev. D 112, 024043 (2025).
  22. Y. Akrami et al. (Planck Collaboration), Planck 2018 results. X. Constraints on inflation, Astron. Astrophys. 641, A10 (2020).
  23. L. M. Burko, Instability of scalar charges in (1+1)-dimensions and (2+1)-dimensions, Classical Quantum Gravity 19, 3745 (2002).
  24. T. C. Quinn, Axiomatic approach to radiation reaction of scalar point particles in curved space-time, Phys. Rev. D 62, 064029 (2000).
  25. E. Poisson, The motion of point particles in curved space-time, Living Rev. Relativity 7, 6 (2004).
  26. P. Creminelli, N. Loayza, F. Serra, E. Trincherini, and L. G. Trombetta, Hairy black-holes in shift-symmetric theories, J. High Energy Phys. 08 (2020) 045.
  27. K. Peeters, Introducing Cadabra: A symbolic computer algebra system for field theory problems, arXiv:hep-th/0701238.
  28. K. Peeters, A field-theory motivated approach to symbolic computer algebra, Comput. Phys. Commun. 176, 550 (2007).
  29. K. Peeters, Cadabra2: Computer algebra for field theory revisited, J. Open Source Software 3, 1118 (2018).
  30. G. Lara, G. Trenkler, and L. G. Trombetta, Primary black-hole scalar charges and kinetic screening in K-essence-Gauss-Bonnet gravity, arXiv:2512.23683.

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Phys. Rev. D 114, 044020– Published 7 August, 2026
  • Received 25 May 2026
  • Accepted 13 July 2026
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