Papers
Topics
Authors
Recent
Detailed Answer
Quick Answer
Concise responses based on abstracts only
Detailed Answer
Well-researched responses based on abstracts and relevant paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses
Gemini 2.5 Flash
Gemini 2.5 Flash 82 tok/s
Gemini 2.5 Pro 48 tok/s Pro
GPT-5 Medium 40 tok/s Pro
GPT-5 High 38 tok/s Pro
GPT-4o 96 tok/s Pro
Kimi K2 185 tok/s Pro
GPT OSS 120B 465 tok/s Pro
Claude Sonnet 4 30 tok/s Pro
2000 character limit reached

The excitation of quadratic quasinormal modes for Kerr black holes (2401.15516v2)

Published 27 Jan 2024 in gr-qc and hep-th

Abstract: The excitation of quadratic quasinormal modes is an important nonlinear phenomenon for a Kerr black hole ringing at a specific linear mode. The amplitude of this second-order effect is proportional to the square of the linear mode amplitude, with the ratio being linked to the nature of the Kerr black hole. Focusing on the linear $(l=m=2,n=0)$ mode, we compute the dependency of the ratio on the dimensionless spin of the black hole, ranging up to 0.99, with the method applicable for more general mode couplings. Our calculation makes use of the frequency-domain, second-order Teukolsky equation, which involves two essential steps (a) analytically reconstructing the metric through the Chrzanowski-Cohen-Kegeles approach and (b) numerically solving the second-order Teukolsky equation using the shooting method along a complex contour. We find that the spin dependence of the ratio shows a strong correlation with the angular overlap between parent and child modes, providing qualitative insights into the origin of the dependence. Depending on the nature of the angular overlap, the ratio decreases with spin in scenarios such as the channel $(l=m=2,n=0)\times(l=m=2,n=0)\to(l=m=4)$ or increases in situations like $(l=m=2,n=0)\times(l=m=2,n=0)\to(l=5,m=4)$. For both cases, the ratios do not vanish in the extremal limit. As a byproduct, we find that the Weyl scalars can be concisely expressed with the Hertz potential.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (38)
  1. B. Carter, Phys. Rev. Lett. 26, 331 (1971).
  2. B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. Lett. 116, 221101 (2016), [Erratum: Phys. Rev. Lett.121,no.12,129902(2018)], arXiv:1602.03841 [gr-qc] .
  3. E. Finch and C. J. Moore, Phys. Rev. D 106, 043005 (2022), arXiv:2205.07809 [gr-qc] .
  4. M. Campanelli and C. O. Lousto, Phys. Rev. D 59, 124022 (1999), arXiv:gr-qc/9811019 .
  5. K. Mitman et al., Phys. Rev. Lett. 130, 081402 (2023), arXiv:2208.07380 [gr-qc] .
  6. M. H.-Y. Cheung et al., Phys. Rev. Lett. 130, 081401 (2023), arXiv:2208.07374 [gr-qc] .
  7. H. Nakano and K. Ioka, Phys. Rev. D 76, 084007 (2007), arXiv:0708.0450 [gr-qc] .
  8. K. Ioka and H. Nakano, Phys. Rev. D 76, 061503 (2007), arXiv:0704.3467 [astro-ph] .
  9. M. Lagos and L. Hui, Phys. Rev. D 107, 044040 (2023), arXiv:2208.07379 [gr-qc] .
  10. H. Zhu et al.,   (2024), arXiv:2401.00805 [gr-qc] .
  11. P. L. Chrzanowski, Phys. Rev. D 11, 2042 (1975).
  12. J. Cohen and L. Kegeles, Physics Letters A 54, 5 (1975).
  13. L. S. Kegeles and J. M. Cohen, Phys. Rev. D 19, 1641 (1979).
  14. K. D. Kokkotas and B. G. Schmidt, Living Rev. Rel. 2, 2 (1999), arXiv:gr-qc/9909058 .
  15. S. Chandrasekhar, The mathematical theory of black holes, Vol. 69 (Oxford university press, 1998).
  16. S. A. Teukolsky, Astrophysical Journal 185, 635 (1973).
  17. R. Penrose and W. Rindler, Spinors and space-time: Volume 1, Two-spinor calculus and relativistic fields, Vol. 1 (Cambridge University Press, 1984).
  18. S. A. Teukolsky, Phys. Rev. Lett. 29, 1114 (1972).
  19. E. W. Leaver, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 402, 285 (1985).
  20. R. M. Wald, Phys. Rev. Lett. 41, 203 (1978).
  21. B. F. Whiting and L. R. Price, Class. Quant. Grav. 22, S589 (2005).
  22. A. Ori, Phys. Rev. D 67, 124010 (2003), arXiv:gr-qc/0207045 .
  23. A. A. Starobinsky, Sov. Phys. JETP 37, 28 (1973).
  24. S. Teukolsky and W. Press, Astrophys. J. 193, 443 (1974).
  25. “Black Hole Perturbation Toolkit,” (bhptoolkit.org).
  26. S. L. Detweiler and E. Szedenits, Astrophys. J. 231, 211 (1979).
  27. E. W. Leaver, Phys. Rev. D 34, 384 (1986).
  28. H. Yang and J. Zhang, Phys. Rev. D 107, 064045 (2023), arXiv:2210.01724 [gr-qc] .
  29. A. Hussain and A. Zimmerman, Phys. Rev. D 106, 104018 (2022), arXiv:2206.10653 [gr-qc] .
  30. “The Spectral Einstein Code,” http://www.black-holes.org/SpEC.html.
  31. L. C. Stein, J. Open Source Softw. 4, 1683 (2019), arXiv:1908.10377 [gr-qc] .
  32. M. Isi and W. M. Farr,   (2021), arXiv:2107.05609 [gr-qc] .
  33. S. Hod, Phys. Lett. B 666, 483 (2008a), arXiv:0810.5419 [gr-qc] .
  34. S. Hod, Phys. Rev. D 78, 084035 (2008b), arXiv:0811.3806 [gr-qc] .
  35. S. Aretakis,   (2010), arXiv:1006.0283 [math.AP] .
  36. S. Aretakis, Commun. Math. Phys. 307, 17 (2011a), arXiv:1110.2007 [gr-qc] .
  37. S. Aretakis, Annales Henri Poincare 12, 1491 (2011b), arXiv:1110.2009 [gr-qc] .
  38. S. Aretakis, Adv. Theor. Math. Phys. 19, 507 (2015), arXiv:1206.6598 [gr-qc] .
Citations (9)
View on Semantic Scholar
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Dice Question Streamline Icon: https://streamlinehq.com

Follow-Up Questions

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Authors (2)

  1. Sizheng Ma
  2. Huan Yang