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New self-consistent effective one-body theory for spinless binaries based on the post-Minkowskian approximation

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Abstract

The effective one-body theories, introduced by Buonanno and Damour, are novel approaches to constructing a gravitational waveform template. By taking a gauge in which ψ B1 and ψ B3 vanish, we find a decoupled equation with separable variables for ψ B4 in the effective metric obtained in the post-Minkowskian approximation. Furthermore, we set up a new self-consistent effective one-body theory for spinless binaries, which can be applicable to any post-Minkowskian orders. This theory not only releases the assumption that v/c should be a small quantity but also resolves the contradiction that the Hamiltonian, radiation-reaction force, and waveform are constructed from different physical models in the effective one-body theory with the post-Newtonian approximation. Compared with our previous theory [Sci. China-Phys. Mech. Astron. 65, 260411 (2022)], the computational effort for the radiation-reaction force and waveform in this new theory will be tremendously reduced.

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References

  1. A. Einstein, Über Gravitationswellen (Nabu Press, Berlin, 1918).

    MATH  Google Scholar 

  2. H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, Proc. R. Soc. London A269, 21 (1962).

    ADS  Google Scholar 

  3. R. K. Sachs, Proc. R. Soc. London A270, 103 (1962).

    ADS  Google Scholar 

  4. P. de Bernardis, P. A. R. Ade, J. J. Bock, J. R. Bond, J. Borrill, A. Boscaleri, K. Coble, B. P. Crill, G. De Gasperis, P. C. Farese, P. G. Ferreira, K. Ganga, M. Giacometti, E. Hivon, V. V. Hristov, A. Iacoangeli, A. H. Jaffe, A. E. Lange, L. Martinis, S. Masi, P. V. Mason, P. D. Mauskopf, A. Melchiorri, L. Miglio, T. Montroy, C. B. Netterfield, E. Pascale, F. Piacentini, D. Pogosyan, S. Prunet, S. Rao, G. Romeo, J. E. Ruhl, F. Scaramuzzi, D. Sforna, and N. Vittorio, Nature 404, 955 (2000), arXiv: astro-ph/0004404.

    Article  ADS  Google Scholar 

  5. E. Komatsu, K. M. Smith, J. Dunkley, C. L. Bennett, B. Gold, G. Hinshaw, N. Jarosik, D. Larson, M. R. Nolta, L. Page, D. N. Spergel, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, G. S. Tucker, J. L. Weiland, E. Wollack, and E. L. Wright, Astrophys. J. Suppl. Ser. 192, 18 (2011), arXiv: 1001.4538.

    Article  ADS  Google Scholar 

  6. S. Perlmutter, G. Aldering, M. della Valle, S. Deustua, R. S. Ellis, S. Fabbro, A. Fruchter, G. Goldhaber, D. E. Groom, I. M. Hook, A. G. Kim, M. Y. Kim, R. A. Knop, C. Lidman, R. G. McMahon, P. Nugent, R. Pain, N. Panagia, C. R. Pennypacker, P. Ruiz-Lapuente, B. Schaefer, and N. Walton, Nature 391, 51 (1998), arXiv: astro-ph/9712212.

    Article  ADS  Google Scholar 

  7. Y. Zou, M. Wang, and J. Jing, Sci. China-Phys. Mech. Astron. 64, 250411 (2021).

    Article  ADS  Google Scholar 

  8. X. K. He, J. L. Jing, and Z. J. Cao, Sci. China-Phys. Mech. Astron. 62, 110422 (2019).

    Article  ADS  Google Scholar 

  9. B. P. Abbott, et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 116, 061102 (2016), arXiv: 1602.03837.

    Article  ADS  MathSciNet  Google Scholar 

  10. B. P. Abbott, et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 116, 241103 (2016), arXiv: 1606.04855.

    Article  ADS  Google Scholar 

  11. B. P. Abbott, et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 118, 221101 (2017), arXiv: 1706.01812.

    Article  ADS  Google Scholar 

  12. B. P. Abbott, et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 119, 141101 (2017), arXiv: 1709.09660.

    Article  ADS  Google Scholar 

  13. B. P. Abbott, et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 119, 161101 (2017), arXiv: 1710.05832.

    Article  ADS  Google Scholar 

  14. B. P. Abbott, et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. X 9, 031040 (2019), arXiv: 1811.12907.

    Google Scholar 

  15. R. Abbott, et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. X 11, 021053 (2021), arXiv: 2010.14527.

    Google Scholar 

  16. R. Abbott et al. (LIGO Scientific Collaboration, Virgo Collaboration and KAGRA Collaboration), arXiv: 2105.15120.

  17. R. Abbott, et al. (LIGO Scientific Collaboration and Virgo Collaboration), arXiv: 2110.09834.

  18. A. H. Nitz, C. D. Capano, S. Kumar, Y. F. Wang, S. Kastha, M. Schafer, R. Dhurkunde, and M. Cabero, arXiv: 2105.09151.

  19. A. Buonanno, and T. Damour, Phys. Rev. D 59, 084006 (1999), arXiv: gr-qc/9811091.

    Article  ADS  MathSciNet  Google Scholar 

  20. A. Buonanno, and T. Damour, Phys. Rev. D 62, 064015 (2000), arXiv: gr-qc/0001013.

    Article  ADS  Google Scholar 

  21. T. Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 62, 084011 (2000), arXiv: gr-qc/0005034.

    Article  ADS  Google Scholar 

  22. T. Damour, Phys. Rev. D 64, 124013 (2001), arXiv: gr-qc/0103018.

    Article  ADS  MathSciNet  Google Scholar 

  23. A. Buonanno, Y. Chen, and T. Damour, Phys. Rev. D 74, 104005 (2006), arXiv: gr-qc/0508067.

    Article  ADS  MathSciNet  Google Scholar 

  24. T. Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 91, 084024 (2015), arXiv: 1502.07245.

    Article  ADS  MathSciNet  Google Scholar 

  25. A. Buonanno, G. B. Cook, and F. Pretorius, Phys. Rev. D 75, 124018 (2007), arXiv: gr-qc/0610122.

    Article  ADS  MathSciNet  Google Scholar 

  26. Y. Pan, A. Buonanno, J. G. Baker, J. Centrella, B. J. Kelly, S. T. McWilliams, F. Pretorius, and J. R. van Meter, Phys. Rev. D 77, 024014 (2008), arXiv: 0704.1964.

    Article  ADS  Google Scholar 

  27. A. Buonanno, Y. Pan, J. G. Baker, J. Centrella, B. J. Kelly, S. T. McWilliams, and J. R. van Meter, Phys. Rev. D 76, 104049 (2007), arXiv: 0706.3732.

    Article  ADS  Google Scholar 

  28. T. Damour, and A. Nagar, Phys. Rev. D 77, 024043 (2008), arXiv: 0711.2628.

    Article  ADS  Google Scholar 

  29. T. Damour, A. Nagar, E. N. Dorband, D. Pollney, and L. Rezzolla, Phys. Rev. D 77, 084017 (2008), arXiv: 0712.3003.

    Article  ADS  Google Scholar 

  30. M. Boyle, A. Buonanno, L. E. Kidder, A. H. Mroué, Y. Pan, H. P. Pfeiffer, and M. A. Scheel, Phys. Rev. D 78, 104020 (2008), arXiv: 0804.4184.

    Article  ADS  Google Scholar 

  31. T. Damour, A. Nagar, M. Hannam, S. Husa, and B. Brügmann, Phys. Rev. D 78, 044039 (2008), arXiv: 0803.3162.

    Article  ADS  Google Scholar 

  32. T. Damour, and A. Nagar, Phys. Rev. D 76, 064028 (2007), arXiv: 0705.2519.

    Article  ADS  MathSciNet  Google Scholar 

  33. A. Buonanno, Y. Pan, H. P. Pfeiffer, M. A. Scheel, L. T. Buchman, and L. E. Kidder, Phys. Rev. D 79, 124028 (2009), arXiv: 0902.0790.

    Article  ADS  Google Scholar 

  34. Y. Pan, A. Buonanno, L. T. Buchman, T. Chu, L. E. Kidder, H. P. Pfeiffer, and M. A. Scheel, Phys. Rev. D 81, 084041 (2010), arXiv: 0912.3466.

    Article  ADS  Google Scholar 

  35. T. Damour, and A. Nagar, Phys. Rev. D 79, 081503 (2009), arXiv: 0902.0136.

    Article  ADS  Google Scholar 

  36. Y. Pan, A. Buonanno, M. Boyle, L. T. Buchman, L. E. Kidder, H. P. Pfeiffer, and M. A. Scheel, Phys. Rev. D 84, 124052 (2011), arXiv: 1106.1021.

    Article  ADS  Google Scholar 

  37. E. Barausse, A. Buonanno, S. A. Hughes, G. Khanna, S. O’Sullivan, and Y. Pan, Phys. Rev. D 85, 024046 (2012), arXiv: 1110.3081.

    Article  ADS  Google Scholar 

  38. A. Taracchini, Y. Pan, A. Buonanno, E. Barausse, M. Boyle, T. Chu, G. Lovelace, H. P. Pfeiffer, and M. A. Scheel, Phys. Rev. D 86, 024011 (2012), arXiv: 1202.0790.

    Article  ADS  Google Scholar 

  39. A. Taracchini, A. Buonanno, Y. Pan, T. Hinderer, M. Boyle, D. A. Hemberger, L. E. Kidder, G. Lovelace, A. H. Mroué, H. P. Pfeiffer, M. A. Scheel, B. Szilágyi, N. W. Taylor, and A. Zenginoglu, Phys. Rev. D 89, 061502 (2014), arXiv: 1311.2544.

    Article  ADS  Google Scholar 

  40. A. Bohé, L. Shao, A. Taracchini, A. Buonanno, S. Babak, I. W. Harry, I. Hinder, S. Ossokine, M. Pürrer, V. Raymond, T. Chu, H. Fong, P. Kumar, H. P. Pfeiffer, M. Boyle, D. A. Hemberger, L. E. Kidder, G. Lovelace, M. A. Scheel, and B. Szilágyi, Phys. Rev. D 95, 044028 (2017), arXiv: 1611.03703.

    Article  ADS  Google Scholar 

  41. Z. Cao, and W. B. Han, Phys. Rev. D 96, 044028 (2017), arXiv: 1708.00166.

    Article  ADS  Google Scholar 

  42. T. Damour, Phys. Rev. D 94, 104015 (2016), arXiv: 1609.00354.

    Article  ADS  MathSciNet  Google Scholar 

  43. D. Bini, and T. Damour, Phys. Rev. D 96, 104038 (2017), arXiv: 1709.00590.

    Article  ADS  MathSciNet  Google Scholar 

  44. D. Bini, and T. Damour, Phys. Rev. D 98, 044036 (2018), arXiv: 1805.10809.

    Article  ADS  MathSciNet  Google Scholar 

  45. T. Damour, Phys. Rev. D 97, 044038 (2018), arXiv: 1710.10599.

    Article  ADS  MathSciNet  Google Scholar 

  46. A. Antonelli, A. Buonanno, J. Steinhoff, M. van de Meent, and J. Vines, Phys. Rev. D 99, 104004 (2019), arXiv: 1901.07102.

    Article  ADS  MathSciNet  Google Scholar 

  47. T. Damour, Phys. Rev. D 102, 024060 (2020), arXiv: 1912.02139.

    Article  ADS  MathSciNet  Google Scholar 

  48. D. Bini, T. Damour, and A. Geralico, Phys. Rev. D 101, 044039 (2020), arXiv: 2001.00352.

    Article  ADS  MathSciNet  Google Scholar 

  49. G. He, and W. Lin, Phys. Rev. D 94, 063011 (2016), arXiv: 2007.11809.

    Article  ADS  MathSciNet  Google Scholar 

  50. L. Blanchet, and A. S. Fokas, Phys. Rev. D 98, 084005 (2018), arXiv: 1806.08347.

    Article  ADS  MathSciNet  Google Scholar 

  51. C. Cheung, I. Z. Rothstein, and M. P. Solon, Phys. Rev. Lett. 121, 251101 (2018), arXiv: 1808.02489.

    Article  ADS  Google Scholar 

  52. J. Vines, J. Steinhoff, and A. Buonanno, Phys. Rev. D 99, 064054 (2019), arXiv: 1812.00956.

    Article  ADS  MathSciNet  Google Scholar 

  53. A. Cristofoli, N. E. J. Bjerrum-Bohr, P. H. Damgaard, and P. Vanhove, Phys. Rev. D 100, 084040 (2019), arXiv: 1906.01579.

    Article  ADS  MathSciNet  Google Scholar 

  54. A. Koemans Collado, P. Di Vecchia, and R. Russo, Phys. Rev. D 100, 066028 (2019), arXiv: 1904.02667.

    Article  ADS  MathSciNet  Google Scholar 

  55. J. Plefka, C. Shi, J. Steinhoff, and T. Wang, Phys. Rev. D 100, 086006 (2019), arXiv: 1906.05875.

    Article  ADS  MathSciNet  Google Scholar 

  56. D. Bini, T. Damour, and A. Geralico, Phys. Rev. D 101, 044039 (2020), arXiv: 2001.00352.

    Article  ADS  MathSciNet  Google Scholar 

  57. C. Cheung, and M. P. Solon, Phys. Rev. Lett. 125, 191601 (2020), arXiv: 2006.06665.

    Article  ADS  MathSciNet  Google Scholar 

  58. Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon, and M. Zeng, Phys. Rev. Lett. 122, 201603 (2019), arXiv: 1901.04424.

    Article  ADS  Google Scholar 

  59. Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon, and M. Zeng, J. High Energ. Phys. 2019(10), 206 (2019).

    Article  ADS  Google Scholar 

  60. J. Jing, S. Chen, M. Sun, X. He, M. Wang, and J. Wang, Sci. China-Phys. Mech. Astron. 65, 260411 (2022), arXiv: 2112.09838.

    Article  ADS  Google Scholar 

  61. J. E. Thompson, H. Chen, and B. F. Whiting, Class. Quantum Grav. 34, 174001 (2017).

    Article  ADS  Google Scholar 

  62. S. Chandrasekhar, The Mathematical Theory of Black Hole (Oxford University Press, New York, Oxford, 1992).

    Google Scholar 

  63. M. Carmeli, Classical Fields: General Relativity and Gauge Theory (A Wiley-Intersclence Publication, New York, 1982).

    MATH  Google Scholar 

  64. S. A. Teukolsky, Astrophys. J. 185, 635 (1973).

    Article  ADS  Google Scholar 

  65. M. Sasaki, and H. Tagoshi, Living Rev. Relativ. 6, 6 (2003), arXiv: gr-qc/0306120.

    Article  ADS  Google Scholar 

  66. M. Sasaki, and T. Nakamura, Phys. Lett. A 87, 85 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  67. E. Poisson, Phys. Rev. D 47, 1497 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  68. H. Tagoshi, and M. Sasaki, Prog. Theor. Phys. 92, 745 (1994), arXiv: gr-qc/9405062.

    Article  ADS  Google Scholar 

  69. L. E. Kidder, Phys. Rev. D 77, 044016 (2008), arXiv: 0710.0614.

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, 410081, China

    Jiliang Jing, Sheng Long, Weike Deng, Mengjie Wang & Jieci Wang

  2. Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou, 225009, China

    Jiliang Jing

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  1. Jiliang Jing
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  2. Sheng Long
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  3. Weike Deng
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  4. Mengjie Wang
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Correspondence to Jiliang Jing, Mengjie Wang or Jieci Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12035005, 12122504, and 11875025), and National Key Research and Development Program of China (Grant No. 2020YFC2201400). We would like to thank professors S. Chen and Q. Pan for useful discussions on the manuscript.

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Jing, J., Long, S., Deng, W. et al. New self-consistent effective one-body theory for spinless binaries based on the post-Minkowskian approximation. Sci. China Phys. Mech. Astron. 65, 100411 (2022). https://doi.org/10.1007/s11433-022-1951-1

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