Skip to main content
SpringerLink
Log in

Energy-Momentum Localization for a Space-Time Geometry Exterior to a Black Hole in the Brane World

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

In general relativity one of the most fundamental issues consists in defining a generally acceptable definition for the energy-momentum density. As a consequence, many coordinate-dependent definitions have been presented, whereby some of them utilize appropriate energy-momentum complexes. We investigate the energy-momentum distribution for a metric exterior to a spherically symmetric black hole in the brane world by applying the Landau-Lifshitz and Weinberg prescriptions. In both the aforesaid prescriptions, the energy thus obtained depends on the radial coordinate, the mass of the black hole and a parameter λ 0, while all the momenta are found to be zero. It is shown that for a special value of the parameter λ 0, the Schwarzschild space-time geometry is recovered. Some particular and limiting cases are also discussed.

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.

Similar content being viewed by others

References

  1. Senovilla, J.M.M.: Class. Quantum Gravity 17, 2799 (2000) and references therein

    Article  MathSciNet  MATH  ADS  Google Scholar 

  2. Szabados, L.B.: Living Rev. Relativ. 7, 4 (2004) and references therein

    ADS  Google Scholar 

  3. Einstein, A.: Preuss. Akad. Wiss. Berl. 47, 778 (1915)

    Google Scholar 

  4. Addendum 47, 799 (1915)

  5. Trautman, A.: In: Witten, L. (ed.) Gravitation: An Introduction to Current Research, p. 169. Wiley, New York (1962)

    Google Scholar 

  6. Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields, p. 280. Pergamon, Elmsford (1987)

    Google Scholar 

  7. Papapetrou, A.: Proc. R. Ir. Acad. A 52, 11 (1948)

    MathSciNet  Google Scholar 

  8. Bergmann, P.G., Thomson, R.: Phys. Rev. 89, 400 (1953)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  9. Møller, C.: Ann. Phys. (NY) 4, 347 (1958)

    Article  ADS  Google Scholar 

  10. Goldberg, J.N.: Phys. Rev. 111, 315 (1958)

    Article  MathSciNet  MATH  ADS  Google Scholar 

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

    Google Scholar 

  12. Qadir, A., Sharif, M.: Phys. Lett. A 167, 331 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  13. Møller, C.: Ann. Phys. 12, 118 (1961)

    Article  ADS  Google Scholar 

  14. Møller, C.: Tetrad fields and conservation laws in general relativity. In: Møller, C. (ed.) Proc. International School of Physics “Enrico Fermi”. Academic Press, London (1962)

    Google Scholar 

  15. Maluf, J.W., Veiga, M.V.O., da Rocha-Neto, J.F.: Gen. Relativ. Gravit. 39, 227 (2007)

    Article  MATH  ADS  Google Scholar 

  16. Nashed, G.G.L.: Eur. Phys. J. C 49, 851 (2007)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  17. Liu, Y.X., Zhao, Z.H., Yang, J., Duan, Y.S.: arXiv:0706.3245 [gr-qc]

  18. Nester, J.M., Loi So, L., Vargas, T.: Phys. Rev. D 78, 044035 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  19. Sharif, M., Taj, S.: Astrophys. Space Sci. 325, 75 (2010)

    Article  MATH  ADS  Google Scholar 

  20. Virbhadra, K.S.: Phys. Rev. D 41, 1086 (1990)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  21. Virbhadra, K.S.: Phys. Rev. D 42, 1066 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  22. Virbhadra, K.S.: Phys. Lett. A 157, 195 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  23. Virbhadra, K.S., Parikh, J.C.: Phys. Lett. B 331, 302 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  24. Chamorro, A., Virbhadra, K.S.: Pramana J. Phys. 45, 181 (1995)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  MATH  ADS  Google Scholar 

  26. Virbhadra, K.S.: Phys. Rev. D 60, 104041 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  27. Bringley, T.: Mod. Phys. Lett. A 17, 157 (2002)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  28. Yang, I.-C., Radinschi, I.: Chin. J. Phys. 41, 326 (2003)

    MathSciNet  Google Scholar 

  29. Sharif, M.: Nuovo Cimento B 119, 463 (2004)

    MathSciNet  ADS  Google Scholar 

  30. Gad, R.M.: Astrophys. Space Sci. 295, 451 (2005)

    Article  ADS  Google Scholar 

  31. Vagenas, E.C.: Int. J. Mod. Phys. D 14, 573 (2005)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  32. Yang, I.-C., Lin, C.-L., Radinschi, I.: Int. J. Theor. Phys. 48, 248 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  33. Radinschi, I., Grammenos, Th., Spanou, A.: Cent. Eur. J. Phys. 9(5), 1173 (2011)

    Article  Google Scholar 

  34. Sharif, M., Amir, M.J.: Can. J. Phys. 86, 1091 (2008)

    Article  ADS  Google Scholar 

  35. Sharif, M., Amir, M.J.: Mod. Phys. Lett. A 23, 3167 (2008)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  36. Sharif, M., Nazir, K.: Braz. J. Phys. 38, 156 (2008)

    Article  ADS  Google Scholar 

  37. Chang, C.-C., Nester, J.M., Chen, C.-M.: Phys. Rev. Lett. 83, 1897 (1999)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  38. So, L.L., Nester, J.M., Chen, H.: Class. Quantum Gravity 26, 085004 (2009)

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  MATH  ADS  Google Scholar 

  40. Virbhadra, K.S.: Phys. Rev. D 60, 104041 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  41. Penrose, R.: Proc. R. Soc. Lond., A 381, 53 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  42. Tod, K.P.: Proc. R. Soc. Lond., A 388, 457 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  43. Lessner, G.: Gen. Relativ. Gravit. 28, 527 (1996)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  44. Cooperstock, F.I.: Mod. Phys. Lett. A 14, 1531 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  45. Maartens, R.: Living Rev. Relativ. 13, 5 (2010)

    ADS  Google Scholar 

  46. Tanahashi, N., Tanaka, T.: Prog. Theor. Phys. Suppl. 189, 227 (2011)

    Article  ADS  Google Scholar 

  47. Kanti, P.: J. Phys. Conf. Ser. 189, 012020 (2009)

    Article  ADS  Google Scholar 

  48. Whisker, R.: Ph.D. Thesis, University of Durham (2006)

  49. Brax, P., van de Bruck, C.: Class. Quantum Gravity 20, R201 (2003)

    Article  MATH  ADS  Google Scholar 

  50. Liu, Y.X., Zhang, L.J., Wang, Y.Q., Duan, Y.S.: Mod. Phys. Lett. A 23, 769 (2008)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  51. Gamal, G., Nashed, L.: Chin. Phys. B 19(2), 020401 (2010)

    Article  Google Scholar 

  52. Casadio, R., Fabbri, A., Mazzacurati, L.: Phys. Rev. D 65, 084040 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  53. Bajc, B., Gabadadze, G.: Phys. Lett. B 474, 282 (2000)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  54. Germani, C., Maartens, R.: Phys. Rev. D 64, 124010 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  55. Bronnikov, K.A., Kim, S.W.: Phys. Rev. D 67, 064027 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  56. Aldrovandi, R., Pereira, J.G.: An Introduction to Teleparallel Gravity. Notes (2007)

Download references

Acknowledgements

The authors would like to thank Dr. G.O. Papadopoulos for his valuable suggestions.

Author information

Authors and Affiliations

  1. Department of Physics, “Gh. Asachi” Technical University, Iasi, 700050, Romania

    Irina Radinschi

  2. Department of Civil Engineering, University of Thessaly, 383 34, Volos, Greece

    Theophanes Grammenos

  3. School of Applied Mathematics and Physical Sciences, National Technical University of Athens, 157 80, Athens, Greece

    Andromahi Spanou

Authors
  1. Irina Radinschi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Theophanes Grammenos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andromahi Spanou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Irina Radinschi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Radinschi, I., Grammenos, T. & Spanou, A. Energy-Momentum Localization for a Space-Time Geometry Exterior to a Black Hole in the Brane World. Int J Theor Phys 52, 757–764 (2013). https://doi.org/10.1007/s10773-012-1384-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-012-1384-3

Keywords

Search

Navigation