Skip to main content
SpringerLink
Log in

Two-Body Problem in Curved Spacetime: the Case of GW150914

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

We compare two versions of the analysis of the gravitational wave signal GW150914 presented previously by the LIGO/Virgo collaboration (LVC). The first version was presented in 2016 by this collaboration along with their announcement of the first experimental detection of gravitational waves [1]. It was based on rigorous general-relativistic treatment of the coalescing two-body problem. The second analysis of this signal by the same authors [2] was based on the quadrupole post-Newtonian (PN) approximation of General Relativity (GR). We revisit this post-Newtonian analysis and estimate the mass of the coalescing binary blackhole system using frequency values read directly from the time-frequency diagram of GW150914. Our estimation, similarly to the PN-result from [2], coincides with the rigorously calculated mass for this system from the LVC first publication. Additionally, we estimate the masses of other coalescing binary systems by using the same quadrupole PN-approximation formula applied to the data from the published gravitational wave transient catalogues. Practically all of our PN-approximation estimates coincide with the published masses based on the rigorous methods. In our view, this coincidence means that the rigorous theory for gravitational waveforms of coalescing blackhole binaries does not fully account for the difference between the source and detector reference frames because the PN-approximation, which is used for the comparison, does not make any distinction between these two reference frames: by design and by the principles and conditions for building the PN-approximation. We discuss possible implications of this conflict and find that the accuracy of the previously estimated characteristic (chirp) masses of coalescing binary blackhole systems is likely to be affected by a systematic error.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Data Availability

The data underlying this article are available in the Gravitational Wave Open Science Center repository, at https://doi.org/10.7935/82H3-HH23, in the GitHub repository at https://github.com/gwastro/2-ogc, https://doi.org/10.7935/qf3a-3z67, and in the public domain resource Stellarcollapse at https://stellarcollapse.org/bhmasses.html.

References

  1. B.P. Abbott et al., LVC (LIGO Scientific and Virgo Collaborations), Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 241102 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  2. B.P. Abbott et al., LVC, The basic physics of the binary black hole merger GW150914. Ann. Phys. 529, 1600209 (2017)

    Article  Google Scholar 

  3. A. Einstein, Approximate Integration of the Field Equations of Gravitation (Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften, Berlin, 1916), pp.688–696

    MATH  Google Scholar 

  4. A. Einstein, über Gravitationswellen (Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften, Berlin, 1918), pp.154–167

    MATH  Google Scholar 

  5. L.D. Landau, E.M. Lifshitz, Theoretical Physics, Vol. II Field Theory, 3-rd Edition, “Fizmatlit”, Moscow (1960)

  6. Zeldovich Ya. B., Novikov I.D., 1967, Relativistic Astrophysics, “Nauka” Publishers, Moscow, p. 82

  7. C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation, W.H. Freeman and Co., San Francisco, Vol. 1, 2, 3 (1973)

  8. T.-P. Cheng, Relativity, Gravitation and Cosmology (Oxford Univ. Press, Oxford, 2005), pp.260–268

    Google Scholar 

  9. M. Maggiore, Gravitational Waves. Oxford Univ Press 1, 236–299 (2008)

    Google Scholar 

  10. P.C. Peters, J. Mathews, Gravitational radiation from point masses in a Keplerian orbit. Phys. Rev. 131, 435–440 (1963)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. R.A. Hulse, J.H. Taylor, Discovery of a pulsar in a binary system. ApJ 195, L51–L53 (1975)

    Article  ADS  Google Scholar 

  12. C.M. Will, On the unreasonable effectiveness of the post-Newtonian approximation in gravitational physics. Proc. Nat. Acad. Sci. 108, 5938–5945 (2011)

    Article  ADS  Google Scholar 

  13. L. Blanchet, Gravitational radiation from post-Newtonian sources and inspiralling compact binaries. Living Rev Relativity 17(2) (187) (2014)

  14. M. Arimoto, H. Asada, M.L. Cherry, M.S. Fujii, Y. Fukazava, A. Harada, K. Hayama, K. Ioka, Y. Itoh, N. Kanda et al., Gravitational wave physics and astronomy in the nascent era. Progr. Theor. Exp. Phys. 042, 83 (2021)

    Google Scholar 

  15. P. Gurfil, M. Efroimsky, Analysis of the PPN two-body problem using non-osculating orbital elements. Adv. Space Res. 69, 538–553 (2022)

    Article  ADS  Google Scholar 

  16. L.D. Landau, E.M. Lifshitz, Theoretical Physics, Vol. II Field Theory, 8-th Edition, “Fizmatlit”, Moscow (2003)

  17. S.A. Kaplan, On circular orbits in Einstein’s gravitation theory. J. Exper. Theor. Phys. (ZhETF) 19, 951–952 (1949)

    ADS  Google Scholar 

  18. A. Buonanno, T. Damour, Effective one-body approach to general relativistic two-body dynamics. Phys. Rev. D 59, 084006 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  19. R. Arnowitt, S. Deser, C.M. Misner, Dynamical structure and definition of energy in general relativity. Phys. Rev. 116, 1322 (1959)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. R. Arnowitt, S. Deser, C.M. Misner, Consistency of the canonical reduction of general relativity. J. Math. Phys. 1, 434–439 (1960)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. G. Schäfer, The gravitational quadrupole radiation-reaction force and the canonical formalism of ADM. Ann. Phys. 161, 81–100 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  22. G. Schäfer, P. Jaranowski, Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries. Living Rev. Relativity 21, 7 (2018)

    Article  ADS  Google Scholar 

  23. V.P. Frolov, I.D. Novikov, Black hole physics, Kluwer Acad Publ., Dordrecht, Boston, London, p.66 (1998)

  24. B.P. Abbott et al., GWTC-1: a gravitational-wave transient catalog of compact binary mergers observed by LIGO and virgo during the first and second observing runs. Phys. Rev. X 9, 031040 (2019)

    Google Scholar 

  25. T. Venumadhav, B. Zackay, J. Roulet, L. Dai, M. Zaldarriaga, New binary black hole mergers in the second observing run of Advanced LIGO and Advanced Virgo. Phys. Rev. D 101, 083030 (2020)

    Article  ADS  Google Scholar 

  26. A.H. Nitz et al., 2-OGC: open gravitational-wave catalog of binary mergers from analysis of public advanced LIGO and virgo data. ApJ 891, 123 (2020)

    Article  ADS  Google Scholar 

  27. B.P. Abbott et al., GW190412: observation of a binary-black-hole coalescence with asymmetric masses. Phys. Rev. D 102, 043015 (2020)

    Article  ADS  Google Scholar 

  28. B.P. Abbott et al., GW190425: Observation of a Compact Binary Coalescence with Total Mass similar to 3.4 M\(_\odot \), ApJ 892, L3 (24pp) (2020b)

  29. R. Abbott, et al., GW190814: Gravitational waves from the coalescence of a 23 solar mass black hole with a 2.6 solar mass compact object. ApJ 896, L44 (20pp) (2020d)

  30. Abbott R. et al., 2021a, GWTC-2.1: Deep extended catalog of compact binary coalescences observed by LIGO and virgo during the first half of the third observing run, e-print arXiv:2108.01045

  31. Abbott R. et al., 2021b, GWTC-3: compact binary coalescences observed by LIGO and virgo during the second part of the third observing run, e-print arXiv:2111.03606

  32. R. Abbott et al., Open data from the first and second observing runs of advanced LIGO and Advanced Virgo. SoftwareX 13, 100658 (2021)

    Article  Google Scholar 

  33. G. Wiktorowicz, K. Belczynski, T. J. Maccarone, Black hole X-ray transients: the formation puzzle, e-print arXiv:1312.5924 (2013)

Download references

Acknowledgements

This research has made use of data or software obtained from the Gravitational Wave Open Science Center (gw-openscience.org), a service of LIGO Laboratory, the LIGO Scientific Collaboration, the Virgo Collaboration, and KAGRA. LIGO Laboratory and Advanced LIGO are funded by the United States National Science Foundation (NSF) as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. Virgo is funded, through the European Gravitational Observatory (EGO), by the French Centre National de Recherche Scientifique (CNRS), the Italian Istituto Nazionale di Fisica Nucleare (INFN) and the Dutch Nikhef, with contributions by institutions from Belgium, Germany, Greece, Hungary, Ireland, Japan, Monaco, Poland, Portugal, Spain. The construction and operation of KAGRA are funded by Ministry of Education, Culture, Sports, Science and Technology (MEXT), and Japan Society for the Promotion of Science (JSPS), National Research Foundation (NRF) and Ministry of Science and ICT (MSIT) in Korea, Academia Sinica (AS) and the Ministry of Science and Technology (MoST) in Taiwan. In particular we have made use of the following archives: GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs [24]; GWTC\(-\)2.1: Deep Extended Catalog of Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run [30]; GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run [31, 32]; 2-OGC: Open Gravitational-wave Catalog of binary mergers from analysis of public Advanced LIGO and Virgo data [26] and the list of blackholes found in Galactic X-ray binaries [33]. We would like to thank Dr. Leslie Morrison, Dr. Alice Breeveld, Prof. Mat Page, Prof. Sergei Soloviev and Prof. Elena N. Polyakhova for useful discussions on the matters in this paper.

Funding

The authors did not receive support from any organization for the submitted work.

Author information

Authors and Affiliations

  1. Moniteye U.K., 30a Upper High Street, Thame, OX9 3EX, UK

    Vladimir N. Yershov

  2. Formerly Mullard Space Science Laboratory, University College London, London, UK

    Vladimir N. Yershov

  3. Special Astrophysical Observatory, Russian Academy of Science, Niznii, 369167, Arkhyz, Russia

    Alexander A. Raikov

  4. Pulkovo Observatory, Russian Academy of Science, Pulkovskoye shosse 65 (1), St.Petersburg, 196140, Russia

    Elena A. Popova

Authors
  1. Vladimir N. Yershov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander A. Raikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Elena A. Popova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir N. Yershov.

Ethics declarations

Conflict of interest

All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.

Ethics approval

This research does not involve human participants and/or animals.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yershov, V.N., Raikov, A.A. & Popova, E.A. Two-Body Problem in Curved Spacetime: the Case of GW150914. Few-Body Syst 64, 33 (2023). https://doi.org/10.1007/s00601-023-01799-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00601-023-01799-9

Search

Navigation