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Five-dimensional gravitational Raman scattering: Scalar wave perturbations in Schwarzschild-Tangherlini spacetime

Samim Akhtar1,2,*, Yilber Fabian Bautista3,†, Cristoforo Iossa4,‡, and Zihan Zhou5,§

  • *Contact author: samimakhtar@imsc.res.in
  • †Contact author: yilber-fabian.bautista-chivata@ipht.fr
  • ‡Contact author: Cristoforo.Iossa@unige.ch
  • §Contact author: zihanz@princeton.edu
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Phys. Rev. D 112, 085018 – Published 23 October, 2025

DOI: https://doi.org/10.1103/rglg-kfxq

Abstract

In this article, we study scalar wave perturbations of arbitrary frequency to the five-dimensional (5D) Schwarzschild-Tangherlini black hole (STBH) within general relativity. For the first time, we derive a closed formula for the 5D partial wave gravitational Raman scattering amplitude applicable to a broad class of boundary conditions, expressed in terms of the Nekrasov-Shatashvili (NS) function for the reduced confluent Heun problem. Furthermore, up to O(G2) we compute the dynamical ℓ=0, and the static ℓ=1, scalar tidal Love numbers of the STBH by matching an effective field theory description for a scalar wave scattering off the black hole, to our novel ultraviolet-NS solutions. The matched Love numbers do not vanish and present renormalization group running behavior.

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References (77)

  1. J. Aasi et al. (LIGO Scientific Collaboration), Classical Quantum Gravity 32, 074001 (2015).
  2. F. Acernese et al. (Virgo Collaboration), Classical Quantum Gravity 32, 024001 (2015).
  3. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 116, 061102 (2016).
  4. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 119, 161101 (2017).
  5. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. X 9, 031040 (2019).
  6. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. X 11, 021053 (2021).
  7. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. D 109, 022001 (2024).
  8. R. Abbott et al. (LIGO Scientific, KAGRA, and Virgo Collaborations), Astrophys. J. Lett. 915, L5 (2021).
  9. T. Akutsu et al. (KAGRA Collaboration), Prog. Theor. Exp. Phys. 2021, 05A102 (2021).
  10. R. Abbott et al. (KAGRA, Virgo, and LIGO Scientific Collaborations), Phys. Rev. X 13, 041039 (2023).
  11. W. D. Goldberger and I. Z. Rothstein, Phys. Rev. D 73, 104029 (2006).
  12. W. D. Goldberger, Handbook of Quantum Gravity (Springer, Singapore, 2022).
  13. R. A. Porto, Phys. Rep. 633, 1 (2016).
  14. G. Kälin and R. A. Porto, J. High Energy Phys. 11 (2020) 106.
  15. C. Cheung, I. Z. Rothstein, and M. P. Solon, Phys. Rev. Lett. 121, 251101 (2018).
  16. D. A. Kosower, B. Maybee, and D. O’Connell, J. High Energy Phys. 02 (2019) 137.
  17. Z. Bern, J. Parra-Martinez, R. Roiban, E. Sawyer, and C.-H. Shen, J. High Energy Phys. 05 (2021) 188.
  18. G. Mogull, J. Plefka, and J. Steinhoff, J. High Energy Phys. 02 (2021) 048.
  19. T. Binnington and E. Poisson, Phys. Rev. D 80, 084018 (2009).
  20. T. Damour and A. Nagar, Phys. Rev. D 80, 084035 (2009).
  21. V. Cardoso, E. Franzin, A. Maselli, P. Pani, and G. Raposo, Phys. Rev. D 95, 084014 (2017); 95, 089901(A) (2017).
  22. O. Combaluzier-Szteinsznaider, L. Hui, L. Santoni, A. R. Solomon, and S. S. C. Wong, J. High Energy Phys. 03 (2025) 124.
  23. W. D. Goldberger, in 2022 Snowmass Summer Study (2022); arXiv:2206.14249.
  24. R. A. Porto, Fortschr. Phys. 64, 723 (2016).
  25. P. Charalambous, S. Dubovsky, and M. M. Ivanov, Phys. Rev. Lett. 127, 101101 (2021).
  26. L. Hui, A. Joyce, R. Penco, L. Santoni, and A. R. Solomon, J. Cosmol. Astropart. Phys. 01 (2022) 032.
  27. P. Charalambous, S. Dubovsky, and M. M. Ivanov, J. High Energy Phys. 10 (2022) 175.
  28. M. M. Ivanov and Z. Zhou, Phys. Rev. Lett. 130, 091403 (2023).
  29. Y. F. Bautista, G. Bonelli, C. Iossa, A. Tanzini, and Z. Zhou, Phys. Rev. D 109, 084071 (2024).
  30. M. V. S. Saketh, Z. Zhou, and M. M. Ivanov, Phys. Rev. D 109, 064058 (2024).
  31. Y. F. Bautista, A. Guevara, C. Kavanagh, and J. Vines, J. High Energy Phys. 03 (2023) 136.
  32. Y. F. Bautista, A. Guevara, C. Kavanagh, and J. Vines, J. High Energy Phys. 05 (2023) 211.
  33. M. M. Ivanov and Z. Zhou, Phys. Rev. D 107, 084030 (2023).
  34. M. V. S. Saketh, Z. Zhou, S. Ghosh, J. Steinhoff, and D. Chatterjee, Phys. Rev. D 110, 103001 (2024).
  35. M. M. Ivanov, Y.-Z. Li, J. Parra-Martinez, and Z. Zhou, Phys. Rev. Lett. 132, 131401 (2024).
  36. S. Caron-Huot, M. Correia, G. Isabella, and M. Solon, arXiv:2503.13593.
  37. N. A. Nekrasov and S. L. Shatashvili, in 16th International Congress on Mathematical Physics (World Scientific, Singapore, 2010), pp. 265–289.
  38. G. Aminov, A. Grassi, and Y. Hatsuda, Ann. Henri Poincare 23, 1951 (2022).
  39. N. A. Nekrasov, Adv. Theor. Math. Phys. 7, 831 (2003).
  40. L. F. Alday, D. Gaiotto, and Y. Tachikawa, Lett. Math. Phys. 91, 167 (2010).
  41. M. M. Ivanov, Y.-Z. Li, J. Parra-Martinez, and Z. Zhou, arXiv:2504.07862.
  42. F. Fucito, J. F. Morales, and R. Russo, Phys. Rev. D 111, 044054 (2025).
  43. B. Kol and M. Smolkin, J. High Energy Phys. 02 (2012) 010.
  44. L. Hui, A. Joyce, R. Penco, L. Santoni, and A. R. Solomon, J. Cosmol. Astropart. Phys. 04 (2021) 052.
  45. D. Glazer, A. Joyce, M. J. Rodriguez, L. Santoni, A. R. Solomon, and L. F. Temoche, arXiv:2412.21090.
  46. M. J. Rodriguez, L. Santoni, A. R. Solomon, and L. F. Temoche, Phys. Rev. D 108, 084011 (2023).
  47. P. Charalambous, S. Dubovsky, and M. M. Ivanov, J. High Energy Phys. 06 (2025) 180.
  48. F. Gray, C. Keeler, D. Kubiznak, and V. Martin, J. High Energy Phys. 03 (2025) 036.
  49. P. Charalambous, J. High Energy Phys. 04 (2024) 122.
  50. F. R. Tangherlini, Nuovo Cimento 27, 636 (1963).
  51. A. Ronveaux, Heun’s Differential Equations (Clarendon Press, Oxford, England, 1995).
  52. Black Hole Physics: Basic Concepts and New Developments, edited by V. P. Frolov and I. D. Novikov (1998).
  53. W. D. Goldberger and I. Z. Rothstein, J. High Energy Phys. 04 (2020) 056.
  54. E. Berti, V. Cardoso, and A. O. Starinets, Classical Quantum Gravity 26, 163001 (2009).
  55. G. Bonelli, C. Iossa, D. Panea Lichtig, and A. Tanzini, Commun. Math. Phys. 397, 635 (2023).
  56. M. Dodelson, A. Grassi, C. Iossa, D. Panea Lichtig, and A. Zhiboedov, SciPost Phys. 14, 116 (2023).
  57. G. Aminov, P. Arnaudo, G. Bonelli, A. Grassi, and A. Tanzini, J. High Energy Phys. 11 (2023) 059.
  58. M. Bianchi, D. Consoli, A. Grillo, and J. F. Morales, Phys. Lett. B 824, 136837 (2022).
  59. M. Bianchi and G. Di Russo, J. High Energy Phys. 08 (2023) 217.
  60. M. Bianchi, G. Di Russo, A. Grillo, J. F. Morales, and G. Sudano, J. High Energy Phys. 12 (2023) 121.
  61. S. Giusto, C. Iossa, and R. Russo, J. High Energy Phys. 10 (2023) 050.
  62. G. Bonelli, C. Iossa, D. P. Lichtig, and A. Tanzini, Phys. Rev. D 105, 044047 (2022).
  63. D. Consoli, F. Fucito, J. F. Morales, and R. Poghossian, J. High Energy Phys. 12 (2022) 115.
  64. F. Fucito and J. F. Morales, J. High Energy Phys. 03 (2024) 106.
  65. G. Di Russo, F. Fucito, and J. F. Morales, J. High Energy Phys. 04 (2024) 149.
  66. M. Bianchi, D. Bini, and G. Di Russo, Phys. Rev. D 110, 084077 (2024).
  67. A. Cipriani, C. Di Benedetto, G. Di Russo, A. Grillo, and G. Sudano, J. High Energy Phys. 07 (2024) 143.
  68. M. Matone, Phys. Lett. B 357, 342 (1995).
  69. R. Flume, F. Fucito, J. F. Morales, and R. Poghossian, J. High Energy Phys. 04 (2004) 008.
  70. V. N. Gribov, The Theory of Complex Angular Momenta: Gribov Lectures on Theoretical Physics, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2007).
  71. S. Caron-Huot, J. High Energy Phys. 09 (2017) 078.
  72. S. Caron-Huot and J. Sandor, J. High Energy Phys. 05 (2021) 059.
  73. L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964).
  74. P. C. Martin, E. D. Siggia, and H. A. Rose, Phys. Rev. A 8, 423 (1973).
  75. H. Kodama and A. Ishibashi, Prog. Theor. Phys. 111, 29 (2004).
  76. H. Kodama, Lect. Notes Phys. 769, 427 (2009).
  77. P. H. Damgaard, L. Plante, and P. Vanhove, J. High Energy Phys. 11 (2021) 213.

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Phys. Rev. D 112, 085018– Published 23 October, 2025
  • Received 2 June 2025
  • Accepted 27 July 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. Funded by SCOAP3.

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