Skip to main content
SpringerLink
Log in

Energy–momentum localization for Bianchi type-IV Universe in general relativity and teleparallel gravity

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

In this study we have investigated the energy–momentum distributions for homogeneous and anisotropic Bianchi type-IV in B class Universe. For this purpose, we have used energy–momentum complexes of Einstein, Bergmann–Thomson, Landau–Lifshitz (LL), Papapetrou, Tolman and Møller in general relativity (GR) is also Einstein, Bergmann–Thomson, Landau–Lifshitz and Møller in teleparallel gravity (TG). From the obtained results we have found that Einstein and Bergmann–Thomson distributions are exactly giving the same results in GR and TG but the Landau–Lifshitz, Papapetrou Tolman and Møller energy–momentum distributions do not provide the same results with Einstein and Bergmann–Thomson in GR and TG. Furthermore, Einstein, Bergmann–Thomson and LL results are the same in different gravitation theories and we get that both GR and TG are equivalent theories for these prescriptions. From the obtained solutions, we could say that these are equivalent theories. Also, Møller energy–momentum distributions do not give the same results in GR and TG. However, we have found that all energy prescriptions are negative and our results agree with Nester et al.

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

Similar content being viewed by others

References

  1. A Einstein, Preuss. Akad. Wiss. Berlin 47, 778 (1915)

    Google Scholar 

  2. A Papapetrou, Proc. R. Irish. Acad. A52, 11 (1948)

    MathSciNet  Google Scholar 

  3. R C Tolman, Relativity, thermodynamics and cosmology (Oxford Univ. Press., London, 1934)

    Google Scholar 

  4. P G Bergmann and R Thomson, Phys. Rev. 89, 400 (1953)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. C Møller, Ann. Phys. (NY) 4, 347 (1958); 12, 118 (1961)

    Google Scholar 

  6. L D LLandau and E M Lifshitz, The classical theory of fields, 4th edn (Pergamon Press, Oxford, 1987)

    Google Scholar 

  7. S Weinberg, Gravitation and cosmology. Principle and applications of general theory of relativity (John Wiley and Sons, Inc., New York, 1972)

    Google Scholar 

  8. A Qadir and M Sharif, Phys. Lett. A167, 331 (1982)

    MathSciNet  ADS  Google Scholar 

  9. T Vargas, Gen. Relativ. Gravit. 36, 1255 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. F I Mikhail, M I Wanas, A Hindawi and E I Lashin, Int. J. Theor. Phys. 32, 1627 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  11. K S Virbhadra, Phys. Rev. D42, 2919 (1990)

    MathSciNet  ADS  Google Scholar 

  12. S S Xulu, Int. J. Mod. Phys. A15, 2979 (2000)

    MathSciNet  ADS  Google Scholar 

  13. K S Virbhadra, Phys. Rev. DX60, 104041 (1999)

    MathSciNet  ADS  Google Scholar 

  14. K S Virbhadra and J C Parikh, Phys. Lett. B317, 312 (1993)

    MathSciNet  ADS  Google Scholar 

  15. K S Virbhadra, Pramana – J. Phys. 45, 215 (1995)

    Google Scholar 

  16. K S Virbhadra, Phys. Rev. D41, 1086 (1990)

    MathSciNet  ADS  Google Scholar 

  17. N Rosen and K S Virbhadra, Gen. Relativ. Gravit. 25, 429 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. S Aygün, M Aygün and İ Tarhan, Acta Phys. Pol. B37, 2781 (2006)

    ADS  Google Scholar 

  19. M Aygün, İ Yılmaz and S Aygün, Acta Phys. Pol. B37, 2795 (2006)

    ADS  Google Scholar 

  20. M Aygün and İ Yılmaz, Acta Phys. Polon. B38, 2497 (2007)

    ADS  Google Scholar 

  21. S Aygün, İ Tarhan and H Baysal, Astrophys. Space Sci. 314, 323 (2008)

    Article  ADS  MATH  Google Scholar 

  22. M Aygün and İ Yılmaz, Int. J. Theor. Phys. 47, 707 (2008)

    Article  MATH  Google Scholar 

  23. S Aygün, Int. J. Theor. Phys. 49, 2288 (2010)

    Article  MATH  Google Scholar 

  24. E C Vagenas, Int. J. Mod. Phys. A18, 5949 (2003)

    MathSciNet  ADS  Google Scholar 

  25. E C Vagenas, Int. J. Mod. Phys. D14, 573 (2005)

    MathSciNet  ADS  Google Scholar 

  26. E C Vagenas, Mod. Phys. Lett. A21, 1947 (2006)

    MathSciNet  ADS  Google Scholar 

  27. I Radinschi, Acta Phys. Slov. 49, 789 (1999)

    ADS  Google Scholar 

  28. I Radinschi, Fizika B9, 203 (2000)

    ADS  Google Scholar 

  29. I Radinschi, Chin. J. Phys. 39, 393 (2001)

    Google Scholar 

  30. I Radinschi, Chin. J. Phys. 39, 231 (2001)

    Google Scholar 

  31. I Ching and I Radinschi, Chin. J. Phys. 41, 326 (2003)

    Google Scholar 

  32. R M Gad, Mod. Phys. Lett. 19, 1847 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. R M Gad, Astrophys. Space Sci. 314, 341 (2008)

    Article  ADS  Google Scholar 

  34. M Sharif and S Taj, Mod. Phys. Lett. A25, 221 (2010)

    MathSciNet  ADS  Google Scholar 

  35. G G Nashed, Phys. Rev. D66, 060415 (2002)

    MathSciNet  Google Scholar 

  36. M Favata, Phys. Rev. D63, 064013 (2001)

    MathSciNet  ADS  Google Scholar 

  37. S S Xulu, Int. J. Theor. Phys. 39, 1153 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  38. N Banerjee and S Sen, Pramana – J. Phys. 49, 609 (1997)

    Article  ADS  Google Scholar 

  39. O Aydoǧdu and M Saltı, Astrophys. Space Sci. 299, 227 (2005)

    Google Scholar 

  40. S L Loi and T Vargas, Chin. J. Phys. 43, 901 (2005)

    Google Scholar 

  41. O Aydoǧdu, Int. J. Mod. Phys. D15, 459 (2006)

    ADS  Google Scholar 

  42. O Aydoǧdu and M Saltı, Czech. J. Phys. 56, 8 (2006)

    Google Scholar 

  43. O Aydoǧdu and M Saltı, Prog. Theor. Phys. 115, 63 (2006)

    Article  ADS  Google Scholar 

  44. M Nester, L L So and T Vargas, Phys. Rev. D78, 044035 (2008)

    MathSciNet  ADS  Google Scholar 

  45. E Di Pietro and J Demaret, Int. J. Mod. Phys. D8, 349 (1999)

    ADS  Google Scholar 

  46. M P Ryan and L C Shepley, Homogeneous relativistic cosmologies (Princeton University Press, Princeton, 1975)

    Google Scholar 

  47. M A H MacCallum, in: General relativity, an Einstein centenary edited by S Hawking and W Israel (Cambridge University Press, New York, 1979)

    Google Scholar 

  48. M E Araujo and J E F Skea, Class. Quantum Grav. 5, 537 (1988)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  49. D Kramer, H Stephani, M A H MacCallum and E Herlt, Exact solutions of Einstein’s field equations (Cambridge University Press, Cambridge, 1980)

    MATH  Google Scholar 

  50. V C de Andrade, L C T Guillen and J G Pereira, in: Contribution to the IX Marcel Grossmann meeting (Rome, Italy, July 2000) gr-qc/0011087

  51. K Hayashi and T Shirafuji, Prog. Theor. Phys. 64, 866 (1980); 65, 525 (1980)

  52. F I Cooperstock, Mod. Phys. Lett. A14, 1531 (1999)

    MathSciNet  ADS  Google Scholar 

  53. T Bringley, Mod. Phys. Lett. A17, 157 (2002)

    MathSciNet  ADS  Google Scholar 

  54. O Patashnick, Int. J. Mod. Phys. D14, 1607 (2005)

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Art and Science Faculty, Çanakkale Onsekiz Mart University, 17020, Çanakkale, Turkey

    SEZGİN AYGÜN & İSMAİL TARHAN

  2. Çanakkale Onsekiz Mart University, Astrophysics Research Center, Çanakkale, Turkey

    SEZGİN AYGÜN & İSMAİL TARHAN

Authors
  1. SEZGİN AYGÜN
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. İSMAİL TARHAN
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to SEZGİN AYGÜN.

Rights and permissions

Reprints and permissions

About this article

Cite this article

AYGÜN, S., TARHAN, İ. Energy–momentum localization for Bianchi type-IV Universe in general relativity and teleparallel gravity. Pramana - J Phys 78, 531–548 (2012). https://doi.org/10.1007/s12043-012-0261-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12043-012-0261-1

Keywords

PACS Nos

Search

Navigation