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Some examples for different descriptions of energy–momentum density in the context of Bianchi IX cosmological model

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Abstract

Based on the Bianchi type IX metric, we calculate the energy and momentum density components of the gravitational field for the five different definitions of energy–momentum, namely, Tolman, Papapetrou, Landau-Lifshitz, Møller and Weinberg. The energy densities of Møller and Weinberg become zero for the spacetime under consideration. In the other prescriptions, i.e., Tolman, Papapetrou and Landau-Lifshitz complexes, we find different non-vanishing energy–momentum densities for the given spacetime, supporting the well-known argument in general relativity that the different definitions may lead to different distributions even in the same spacetime background.

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Notes

  1. Throughout this paper, Latin indices (i, j,…) represent the spatial coordinate values while Greek indices (μ, ν,…) represent the spacetime labels. We set the fundamental constants equal to unity; G = c = 1.

References

  1. S S Xulu The energy–momentum problem in general relativity. PhD Thesis (arXiv:hep-th/0308070)

  2. A Einstein Preuss. Akad. Wiss. Berlin 47 778 (1915); Addendum-ibid. 47 799 (1915)

    Google Scholar 

  3. R C Tolman Relativity, Thermodynamics and Cosmology (London: Oxford University Press) p 227 (1934)

    Google Scholar 

  4. A Papapetrou Proc. R. Ir. Acad. A 52 11 (1948)

    MathSciNet  Google Scholar 

  5. L D Landau and E M Lifshitz The Classical Theory of Fields (USA: Addison Wesley Press) p 317 (1951)

    MATH  Google Scholar 

  6. P G Bergmann and R Thompson Phys. Rev. 89 400 (1953)

    Article  ADS  MATH  Google Scholar 

  7. J N Goldberg Phys. Rev. 111 315 (1958)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. C Møller Ann. Phys. (N.Y.) 4 347 (1958)

    Article  ADS  Google Scholar 

  9. S Weinberg Gravitation and Cosmology: Principles and Applications of General Theory of Relativity (New York: Wiley) p 165 (1972)

    Google Scholar 

  10. R Penrose Proc. R. Soc. Lond. A 381 53 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  11. K S Virbhadra Pramana 38 31 (1992)

  12. N Rosen and K S Virbhadra Gen. Rel. Grav. 25 429 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. K S Virbhadra Pramana 44 317 (1995)

    Article  ADS  Google Scholar 

  14. K S Virbhadra Pramana 45 215 (1995)

    Article  ADS  Google Scholar 

  15. S S Xulu Int. J. Theor. Phys. 37 1773 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  16. S S Xulu Mod. Phys. Lett. A 15 1511 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. M Sharif Int. J. Mod. Phys. A 17 1175 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. S S Xulu Int. J. Theor. Phys. 46 2915 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  19. A M Abbassi S Mirshekari and A H Abbassi Phys. Rev. D 78 064053 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  20. M Sharif and M F Shamir Gen. Relativ. Grav. 42 1557 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. A Tyagi K Sharma and P Jain Chin. Phys. Lett. 27 079801 (2010)

    Article  Google Scholar 

  22. K S Virbhadra Phys. Rev. D 60 104041 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  23. A P Mishra, R K Mohapatra, P S Saumia and A M Srivastava Indian J. Phys. 85 909 (2011)

    Article  ADS  Google Scholar 

  24. D S Wamalwa and J A Omolo Indian J. Phys. 84 1241 (2010)

    Article  ADS  Google Scholar 

  25. V A Belinski, I M Khalatnikov and E M Lifshitz Adv. Phys. 19 525 (1970)

    Article  ADS  Google Scholar 

  26. C Misner Phys. Rev. Lett. 22 1071 (1969)

    Article  ADS  MATH  Google Scholar 

  27. T Damour, M Henneaux and H Nicolai Class. Quant. Grav. 20 R145 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. A Pradhan and K Jotania Indian J. Phys. 85 497 (2011); S Agarwal, R K Pandey and A Pradhan Indian J. Phys. 86 61 (2012)

  29. P Das and A Deshamukhya Indian J. Phys. 84 617 (2010)

    Article  Google Scholar 

  30. S Kalita, H L Duorah and K Duorah Indian J. Phys. 84 629 (2010)

    Article  Google Scholar 

  31. J Perez Dynamics of Anisotropic Universes (arXiv:gr-qc/0603124)

  32. A Kheyfets, W A Miller and R Vaulin Class. Quant. Grav. 23 4333 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. I Bakas, F Bourliot, D Lust and M Petropoulos Class. Quant. Grav. 27 045013 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  34. T Damour and P Spindel Phys. Rev. D 83 123520 (2011)

    Article  ADS  Google Scholar 

  35. J D Barrow and K Yamamoto The Instabilities of Bianchi Type IX Einstein Static Universes (arXiv:1108.3962)

  36. V A Belinsky, E M Lifshitz and I M Khalatnikov Sov. Phys. JETP 33 1061 (1971)

    ADS  Google Scholar 

  37. V A Belinsky and I M Khalatnikov Sov. Phys. JETP 29 911 (1969)

    ADS  Google Scholar 

  38. K S Virbhadra Phys. Rev. D 41 1086 (1990)

  39. K S Virbhadra Phys. Rev. D 42 1066 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  40. K S Virbhadra Phys. Rev. D 42 2919 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  41. K S Virbhadra and J C Parikh Phys. Lett. B 317 312 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  42. K S Virbhadra and J C Parikh Phys. Lett. B 331 302 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  43. A Chamorro and K S Virbhardra Int. J. Mod. Phys. D 5 251 (1997)

    Article  ADS  Google Scholar 

  44. J M Aguirregabiria, A Chamorro and K S Virbhadra Gen. Relativ. Gravit. 28 1393 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  45. S S Xulu Int. J. Mod. Phys. D 7 773 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  46. S S Xulu Int. J. Mod. Phys. A 15 2979 (2000)

    MathSciNet  ADS  MATH  Google Scholar 

  47. S S Xulu Astrophys. Space Sci. 283 23 (2003)

    Article  ADS  MATH  Google Scholar 

  48. G Bergqvist Class. Quant. Grav. 9 1753 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  49. G Bergqvist Class. Quant. Grav. 9 1917 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  50. F I Cooperstock and R S Sarracino J. Phys. A 11 877 (1978)

    Article  MathSciNet  ADS  Google Scholar 

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Acknowledgments

ZN thanks H. Farajollahi for discussions. We thank the anonymous referees for their useful comments.

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Authors and Affiliations

  1. Bandaranzali Branch, Islamic Azad University, Bandaranzali, Iran

    Z. Nourinezhad

  2. Lahijan Branch, Islamic Azad University, P.O. Box 1616, Lahijan, Iran

    S. H. Mehdipour

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  1. Z. Nourinezhad
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  2. S. H. Mehdipour
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Correspondence to S. H. Mehdipour.

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Nourinezhad, Z., Mehdipour, S.H. Some examples for different descriptions of energy–momentum density in the context of Bianchi IX cosmological model. Indian J Phys 86, 919–923 (2012). https://doi.org/10.1007/s12648-012-0131-1

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  • DOI: https://doi.org/10.1007/s12648-012-0131-1

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