Skip to main content
Log in

The Canonical Structure of Bigravity

  • Published:
Astronomy Reports Aims and scope Submit manuscript

Abstract

This work is motivated by the intention to make the theory of bigravity more comprehensible. Bigravity is a modification of the General Relativity (GR), maybe even the most natural one because it is based on the equivalence principle. The Hamiltonian formalism in tetrad variables demonstrates the structure of bigravity most transparently.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. C. de Rham, G. Gabadadze, and A. J. Tolley, Phys. Lett. B 711, 190 (2012); arXiv: 1107.3820.

    Article  ADS  MathSciNet  Google Scholar 

  2. C. de Rham, G. Gabadadze, and A. J. Tolley, Phys. Rev. Lett. 106, 231101 (2011); arXiv: 1011.1232.

    Article  ADS  Google Scholar 

  3. C. de Rham, Living Rev. Relat. 17, 7 (2014); arXiv: 1401.4173.

  4. K. Hinterbichler and R. A. Rosen, J. High Energy Phys. 2012, 47 (2012); arXiv: 1203.5783.

    Article  Google Scholar 

  5. S. F. Hassan and R. A. Rosen, Phys. Rev. Lett. 108, 041101 (2012); arXiv: 1106.3344.

    Article  ADS  Google Scholar 

  6. S. F. Hassan, R. A. Rosen, and A. Schmidt-May, J. High Energy Phys. 2012, 26 (2012); arXiv: 1109.3230.

    Article  Google Scholar 

  7. S. F. Hassan and R. A. Rosen, J. High Energy Phys. 2012, 126 (2012); arXiv: 1109.3515.

    Article  Google Scholar 

  8. S. F. Hassan and R. A. Rosen, J. High Energy Phys. 2012, 123 (2012); arXiv: 1111.2070.

    Article  Google Scholar 

  9. S. F. Hassan, M. Kocic, and A. Schmidt-May, arXiv: 1409.1909 (2014).

  10. M. Kocic, arXiv: 1803.09752 (2018).

  11. P. A. M. Dirac, Can. J. Math. 2, 129 (1950).

    Article  Google Scholar 

  12. P. A. M. Dirac, Lectures on Quantum Mechanics, Belfer Graduate School of Science Monographs (Belfer Graduate School of Science, New York, NY, 1964). https://cds.cern.ch/record/113811.

    Google Scholar 

  13. R. Arnowitt, S. Deser, and C. W. Misner, in Gravitation, an Introduction to Current Research, Ed. by L. Witten (Wiley, New York, 1962), p. 227.

    MATH  Google Scholar 

  14. J. York, in Sources of Gravitational Radiation, Ed. by L. L. Smarr (Cambridge Univ. Press, New York, 1979), p. 83.

    Google Scholar 

  15. D. G. Boulware and S. Deser, Phys. Rev. D 6, 3368 (1972).

    Article  ADS  Google Scholar 

  16. K. Kuchař, in Relativity, Astrophysics and Cosmology, Proceedings of the Summer School, August 14–26, 1972, Banff, Alberta, Vol. 38 of Astrophysics and Space Science Library (Springer, 1973), p. 238.

  17. K. Kuchař, J. Math. Phys. 17, 777 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  18. K. Kuchař, J. Math. Phys. 17, 792 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  19. K. Kuchař, J. Math. Phys. 17, 801 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  20. K. Kuchař, J. Math. Phys. 18, 1589 (1977).

    Article  ADS  MathSciNet  Google Scholar 

  21. S. Deser and C. J. Isham, Phys. Rev. D 14, 2505 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  22. J. E. Nelson and C. Teitelboim, Ann. Phys. 116, 86 (1978).

    Article  ADS  Google Scholar 

  23. M. Henneaux, Gen. Relat. Grav. 9, 1031 (1978).

    Article  ADS  Google Scholar 

  24. M. Henneaux, Phys. Rev. D 27, 986 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  25. S. Alexandrov, Gen. Relat. Grav. 46, 1639 (2014); arXiv: 1308.6586.

  26. S. Alexandrov, K. Krasnov, and S. Speziale, J. High Energy Phys. 2013, 68 (2013); arXiv: 1212.3614.

    Article  Google Scholar 

  27. J. Klusoň, Eur. Phys. J. C 74, 2985 (2014); arXiv: 1307.1974.

    Article  ADS  Google Scholar 

  28. S. F. Hassan and A. Lundkvist, J. High Energy Phys. 2018, 182 (2018); arXiv: 1802.07267.

  29. D. Comelli, M. Crisostomi, F. Nesti, and L. Pilo, Phys. Rev. D 86, 101502 (2012); arXiv: 1204.1027.

    Article  ADS  Google Scholar 

  30. D. Comelli, F. Nesti, and L. Pilo, Phys. Rev. D 87, 124021 (2013); arXiv: 1302.4447.

    Article  ADS  Google Scholar 

  31. D. Comelli, F. Nesti, and L. Pilo, J. High Energy Phys., No. 07, 161 (2013); arXiv: 1305.0236.

  32. V. O. Soloviev and M. V. Chichikina, Theor. Math. Phys. 176, 1163 (2013); arXiv: 1211.6530.

    Article  Google Scholar 

  33. V. O. Soloviev and M. V. Tchichikina, Phys. Rev. D 88, 084026 (2013); arXiv: 1302.5096.

    Article  ADS  Google Scholar 

  34. V. O. Soloviev, Theor. Math. Phys. 182, 294 (2015).

    Article  Google Scholar 

  35. V. O. Soloviev, Phys. Part. Nucl. 48, 287 (2017).

    Article  Google Scholar 

  36. D. B. Fairlie and A. N. Leznov, J. Geom. Phys. 16, 385 (1995); hep-th/9403134.

    Article  ADS  MathSciNet  Google Scholar 

Download references

ACKNOWLEDGMENTS

The author is most grateful to the Organizing Committee of the IV Zeldovich Meeting for the opportunity to participate in this exciting conference.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. O. Soloviev.

Additional information

Paper presented at the Fourth Zeldovich meeting, an international conference in honor of Ya.B. Zeldovich held in Minsk, Belarus, on September 7–11, 2020. Published by the recommendation of the special editors: S.Ya. Kilin, R. Ruffini, and G.V. Vereshchagin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Soloviev, V.O. The Canonical Structure of Bigravity. Astron. Rep. 65, 1057–1061 (2021). https://doi.org/10.1134/S1063772921100383

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063772921100383

Navigation