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  • Letter
  • Open Access

Gravitational scattering of two neutron stars

Joan Fontbuté1,*, Sebastiano Bernuzzi1,†, Piero Rettegno2, Simone Albanesi1,3, and Wolfgang Tichy4

  • *Contact author: joan.fontbute@uni-jena.de
  • †Contact author: sebastiano.bernuzzi@uni-jena.de
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Phys. Rev. D 112, L121501 – Published 1 December, 2025

DOI: https://doi.org/10.1103/d7j1-wsp4

Abstract

We present the first numerical relativity simulations of the gravitational scattering of two neutron stars. Constraint-satisfying initial data for two equal-mass nonspinning sequences are constructed at fixed energy and various initial angular momenta (impact parameter) and evolved with Einstein equations through the scattering process. The strong-field scattering dynamics are explored up to scattering angles of 220° and the threshold of dynamical captures. The transition to bound orbits is aided by significant mass ejecta up to baryon mass ∼0.1M⊙. A quantitative comparison with predictions of the scattering angle from state-of-the-art effective-one-body and post-Minkowskian calculations indicates quantitative agreement for large initial angular momenta, although significant discrepancies in the tidal contribution emerge toward the capture threshold. Gravitational waveforms and radiated energy are in qualitative agreement with the analogous black hole problem and state-of-the-art effective-one-body predictions. Toward the capture threshold, waveforms from scattering dynamics carry a strong imprint of matter effects, including the stars’ f-mode excitations during the close encounter. Overall, our simulations open a new avenue to study tidal interactions in the relativistic two-body problem.

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References (104)

  1. F. Pretorius, Classical Quantum Gravity 23, S529 (2006).
  2. J. G. Baker, J. Centrella, D.-I. Choi, M. Koppitz, and J. van Meter, Phys. Rev. Lett. 96, 111102 (2006).
  3. M. Campanelli, C. O. Lousto, P. Marronetti, and Y. Zlochower, Phys. Rev. Lett. 96, 111101 (2006).
  4. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 116, 061102 (2016).
  5. M. Shibata, H. Okawa, and T. Yamamoto, Phys. Rev. D 78, 101501 (2008).
  6. U. Sperhake, V. Cardoso, F. Pretorius, E. Berti, T. Hinderer et al., Phys. Rev. Lett. 103, 131102 (2009).
  7. R. Gold and B. Brügmann, Phys. Rev. D 88, 064051 (2013).
  8. U. Sperhake, E. Berti, V. Cardoso, and F. Pretorius, Phys. Rev. Lett. 111, 041101 (2013).
  9. T. Damour, F. Guercilena, I. Hinder, S. Hopper, A. Nagar, and L. Rezzolla, Phys. Rev. D 89, 081503 (2014).
  10. S. Hopper, A. Nagar, and P. Rettegno, Phys. Rev. D 107, 124034 (2023).
  11. P. Rettegno, G. Pratten, L. M. Thomas, P. Schmidt, and T. Damour, Phys. Rev. D 108, 124016 (2023).
  12. O. Long, C. Whittall, and L. Barack, Phys. Rev. D 110, 044039 (2024).
  13. 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).
  14. S. Swain, G. Pratten, and P. Schmidt, Phys. Rev. D 111, 064048 (2025).
  15. M. A. M. Smith, V. Paschalidis, and G. Bozzola, Phys. Rev. D 111, 104031 (2025).
  16. M. A. M. Smith, V. Paschalidis, and G. Bozzola, Phys. Rev. D 111, 104032 (2025).
  17. J. Fontbuté, T. Andrade, R. Luna, J. Calderón Bustillo, G. Morrás, S. Jaraba, J. García-Bellido, and G. L. Izquierdo, Phys. Rev. D 111, 044024 (2025).
  18. S. Albanesi, R. Gamba, S. Bernuzzi, J. Fontbuté, A. Gonzalez, and A. Nagar, arXiv:2503.14580.
  19. M. Punturo, M. Abernathy, F. Acernese, B. Allen, N. Andersson et al., Classical Quantum Gravity 27, 194002 (2010).
  20. P. Amaro-Seoane et al. (LISA Collaboration), arXiv:1702.00786.
  21. D. Reitze et al., Bull. Am. Astron. Soc. 51, 035 (2019), https://inspirehep.net/literature/1743201.
  22. N. Afshordi et al. (LISA Consortium Waveform Working Group Collaboration), Living Rev. Relativity 28, 9 (2025).
  23. A. Abac et al., arXiv:2503.12263.
  24. A. Buonanno and T. Damour, Phys. Rev. D 59, 084006 (1999).
  25. A. Buonanno and T. Damour, Phys. Rev. D 62, 064015 (2000).
  26. A. Nagar and P. Rettegno, Phys. Rev. D 104, 104004 (2021).
  27. A. Nagar, D. Chiaramello, R. Gamba, S. Albanesi, S. Bernuzzi, V. Fantini, M. Panzeri, and P. Rettegno, Phys. Rev. D 111, 064050 (2025).
  28. L. Pompili et al., Phys. Rev. D 108, 124035 (2023).
  29. A. Gamboa et al., Phys. Rev. D 112, 044038 (2025).
  30. G. Kälin and R. A. Porto, J. High Energy Phys. 11 (2020) 106.
  31. G. Kälin, Z. Liu, and R. A. Porto, Phys. Rev. Lett. 125, 261103 (2020).
  32. C. Dlapa, G. Kälin, Z. Liu, and R. A. Porto, Phys. Rev. Lett. 128, 161104 (2022).
  33. C. Dlapa, G. Kälin, Z. Liu, J. Neef, and R. A. Porto, Phys. Rev. Lett. 130, 101401 (2023).
  34. J. Vines, Classical Quantum Gravity 35, 084002 (2018).
  35. A. Guevara, A. Ochirov, and J. Vines, Phys. Rev. D 100, 104024 (2019).
  36. Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, Phys. Rev. Lett. 122, 201603 (2019).
  37. 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).
  38. 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).
  39. A. V. Manohar, A. K. Ridgway, and C.-H. Shen, Phys. Rev. Lett. 129, 121601 (2022).
  40. A. Koemans Collado, P. Di Vecchia, and R. Russo, Phys. Rev. D 100, 066028 (2019).
  41. P. Di Vecchia, S. G. Naculich, R. Russo, G. Veneziano, and C. D. White, J. High Energy Phys. 03 (2020) 173.
  42. P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, J. High Energy Phys. 07 (2021) 169.
  43. P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, Phys. Lett. B 818, 136379 (2021).
  44. D. Bini and T. Damour, Phys. Rev. D 106, 124049 (2022).
  45. D. Bini, T. Damour, and A. Geralico, Phys. Rev. D 107, 024012 (2023).
  46. G. U. Jakobsen, G. Mogull, J. Plefka, B. Sauer, and Y. Xu, Phys. Rev. Lett. 131, 151401 (2023).
  47. M. Driesse, G. U. Jakobsen, G. Mogull, J. Plefka, B. Sauer, and J. Usovitsch, Phys. Rev. Lett. 132, 241402 (2024).
  48. D. Bini, T. Damour, and A. Geralico, Phys. Rev. D 101, 044039 (2020).
  49. Z. Bern, J. Parra-Martinez, R. Roiban, E. Sawyer, and C.-H. Shen, J. High Energy Phys. 05 (2021) 188.
  50. C. Cheung and M. P. Solon, Phys. Rev. Lett. 125, 191601 (2020).
  51. G. Kälin, Z. Liu, and R. A. Porto, Phys. Rev. D 102, 124025 (2020).
  52. G. U. Jakobsen, G. Mogull, J. Plefka, and B. Sauer, Phys. Rev. D 109, L041504 (2024).
  53. S. J. Kovacs and K. S. Thorne, Astrophys. J. 217, 252 (1977).
  54. A. Brandhuber, G. R. Brown, G. Chen, S. De Angelis, J. Gowdy, and G. Travaglini, J. High Energy Phys. 06 (2023) 048.
  55. A. Georgoudis, C. Heissenberg, and I. Vazquez-Holm, J. High Energy Phys. 06 (2023) 126.
  56. M. Khalil, A. Buonanno, J. Steinhoff, and J. Vines, Phys. Rev. D 106, 024042 (2022).
  57. T. Damour and P. Rettegno, Phys. Rev. D 107, 064051 (2023).
  58. A. Buonanno, G. U. Jakobsen, and G. Mogull, Phys. Rev. D 110, 044038 (2024).
  59. T. Damour, Phys. Rev. D 94, 104015 (2016).
  60. A. Buonanno, G. Mogull, R. Patil, and L. Pompili, Phys. Rev. Lett. 133, 211402 (2024).
  61. T. Damour, A. Nagar, A. Placidi, and P. Rettegno, arXiv:2503.05487.
  62. T. Baumgarte, G. Cook, M. Scheel, S. Shapiro, and S. Teukolsky, Phys. Rev. D 57, 7299 (1998).
  63. H. P. Pfeiffer and J. W. York, Jr., Phys. Rev. D 67, 044022 (2003).
  64. J. A. Isenberg, Int. J. Mod. Phys. D 17, 265 (2008).
  65. N. Moldenhauer, C. M. Markakis, N. K. Johnson-McDaniel, W. Tichy, and B. Brügmann, Phys. Rev. D 90, 084043 (2014).
  66. W. Tichy, Phys. Rev. D 84, 024041 (2011).
  67. W. Tichy, Phys. Rev. D 86, 064024 (2012).
  68. T. Dietrich, N. Moldenhauer, N. K. Johnson-McDaniel, S. Bernuzzi, C. M. Markakis, B. Brügmann, and W. Tichy, Phys. Rev. D 92, 124007 (2015).
  69. W. Tichy, A. Rashti, T. Dietrich, R. Dudi, and B. Brügmann, Phys. Rev. D 100, 124046 (2019).
  70. J. S. Read, B. D. Lackey, B. J. Owen, and J. L. Friedman, Phys. Rev. D 79, 124032 (2009).
  71. T. Damour and A. Nagar, Phys. Rev. D 81, 084016 (2010).
  72. T. Damour, A. Nagar, and L. Villain, Phys. Rev. D 85, 123007 (2012).
  73. S. Bernuzzi and D. Hilditch, Phys. Rev. D 81, 084003 (2010).
  74. D. Hilditch, S. Bernuzzi, M. Thierfelder, Z. Cao, W. Tichy, and B. Bruegmann, Phys. Rev. D 88, 084057 (2013).
  75. M. Alcubierre, B. Brügmann, P. Diener, F. S. Guzman, I. Hawke et al., Phys. Rev. D 72, 044004 (2005).
  76. J. G. Baker, J. R. van Meter, S. T. McWilliams, J. Centrella, and B. J. Kelly, Phys. Rev. Lett. 99, 181101 (2007).
  77. J. M. Bowen and J. W. York, Jr., Phys. Rev. D 21, 2047 (1980).
  78. S. Brandt and B. Brügmann, Phys. Rev. Lett. 78, 3606 (1997).
  79. M. Ansorg, B. Brügmann, and W. Tichy, Phys. Rev. D 70, 064011 (2004).
  80. B. Brügmann, J. A. Gonzalez, M. Hannam, S. Husa, U. Sperhake et al., Phys. Rev. D 77, 024027 (2008).
  81. M. Thierfelder, S. Bernuzzi, and B. Brügmann, Phys. Rev. D 84, 044012 (2011).
  82. S. Bernuzzi, A. Nagar, M. Thierfelder, and B. Brügmann, Phys. Rev. D 86, 044030 (2012).
  83. J. Fontbuté, S. Bernuzzi, S. Albanesi, D. Radice, A. Rashti, W. Cook, B. Daszuta, and A. Nagar, arXiv:2508.03799.
  84. D. Radice, F. Galeazzi, J. Lippuner, L. F. Roberts, C. D. Ott, and L. Rezzolla, Mon. Not. R. Astron. Soc. 460, 3255 (2016).
  85. L. J. Papenfort, R. Gold, and L. Rezzolla, Phys. Rev. D 98, 104028 (2018).
  86. S. V. Chaurasia, T. Dietrich, N. K. Johnson-McDaniel, M. Ujevic, W. Tichy, and B. Brügmann, Phys. Rev. D 98, 104005 (2018).
  87. A. Neuweiler, T. Dietrich, and B. Brügmann, Phys. Rev. D 112, 023033 (2025).
  88. R. Gamba et al., arXiv:2307.15125.
  89. D. Bini, T. Damour, and G. Faye, Phys. Rev. D 85, 124034 (2012).
  90. S. Bernuzzi, A. Nagar, T. Dietrich, and T. Damour, Phys. Rev. Lett. 114, 161103 (2015).
  91. S. Akcay, S. Bernuzzi, F. Messina, A. Nagar, N. Ortiz, and P. Rettegno, Phys. Rev. D 99, 044051 (2019).
  92. G. U. Jakobsen, G. Mogull, J. Plefka, and B. Sauer, Phys. Rev. Lett. 131, 241402 (2023).
  93. M. Campanelli, B. J. Kelly, and C. O. Lousto, Phys. Rev. D 73, 064005 (2006).
  94. H. Nakano, J. Healy, C. O. Lousto, and Y. Zlochower, Phys. Rev. D 91, 104022 (2015).
  95. C. Reisswig and D. Pollney, Classical Quantum Gravity 28, 195015 (2011).
  96. Y. B. Zel’dovich and A. G. Polnarev, Sov. Astron. 18, 17 (1974), https://inspirehep.net/literature/1760701.
  97. V. B. Braginsky and L. P. Grishchuk, Sov. Phys. JETP 62, 427 (1985), https://inspirehep.net/literature/237866.
  98. D. Chiaramello and A. Nagar, Phys. Rev. D 101, 101501 (2020).
  99. R. Gold, S. Bernuzzi, M. Thierfelder, B. Brügmann, and F. Pretorius, Phys. Rev. D 86, 121501 (2012).
  100. B. P. Abbott et al. (Virgo and LIGO Scientific Collaborations), Phys. Rev. Lett. 119, 161101 (2017).
  101. S. De, D. Finstad, J. M. Lattimer, D. A. Brown, E. Berger, and C. M. Biwer, Phys. Rev. Lett. 121, 091102 (2018); 121, 259902(E) (2018).
  102. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. X 9, 011001 (2019).
  103. S. Rosswog, T. Piran, and E. Nakar, Mon. Not. R. Astron. Soc. 430, 2585 (2013).
  104. www.gauss-centre.eu.

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Phys. Rev. D 112, L121501– Published 1 December, 2025
  • Received 23 June 2025
  • Accepted 7 November 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.

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