- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Coupling between gravitational and electromagnetic perturbations on Kerr spacetime

Fawzi Aly* and Dejan Stojkovic†

  • *Contact author: mabbasal@buffalo.edu
  • †Contact author: ds77@buffalo.edu
PDF

Phys. Rev. D 113, 104003 – Published 4 May, 2026

DOI: https://doi.org/10.1103/p4km-1fgf

Abstract

We extend our previous Schwarzschild metric-based studies of gravitational-electromagnetic (GEM) coupling to rotating black holes by working directly in a curvature-based Newman-Penrose/Teukolsky framework on Kerr spacetime. Within a minimally coupled Einstein-Maxwell system, we derive explicit quadratic electromagnetic source terms for the spin-−2 Teukolsky equation, providing a foundation for future numerical studies of GEM interactions in the framework of black-hole spectroscopy. Moreover, we give order-of-magnitude arguments showing that GEM quadratic quasinormal modes (QQNMs) can become relevant in a range of charged and magnetized astrophysical scenarios. Finally, we show through a brief dilaton-theory example that the GEM QQNM spectrum is sensitive to how gravity couples to electromagnetism, thereby providing a model-based way to test minimal coupling and to constrain hidden U(1) sectors with gravitational-wave observations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (76)

  1. K. Mitman, M. Lagos, L. C. Stein, S. Ma, L. Hui, Y. Chen, N. Deppe, F. Hébert, L. E. Kidder, J. Moxon, M. A. Scheel, S. A. Teukolsky, W. Throwe, and N. L. Vu, Phys. Rev. Lett. 130, 081402 (2023).
  2. M. H.-Y. Cheung, V. Baibhav, E. Berti, V. Cardoso, G. Carullo, R. Cotesta, W. Del Pozzo, F. Duque, T. Helfer, E. Shukla, and K. W. K. Wong, Phys. Rev. Lett. 130, 081401 (2023).
  3. 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).
  4. S. Ma, K. Mitman, L. Sun, N. Deppe, F. Hébert, L. E. Kidder, J. Moxon, W. Throwe, N. L. Vu, and Y. Chen, Phys. Rev. D 106, 084036 (2022).
  5. L. London, D. Shoemaker, and J. Healy, Phys. Rev. D 90, 124032 (2014).
  6. F. Aly and D. Stojkovic, Classical Quantum Gravity 40, 235010 (2023).
  7. J. Redondo-Yuste, G. Carullo, J. L. Ripley, E. Berti, and V. Cardoso, Phys. Rev. D 109, L101503 (2024).
  8. H. Zhu, J. L. Ripley, F. Pretorius, S. Ma, K. Mitman, R. Owen, M. Boyle, Y. Chen, N. Deppe, L. E. Kidder, J. Moxon, K. C. Nelli, H. P. Pfeiffer, M. A. Scheel, W. Throwe, and N. L. Vu, Phys. Rev. D 109, 104050 (2024).
  9. M. H.-Y. Cheung, E. Berti, V. Baibhav, and R. Cotesta, Phys. Rev. D 109, 044069 (2024).
  10. 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).
  11. S. Ma and H. Yang, Phys. Rev. D 109, 104070 (2024).
  12. L. Sberna, P. Bosch, W. E. East, S. R. Green, and L. Lehner, Phys. Rev. D 105, 064046 (2022).
  13. M. Lagos and L. Hui, Phys. Rev. D 107, 044040 (2023).
  14. N. Loutrel, J. L. Ripley, E. Giorgi, and F. Pretorius, Phys. Rev. D 103, 104017 (2021).
  15. J. L. Ripley, N. Loutrel, E. Giorgi, and F. Pretorius, Phys. Rev. D 103, 104018 (2021).
  16. A. Pound, B. Wardell, N. Warburton, and J. Miller, Phys. Rev. Lett. 124, 021101 (2020).
  17. A. Pound, Phys. Rev. D 95, 104056 (2017).
  18. A. Spiers, A. Pound, and J. Moxon, Phys. Rev. D 108, 064002 (2023).
  19. A. Spiers, A. Pound, and B. Wardell, Phys. Rev. D 110, 064030 (2024).
  20. A. Albertini, A. Nagar, A. Pound, N. Warburton, B. Wardell, L. Durkan, and J. Miller, Phys. Rev. D 106, 084061 (2022).
  21. M. Punturo et al., Classical Quantum Gravity 27, 194002 (2010).
  22. M. Maggiore et al., J. Cosmol. Astropart. Phys. 03 (2020) 050.
  23. D. Reitze et al., Bull. Am. Astron. Soc. 51, 035 (2019).
  24. M. Evans et al., arXiv:2109.09882.
  25. P. Amaro-Seoane et al., arXiv:1702.00786.
  26. K. Chamberlain and N. Yunes, Phys. Rev. D 96, 084039 (2017).
  27. B. Goncharov, L. Donnay, and J. Harms, Phys. Rev. Lett. 132, 241401 (2024).
  28. E. Berti, V. Cardoso, and C. M. Will, Phys. Rev. D 73, 064030 (2006).
  29. V. Baibhav, E. Berti, and V. Cardoso, Phys. Rev. D 101, 084053 (2020).
  30. A. Neronov, J. Phys. Conf. Ser. 1263, 012001 (2019).
  31. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Astrophys. J. Lett. 848, L12 (2017).
  32. B. Margalit and B. D. Metzger, Astrophys. J. Lett. 850, L19 (2017).
  33. M. Branchesi, J. Phys. Conf. Ser. 718, 022004 (2016).
  34. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 119, 161101 (2017).
  35. I. Gupta, S. Borhanian, A. Dhani, D. Chattopadhyay, R. Kashyap, V. A. Villar, and B. S. Sathyaprakash, Phys. Rev. D 107, 124007 (2023).
  36. B. P. Abbott et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Phys. Rev. X 13, 011048 (2023).
  37. F. Aly, M. A. Mansour, and D. Stojkovic, Phys. Rev. D 111, 104083 (2025).
  38. F. Aly, M. A. Mansour, and D. Stojkovic, Phys. Rev. D 111, 104082 (2025).
  39. S. A. Teukolsky, Astrophys. J. 185, 635 (1973).
  40. S. Chandrasekhar, The Mathematical Theory of Black Holes (Clarendon Press, New York, 1983).
  41. A. Pound and B. Wardell, Black hole perturbation theory and gravitational self-force, in Handbook of Gravitational Wave Astronomy (Springer, Singapore, 2021), p. 1–119.
  42. A. Spiers, Phys. Rev. D 109, 104059 (2024).
  43. E. Berti, V. Cardoso, and A. O. Starinets, Classical Quantum Gravity 26, 163001 (2009).
  44. K. D. Kokkotas and B. G. Schmidt, Living Rev. Relativity 2, 2 (1999).
  45. R. A. Konoplya and A. Zhidenko, Rev. Mod. Phys. 83, 793 (2011).
  46. V. Ferrari and L. Gualtieri, Gen. Relativ. Gravit. 40, 945 (2008).
  47. C. Pacilio and R. Brito, Phys. Rev. D 98, 104042 (2018).
  48. L. S. Kegeles and J. M. Cohen, Phys. Rev. D 19, 1641 (1979).
  49. P. L. Chrzanowski, Phys. Rev. D 11, 2042 (1975).
  50. R. Brito, QNM_EMD github repository (2018), https://github.com/richbrito/QNM_EMD/ (accessed February 5, 2025).
  51. A. B. Balakin and J. P. S. Lemos, Classical Quantum Gravity 22, 1867 (2005).
  52. T. Dereli and Ö. Sert, Eur. Phys. J. C 71, 1589 (2011).
  53. Y. S. Myung and D.-C. Zou, Phys. Lett. B 790, 400 (2019).
  54. J. L. Blázquez-Salcedo, C. A. R. Herdeiro, S. Kahlen, J. Kunz, A. M. Pombo, and E. Radu, Eur. Phys. J. C 81, 155 (2021).
  55. W.-D. Guo and Q. Tan, Universe 9, 320 (2023).
  56. R. J. Gleiser, C. O. Nicasio, R. H. Price, and J. Pullin, Phys. Rev. Lett. 77, 4483 (1996).
  57. M. Zilhão, V. Cardoso, C. Herdeiro, L. Lehner, and U. Sperhake, Phys. Rev. D 85, 124062 (2012).
  58. M. Zilhão, V. Cardoso, C. Herdeiro, L. Lehner, and U. Sperhake, Phys. Rev. D 89, 044008 (2014).
  59. V. Cardoso, C. F. B. Macedo, P. Pani, and V. Ferrari, J. Cosmol. Astropart. Phys. 05 (2016) 054.
  60. S. L. Liebling and C. Palenzuela, Phys. Rev. D 94, 064046 (2016).
  61. G. Bozzola and V. Paschalidis, Phys. Rev. Lett. 126, 041103 (2021).
  62. G. Bozzola and V. Paschalidis, Phys. Rev. D 104, 044004 (2021).
  63. R. Luna, G. Bozzola, V. Cardoso, V. Paschalidis, and M. Zilhão, Phys. Rev. D 106, 084017 (2022).
  64. P. J. Nee, S. H. Völkel, and H. P. Pfeiffer, Phys. Rev. D 108, 044032 (2023).
  65. B. Bucciotti, L. Juliano, A. Kuntz, and E. Trincherini, J. High Energy Phys. 09 (2024) 119.
  66. B. Bucciotti, A. Kuntz, F. Serra, and E. Trincherini, J. High Energy Phys. 12 (2023) 048.
  67. P. Bourg, R. P. Macedo, A. Spiers, B. Leather, B. Bonga, and A. Pound, Phys. Rev. Lett. 134, 061401 (2025).
  68. H. Nakano and K. Ioka, Phys. Rev. D 76, 084007 (2007).
  69. Z. Mark, H. Yang, A. Zimmerman, and Y. Chen, Phys. Rev. D 91, 044025 (2015).
  70. E. Berti and K. D. Kokkotas, Phys. Rev. D 71, 124008 (2005).
  71. P. Pani, E. Berti, and L. Gualtieri, Phys. Rev. Lett. 110, 241103 (2013).
  72. J. B. Griffiths and J. Podolský, Exact Space-Times in Einstein’s General Relativity (Cambridge University Press, Cambridge, England, 2012).
  73. F. Aly and D. Stojkovic, Classical Quantum Gravity 41, 135005 (2024).
  74. E. R. Most, A. Nathanail, and L. Rezzolla, Astrophys. J. 864, 117 (2018).
  75. E. R. Most, A. M. Beloborodov, and B. Ripperda, Astrophys. J. Lett. 974, L12 (2024).
  76. P. Mourier, X. Jiménez Forteza, D. Pook-Kolb, B. Krishnan, and E. Schnetter, Phys. Rev. D 103, 044054 (2021).

Outline

Information

Phys. Rev. D 113, 104003– Published 4 May, 2026
  • Received 25 November 2025
  • Accepted 10 April 2026
Article part of CHORUS
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation