- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Strong field scattering of two black holes: Exploring gauge flexibility

Adam Clark* and Geraint Pratten†

  • *Contact author: axc157@student.bham.ac.uk
  • †Contact author: g.pratten@bham.ac.uk
PDF

Phys. Rev. D 112, 104074 – Published 25 November, 2025

DOI: https://doi.org/10.1103/cv6l-4zzs

Abstract

Recent advances in post-Minkowskian (PM) gravity provide new avenues for the high precision modeling of compact binaries. In conjunction with the effective one body (EOB) formalism, highly accurate PM informed models of binary black holes on scattering trajectories have emerged. Several complementary approaches currently exist, in particular the spinning effective one body (SEOB)-PM model, the wEOB framework and the recent lagrangian effective one body (LEOB) approach. These models incorporate PM results in fundamentally different ways, employing distinct resummation schemes and gauge choices. Notably, both SEOB-PM and LEOB have been used to compute gravitational waves of bound systems, showing excellent agreement with numerical relativity. The essential component to all of the models is the EOB mass-shell condition describing the dynamics of the two-body spacetime. In this work we will investigate how this mass-shell condition is constructed, paying particular attention to the impact of gauge choices and how they interact with different resummation schemes, showing that there is a strong dependence on both coordinate choice and EOB gauge. For the region of parameter space considered, we find that the best performing gauges coincide with the choices made in SEOB-PM and wEOB, with other choices exhibiting worse performance. The case of spinning black holes is also considered, where the current techniques for spinning EOB-PM are reviewed and compared. We also introduce a new gauge based upon the centrifugal radius, which improves upon previous models, particularly for large and negative spins. This offers a promising avenue for further resummation of spin information within the EOB-PM framework.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (93)

  1. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. X 9, 031040 (2019).
  2. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. X 11, 021053 (2021).
  3. R. Abbott et al. (KAGRA, Virgo, and LIGO Scientific Collaborations), Phys. Rev. X 13, 041039 (2023).
  4. L. Blanchet, Living Rev. Relativity 17, 2 (2014).
  5. A. Buonanno and T. Damour, Phys. Rev. D 59, 084006 (1999).
  6. A. Buonanno and T. Damour, Phys. Rev. D 62, 064015 (2000).
  7. A. Nagar et al., Phys. Rev. D 98, 104052 (2018).
  8. D. Chiaramello and A. Nagar, Phys. Rev. D 101, 101501 (2020).
  9. L. Pompili et al., Phys. Rev. D 108, 124035 (2023).
  10. A. Ramos-Buades, A. Buonanno, H. Estellés, M. Khalil, D. P. Mihaylov, S. Ossokine, L. Pompili, and M. Shiferaw, Phys. Rev. D 108, 124037 (2023).
  11. M. Khalil, A. Buonanno, H. Estelles, D. P. Mihaylov, S. Ossokine, L. Pompili, and A. Ramos-Buades, Phys. Rev. D 108, 124036 (2023).
  12. A. Gamboa, M. Khalil, and A. Buonanno, Phys. Rev. D 112, 044037 (2025).
  13. A. Nagar, R. Gamba, P. Rettegno, V. Fantini, and S. Bernuzzi, Phys. Rev. D 110, 084001 (2024).
  14. L. Bel, T. Damour, N. Deruelle, J. Ibanez, and J. Martin, Gen. Relativ. Gravit. 13, 963 (1981).
  15. K. Westpfahl and M. Goller, Lett. Nuovo Cimento 26, 573 (1979).
  16. K. Westpfahl, Fortschr. Phys. 33, 417 (1985).
  17. L. Blanchet and T. Damour, Phil. Trans. R. Soc. A 320, 379 (1986).
  18. T. Damour, Phys. Rev. D 94, 104015 (2016).
  19. T. Damour, Phys. Rev. D 97, 044038 (2018).
  20. T. Damour, Phys. Rev. D 102, 024060 (2020).
  21. Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, Phys. Rev. Lett. 122, 201603 (2019).
  22. Z. Bern, A. Luna, R. Roiban, C.-H. Shen, and M. Zeng, Phys. Rev. D 104, 065014 (2021).
  23. Z. Bern, J. Parra-Martinez, R. Roiban, M. S. Ruf, C.-H. Shen, M. P. Solon, and M. Zeng, Phys. Rev. Lett. 126, 171601 (2021).
  24. Z. Bern, J. Parra-Martinez, R. Roiban, M. S. Ruf, C.-H. Shen, M. P. Solon, and M. Zeng, Phys. Rev. Lett. 128, 161103 (2022).
  25. G. Kälin and R. A. Porto, J. High Energy Phys. 11 (2020) 106.
  26. G. Kälin, J. Neef, and R. A. Porto, J. High Energy Phys. 01 (2023) 140.
  27. G. Kälin, Z. Liu, and R. A. Porto, Phys. Rev. Lett. 125, 261103 (2020).
  28. C. Dlapa, G. Kälin, Z. Liu, and R. A. Porto, Phys. Lett. B 831, 137203 (2022).
  29. C. Dlapa, G. Kälin, Z. Liu, and R. A. Porto, Phys. Rev. Lett. 128, 161104 (2022).
  30. C. Dlapa, G. Kälin, Z. Liu, J. Neef, and R. A. Porto, Phys. Rev. Lett. 130, 101401 (2023).
  31. G. Mogull, J. Plefka, and J. Steinhoff, J. High Energy Phys. 02 (2021) 048.
  32. G. U. Jakobsen, G. Mogull, J. Plefka, and J. Steinhoff, Phys. Rev. Lett. 126, 201103 (2021).
  33. G. U. Jakobsen, G. Mogull, J. Plefka, and B. Sauer, J. High Energy Phys. 10 (2022) 128.
  34. M. Driesse, G. U. Jakobsen, G. Mogull, J. Plefka, B. Sauer, and J. Usovitsch, Phys. Rev. Lett. 132, 241402 (2024).
  35. M. Driesse, G. U. Jakobsen, A. Klemm, G. Mogull, C. Nega, J. Plefka, B. Sauer, and J. Usovitsch, Nature (London) 641, 603 (2025).
  36. J. Vines, Classical Quantum Gravity 35, 084002 (2018).
  37. R. Aoude, K. Haddad, and A. Helset, Phys. Rev. Lett. 129, 141102 (2022).
  38. R. Aoude, K. Haddad, and A. Helset, Phys. Rev. D 108, 024050 (2023).
  39. D. Akpinar, F. Febres Cordero, M. Kraus, A. Smirnov, and M. Zeng, Phys. Rev. Lett. 135, 041602 (2025).
  40. G. U. Jakobsen, G. Mogull, J. Plefka, and B. Sauer, Phys. Rev. Lett. 131, 241402 (2023).
  41. N. Gupte et al., arXiv:2404.14286.
  42. G. Morras, G. Pratten, and P. Schmidt, Phys. Rev. D 111, 084052 (2025).
  43. G. Morras, G. Pratten, and P. Schmidt, arXiv:2503.15393.
  44. M. d. L. Planas, S. Husa, A. Ramos-Buades, and J. Valencia, arXiv:2506.01760.
  45. C. Cheung, I. Z. Rothstein, and M. P. Solon, Phys. Rev. Lett. 121, 251101 (2018).
  46. A. Buonanno, G. Mogull, R. Patil, and L. Pompili, Phys. Rev. Lett. 133, 211402 (2024).
  47. T. Damour, A. Nagar, A. Placidi, and P. Rettegno, arXiv:2503.05487.
  48. G. Kälin and R. A. Porto, J. High Energy Phys. 01 (2020) 072.
  49. G. Kälin and R. A. Porto, J. High Energy Phys. 02 (2020) 120.
  50. P. Rettegno, G. Pratten, L. M. Thomas, P. Schmidt, and T. Damour, Phys. Rev. D 108, 124016 (2023).
  51. S. Swain, G. Pratten, and P. Schmidt, Phys. Rev. D 111, 064048 (2025).
  52. T. Damour and P. Rettegno, Phys. Rev. D 107, 064051 (2023).
  53. A. Buonanno, G. U. Jakobsen, and G. Mogull, Phys. Rev. D 110, 044038 (2024).
  54. T. Damour, P. Jaranowski, and G. Schaefer, Phys. Rev. D 78, 024009 (2008).
  55. A. Placidi, P. Rettegno, and A. Nagar, Phys. Rev. D 109, 084065 (2024).
  56. M. Khalil, A. Buonanno, J. Steinhoff, and J. Vines, Phys. Rev. D 106, 024042 (2022).
  57. R. M. Wald, General Relativity (Chicago University Press, Chicago, USA, 1984).
  58. T. Damour, Phys. Rev. D 64, 124013 (2001).
  59. P. H. Damgaard, J. Hoogeveen, A. Luna, and J. Vines, Phys. Rev. D 106, 124030 (2022).
  60. T. Damour and A. Nagar, Phys. Rev. D 90, 044018 (2014).
  61. R. Geroch, J. Math. Phys. (N.Y.) 11, 1955 (1970).
  62. R. O. Hansen, J. Math. Phys. (N.Y.) 15, 46 (1974).
  63. K. S. Thorne, Rev. Mod. Phys. 52, 299 (1980).
  64. R. Beig and W. Simon, Proc. R. Soc. A 376, 333 (1981).
  65. S. Balmelli and T. Damour, Phys. Rev. D 92, 124022 (2015).
  66. B. Carter, Phys. Rev. 174, 1559 (1968).
  67. J. Vines and J. Steinhoff, Phys. Rev. D 97, 064010 (2018).
  68. G. U. Jakobsen, G. Mogull, J. Plefka, and B. Sauer, Phys. Rev. D 109, L041504 (2024).
  69. G. U. Jakobsen and G. Mogull, Phys. Rev. Lett. 128, 141102 (2022).
  70. D. Amati, M. Ciafaloni, and G. Veneziano, Nucl. Phys. B347, 550 (1990).
  71. Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, J. High Energy Phys. 10 (2019) 206.
  72. P. Di Vecchia, S. G. Naculich, R. Russo, G. Veneziano, and C. D. White, J. High Energy Phys. 03 (2020) 173.
  73. D. Bini, T. Damour, and A. Geralico, Phys. Rev. D 104, 084031 (2021).
  74. A. V. Manohar, A. K. Ridgway, and C.-H. Shen, Phys. Rev. Lett. 129, 121601 (2022).
  75. D. Bini, T. Damour, and A. Geralico, Phys. Rev. D 107, 024012 (2023).
  76. D. Bini and T. Damour, Phys. Rev. D 86, 124012 (2012).
  77. A. Antonelli, A. Buonanno, J. Steinhoff, M. van de Meent, and J. Vines, Phys. Rev. D 99, 104004 (2019).
  78. S. Hopper, A. Nagar, and P. Rettegno, Phys. Rev. D 107, 124034 (2023).
  79. S. Albanesi, A. Rashti, F. Zappa, R. Gamba, W. Cook, B. Daszuta, S. Bernuzzi, A. Nagar, and D. Radice, Phys. Rev. D 111, 024069 (2025).
  80. S. Albanesi, R. Gamba, S. Bernuzzi, J. Fontbuté, A. Gonzalez, and A. Nagar, arXiv:2503.14580.
  81. O. Long, H. P. Pfeiffer, A. Buonanno, G. U. Jakobsen, G. Mogull, A. Ramos-Buades, H. R. Rüter, L. E. Kidder, and M. A. Scheel, arXiv:2507.08071.
  82. T. Damour, P. Jaranowski, and G. Schaefer, Phys. Rev. D 62, 084011 (2000).
  83. S. Akcay, L. Barack, T. Damour, and N. Sago, Phys. Rev. D 86, 104041 (2012).
  84. T. Damour and G. Schaefer, Nuovo Cimento B 101, 127 (1988).
  85. D. Bini, T. Damour, and A. Geralico, Phys. Rev. Lett. 123, 231104 (2019).
  86. D. Bini, T. Damour, and A. Geralico, Phys. Rev. D 102, 084047 (2020).
  87. C. Dlapa, G. Kälin, Z. Liu, and R. A. Porto, Phys. Rev. Lett. 132, 221401 (2024).
  88. C. Dlapa, G. Kälin, Z. Liu, and R. A. Porto, arXiv:2506.20665.
  89. T. Damour, F. Guercilena, I. Hinder, S. Hopper, A. Nagar, and L. Rezzolla, Phys. Rev. D 89, 081503 (2014).
  90. J. Fontbuté, S. Bernuzzi, P. Rettegno, S. Albanesi, and W. Tichy, arXiv:2506.11204.
  91. T. Damour, B. R. Iyer, and B. S. Sathyaprakash, Phys. Rev. D 57, 885 (1998).
  92. E. Barausse and A. Buonanno, Phys. Rev. D 81, 084024 (2010).
  93. A. Nagar, Phys. Rev. D 84, 084028 (2011); 88, 089901(E) (2013).

Outline

Information

Phys. Rev. D 112, 104074– Published 25 November, 2025
  • Received 27 August 2025
  • Accepted 7 November 2025
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation