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AdS perspective on the nonlinear tails in black hole ringdowns

Alex Kehagias1,2 and Antonio Riotto3

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Phys. Rev. D 112, 084068 – Published 28 October, 2025

DOI: https://doi.org/10.1103/yk6g-sdbw

Abstract

Black holes gradually settle into their static configuration by emitting gravitational waves, whose amplitudes diminish over time according to a power-law decay at fixed spatial locations. We show that the nonlinear tails in the presence of a quadratic source, which have been recently found to potentially dominate over the linear ones, can be simply derived from the AdS2×S2 spacetime perspective with their amplitudes being related to the Aretakis constants.

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References (81)

  1. E. Berti et al., Classical Quantum Gravity 32, 243001 (2015).
  2. E. Berti, K. Yagi, H. Yang, and N. Yunes, Gen. Relativ. Gravit. 50, 49 (2018).
  3. G. Franciolini, L. Hui, R. Penco, L. Santoni, and E. Trincherini, J. High Energy Phys. 02 (2019) 127.
  4. R. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. D 103, 122002 (2021).
  5. E. Berti, V. Cardoso, and C. M. Will, Phys. Rev. D 73, 064030 (2006).
  6. B. P. Abbott et al. (KAGRA Collaboration, LIGO Scientific Collaboration, and Virgo Collaboration), Living Rev. Relativity 19, 1 (2016).
  7. B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 116, 061102 (2016).
  8. R. Abbott et al. (KAGRA Collaboration, VIRGO Collaboration, and LIGO Scientific Collaboration), Phys. Rev. X 13, 041039 (2023).
  9. A. G. Abac et al. (LIGO Scientific Collaboration, KAGRA Collaboration, and VIRGO Collaboration), Astrophys. J. 973, 132 (2024).
  10. E. Berti et al., arXiv:2505.23895.
  11. R. H. Price, Phys. Rev. D 5, 2419 (1972).
  12. R. H. Price, Phys. Rev. D 5, 2439 (1972).
  13. E. W. Leaver, Phys. Rev. D 34, 384 (1986).
  14. C. Gundlach, R. H. Price, and J. Pullin, Phys. Rev. D 49, 883 (1994).
  15. C. Gundlach, R. H. Price, and J. Pullin, Phys. Rev. D 49, 890 (1994).
  16. E. S. C. Ching, P. T. Leung, W. M. Suen, and K. Young, Phys. Rev. D 52, 2118 (1995).
  17. S. Chandrasekhar and S. L. Detweiler, Proc. R. Soc. A 344, 441 (1975).
  18. K. Martel and E. Poisson, Phys. Rev. D 71, 104003 (2005).
  19. L. Barack, Phys. Rev. D 59, 044017 (1999).
  20. E. Berti, V. Cardoso, and A. O. Starinets, Classical Quantum Gravity 26, 163001 (2009).
  21. E. S. C. Ching, P. T. Leung, W. M. Suen, and K. Young, Phys. Rev. Lett. 74, 2414 (1995).
  22. W. Krivan, P. Laguna, and P. Papadopoulos, Phys. Rev. D 54, 4728 (1996).
  23. W. Krivan, P. Laguna, P. Papadopoulos, and N. Andersson, Phys. Rev. D 56, 3395 (1997).
  24. W. Krivan, Phys. Rev. D 60, 101501 (1999).
  25. L. M. Burko and G. Khanna, Phys. Rev. D 67, 081502 (2003).
  26. L. M. Burko and G. Khanna, Classical Quantum Gravity 26, 015014 (2009).
  27. S. Hod, Classical Quantum Gravity 26, 028001 (2009).
  28. L. M. Burko and G. Khanna, Classical Quantum Gravity 28, 025012 (2011).
  29. I. Racz and G. Z. Toth, Classical Quantum Gravity 28, 195003 (2011).
  30. A. Zenginoǧlu, G. Khanna, and L. M. Burko, Gen. Relativ. Gravit. 46, 1672 (2014).
  31. L. M. Burko and G. Khanna, Phys. Rev. D 89, 044037 (2014).
  32. V. Baibhav, M. H.-Y. Cheung, E. Berti, V. Cardoso, G. Carullo, R. Cotesta, W. Del Pozzo, and F. Duque, Phys. Rev. D 108, 104020 (2023).
  33. R. F. Rosato and P. Pani, Phys. Rev. D 112, 024080 (2025).
  34. R. J. Gleiser, C. O. Nicasio, R. H. Price, and J. Pullin, Classical Quantum Gravity 13, L117 (1996).
  35. R. J. Gleiser, C. O. Nicasio, R. H. Price, and J. Pullin, Phys. Rep. 325, 41 (2000).
  36. M. Campanelli and C. O. Lousto, Phys. Rev. D 59, 124022 (1999).
  37. A. Garat and R. H. Price, Phys. Rev. D 61, 044006 (2000).
  38. Y. Zlochower, R. Gomez, S. Husa, L. Lehner, and J. Winicour, Phys. Rev. D 68, 084014 (2003).
  39. D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 74, 044039 (2006).
  40. D. Brizuela, J. M. Martin-Garcia, and G. A. M. Marugan, Phys. Rev. D 76, 024004 (2007).
  41. H. Nakano and K. Ioka, Phys. Rev. D 76, 084007 (2007).
  42. D. Brizuela, J. M. Martin-Garcia, and M. Tiglio, Phys. Rev. D 80, 024021 (2009).
  43. J. L. Ripley, N. Loutrel, E. Giorgi, and F. Pretorius, Phys. Rev. D 103, 104018 (2021).
  44. N. Loutrel, J. L. Ripley, E. Giorgi, and F. Pretorius, Phys. Rev. D 103, 104017 (2021).
  45. E. Pazos, D. Brizuela, J. M. Martin-Garcia, and M. Tiglio, Phys. Rev. D 82, 104028 (2010).
  46. L. Sberna, P. Bosch, W. E. East, S. R. Green, and L. Lehner, Phys. Rev. D 105, 064046 (2022).
  47. J. Redondo-Yuste, G. Carullo, J. L. Ripley, E. Berti, and V. Cardoso, Phys. Rev. D 109, L101503 (2024).
  48. K. Mitman et al., Phys. Rev. Lett. 130, 081402 (2023).
  49. M. H.-Y. Cheung et al., Phys. Rev. Lett. 130, 081401 (2023).
  50. K. Ioka and H. Nakano, Phys. Rev. D 76, 061503 (2007).
  51. A. Kehagias, D. Perrone, A. Riotto, and F. Riva, Phys. Rev. D 108, L021501 (2023).
  52. N. Khera, A. Ribes Metidieri, B. Bonga, X. Jiménez Forteza, B. Krishnan, E. Poisson, D. Pook-Kolb, E. Schnetter, and H. Yang, Phys. Rev. Lett. 131, 231401 (2023).
  53. B. Bucciotti, A. Kuntz, F. Serra, and E. Trincherini, J. High Energy Phys. 12 (2023) 048.
  54. A. Spiers, A. Pound, and J. Moxon, Phys. Rev. D 108, 064002 (2023).
  55. S. Ma and H. Yang, Phys. Rev. D 109, 104070 (2024).
  56. H. Zhu et al., Phys. Rev. D 109, 104050 (2024).
  57. J. Redondo-Yuste, D. Pereñiguez, and V. Cardoso, Phys. Rev. D 109, 044048 (2024).
  58. P. Bourg, R. Panosso Macedo, A. Spiers, B. Leather, B. Bonga, and A. Pound, Phys. Rev. Lett. 134, 061401 (2025).
  59. M. Lagos, T. Andrade, J. Rafecas-Ventosa, and L. Hui, Phys. Rev. D 111, 024018 (2025).
  60. D. Perrone, T. Barreira, A. Kehagias, and A. Riotto, Nucl. Phys. B999, 116432 (2024).
  61. A. Kehagias and A. Riotto, Phys. Rev. D 111, L041506 (2025).
  62. B. Bucciotti, V. Cardoso, A. Kuntz, D. Pereñiguez, and J. Redondo-Yuste, Phys. Rev. D 111, L081502 (2025).
  63. P. Bourg, R. P. Macedo, A. Spiers, B. Leather, B. Béatrice, and A. Pound, Phys. Rev. D 112, 044049 (2025).
  64. J. Ben Achour and H. Roussille, J. Cosmol. Astropart. Phys. 07 (2024) 085.
  65. A. Kehagias, D. Perrone, and A. Riotto, arXiv:2503.09350.
  66. S. Okuzumi, K. Ioka, and M. Sakagami, Phys. Rev. D 77, 124018 (2008).
  67. M. Lagos and L. Hui, Phys. Rev. D 107, 044040 (2023).
  68. V. Cardoso, G. Carullo, M. De Amicis, F. Duque, T. Katagiri, D. Pereniguez, J. Redondo-Yuste, T. F. M. Spieksma, and Z. Zhong, Phys. Rev. D 109, L121502 (2024).
  69. M. De Amicis et al., arXiv:2412.06887.
  70. S. Ma, M. A. Scheel, J. Moxon, K. C. Nelli, N. Deppe, L. E. Kidder, W. Throwe, and N. L. Vu, Phys. Rev. D 112, 024003 (2025).
  71. S. Ling, S. Shah, and S. S. C. Wong, Phys. Rev. D 112, 024008 (2025).
  72. A. Kehagias and A. Riotto, Phys. Rev. D 112, 024023 (2025).
  73. C. P. Burgess and C. A. Lutken, Phys. Lett. 153B, 137 (1985).
  74. Y. Satoh and J. Troost, J. High Energy Phys. 01 (2003) 027.
  75. N. Andersson, Phys. Rev. D 55, 468 (1997).
  76. M. Spradlin and A. Strominger, J. High Energy Phys. 11 (1999) 021.
  77. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, (NBS, Washington, DC, 1964), pp. 32–33.
  78. S. Aretakis, Commun. Math. Phys. 307, 17 (2011).
  79. S. Aretakis, Ann. Henri Poincare 12, 1491 (2011).
  80. S. Aretakis, Adv. Theor. Math. Phys. 19, 507 (2015).
  81. J. Lucietti, K. Murata, H. S. Reall, and N. Tanahashi, J. High Energy Phys. 03 (2013) 035.

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Phys. Rev. D 112, 084068– Published 28 October, 2025
  • Received 18 June 2025
  • Accepted 12 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by CERN.

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