Skip to main content

Advertisement

SpringerLink
Log in

On the relative energy associated with space-times of diagonal metrics

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

In order to evaluate the energy distribution (due to matter and fields including gravitation) associated with a space-time model of generalized diagonal metric, we consider the Einstein, Bergmann-Thomson and Landau-Lifshitz energy and/or momentum definitions both in Einstein’s theory of general relativity and the teleparallel gravity (the tetrad theory of gravitation). We find same energy distribution using Einstein and Bergmann-Thomson formulations, but we also find that the energy-momentum prescription of Landau-Lifshitz disagree in general with these definitions. We also give eight different well-known space-time models as examples, and considering these models and using our results, we calculate the energy distributions associated with them. Furthermore, we show that for the Bianchi Type-I models all the formulations give the same result. This result agrees with the previous works of Cooperstock-Israelit, Rosen, Johri et al, Banerjee-Sen, Xulu, Vargas and Saltı et al and supports the viewpoints of Albrow and Tryon.

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. R C Tolman, Relativity, thermodynamics and cosmology (Oxford University Press, London, 1934) p. 227

    Google Scholar 

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

    MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  ADS  Google Scholar 

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

    Article  MATH  ADS  Google Scholar 

  5. C Møller, Ann. Phys. (NY) 12, 118 (1961)

    Article  MATH  ADS  Google Scholar 

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

    Google Scholar 

  7. A Qadir and M Sharif, Phys. Lett. A167, 331 (1992)

    MathSciNet  ADS  Google Scholar 

  8. L D Landau and E M Lifshitz, The classical theory of fields, 4th edition (Pergamon Press, Oxford, 1987) (Reprinted in 2002)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. I Radinschi, Mod. Phys. Lett. A15, 2171 (2000)

    MathSciNet  ADS  Google Scholar 

  12. I Radinschi, Fizika B9, 43 (2000); Chin. J. Phys. 42, 40 (2004); Fizika B14, 3 (2005); Mod. Phys. Lett. A17, 1159 (2002); U.V.T., Physics Series 42, 11 (2001); Mod. Phys. Lett. A16, 673 (2001); Acta Phys. Slov. 49, 789 (1999); Acta Phys. Slov. 50, 609 (2000); Mod. Phys. Lett. A15, 803 (2000)

    ADS  Google Scholar 

  13. Th Grammenos and I Radinschi, gr-qc/0602105

  14. I-Ching Yang and Irina Radinschi, Chin. J. Phys. 41, 326 (2003)

    MathSciNet  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  17. K S Virbhadra, Phys. Rev. D60, 104041 (1999)

    Google Scholar 

  18. F I Cooperstock and S A Richardson, in Proc. 4th Canadian Conf. on General Relativity and Relativistic Astrophysics (World Scientific, Singapore, 1991)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  20. K S Virbhadra, Pramana — J. Phys. 45, 215 (1995)

    ADS  Google Scholar 

  21. A Chamorro and K S Virbhadra, Pramana — J. Phys. 45, 181 (1995)

    ADS  Google Scholar 

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

    Article  MATH  MathSciNet  ADS  Google Scholar 

  23. A Chamorro and K S Virbhadra, Int. J. Mod. Phys. D5, 251 (1996)

    MathSciNet  ADS  Google Scholar 

  24. S S Xulu, Int. J. Mod. Phys. A15, 4849 (2000)

    MathSciNet  ADS  Google Scholar 

  25. E C Vagenas, Int. J. Mod. Phys. A18, 5781 (2003); Int. J. Mod. Phys. A18, 5949 (2003); Mod. Phys. Lett. A19, 213 (2004); Int. J. Mod. Phys. D14, 573 (2005); Int. J. Mod. Phys. A21, 1947 (2006)

    MathSciNet  ADS  Google Scholar 

  26. H V Fagundes, Gen. Relativ. Gravit. 24(2), (1992)

  27. M Saltı and A Havare, Int. J. Mod. Phys. A20, 2169 (2005)

    ADS  Google Scholar 

  28. M Saltı, Astrophys. Space Sci. 299, 159 (2005); Mod. Phys. Lett. A20, 2175 (2005); Acta Phys. Slov. 55, 563 (2005); Czech. J. Phys. 56, 177 (2006)

    Article  ADS  Google Scholar 

  29. M Saltı and O Aydogdu, Found. Phys. Lett. 19, 269 (2006)

    Article  MathSciNet  Google Scholar 

  30. O Aydogdu and M Saltı, Prog. Theor. Phys. 115, 63 (2006)

    Article  MATH  ADS  Google Scholar 

  31. O Aydogdu, M Saltı and M Korunur, Acta Phys. Slov. 55, 537 (2005)

    Google Scholar 

  32. A Havare, M Korunur and M Saltı, Astrophys. Space Sci. 301, 43 (2006)

    Article  ADS  Google Scholar 

  33. J A Plebanski and M Demianski, Ann. Phys. (NY) 98, 98 (1976)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  34. O J C Dias and J P S Lemos, Phys. Rev. D67, 064001 (2003)

  35. C Wu, Gen. Relativ. Gravit. 3, 625 (1969)

    Google Scholar 

  36. A H Guth, Phys. Rev. D23, 347 (1981)

    ADS  Google Scholar 

  37. A D Linde, Phys. Lett. B108, 389 (1982)

    MathSciNet  ADS  Google Scholar 

  38. A D Linde, Phys. Lett. B129, 177 (1983)

    MathSciNet  ADS  Google Scholar 

  39. A Albrecht and P J Steinhardt, Phys. Rev. D48, 1220 (1982)

    ADS  Google Scholar 

  40. J D Barrow, Phys. Rev. D55, 7451 (1997)

    ADS  Google Scholar 

  41. O Heckmann and E Schucking, Newtonsche and Einsteinsche Kosmologie, Handbuch der Physik 53, 489 (1959)

    ADS  Google Scholar 

  42. R Weitzenböck, Invariantten theorie (Gronningen, Noordhoff, 1923)

    Google Scholar 

  43. K Hayashi and T Shirafuji, Phys. Rev. D19, 3524 (1978)

    MathSciNet  ADS  Google Scholar 

  44. V V de Andrade and J G Pereira, Phys. Rev. D56, 4689 (1997)

    ADS  Google Scholar 

  45. C Møller, Mat. Fys. Medd. K. Vidensk. Selsk. 39, 13 (1978); 1, 10 (1961)

    Google Scholar 

  46. D Saez, Phys. Rev. D27, 2839 (1983)

    MathSciNet  ADS  Google Scholar 

  47. H Meyer, Gen. Relativ. Gravit. 14, 531 (1982)

    Article  Google Scholar 

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

    MATH  MathSciNet  ADS  Google Scholar 

  49. F W Hehl, J Nitsch and P von der Heyde, General relativity and gravitation edited by A Held (Plenum, New York, 1980)

    Google Scholar 

  50. M G Albrow, Nature (London) 241, 56 (1973)

    ADS  Google Scholar 

  51. E P Tryon, Nature (London) 246, 396 (1973)

    Article  ADS  Google Scholar 

  52. F I Cooperstock, Gen. Relativ. Gravit. 26, 323 (1994)

    Article  Google Scholar 

  53. F I Cooperstock and M Israelit, Found. Phys. 25, 631 (1995)

    Article  MathSciNet  Google Scholar 

  54. N Rosen, Gen. Relativ. Gravit. 26, 319 (1994)

    Article  Google Scholar 

  55. V B Johri, D Kalligas, G P Singh and C W F Everitt, Gen. Relativ. Gravit. 27, 323 (1995)

    Article  MathSciNet  Google Scholar 

  56. N Banerjee and S Sen, Pramana — J. Phys. 49, 609 (1997)

    ADS  Google Scholar 

  57. S S Xulu, Int. J. Theor. Phys. 30, 1153 (2000)

    Article  MathSciNet  Google Scholar 

  58. M Saltı, Nuovo Cimento B120, 53 (2005)

    ADS  Google Scholar 

  59. G Gamow, Nature (London) 158, 549 (1946)

    Google Scholar 

  60. K Gödel, Rev. Mod. Phys. 21, 447 (1949)

    Article  MATH  ADS  Google Scholar 

  61. O Gron and H H Soleng, Acta Phys. Pol. B20, 557 (1989)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Dicle University, 21280, Diyarbakir, Turkey

    Murat Korunur

  2. Department of Physics, Middle East Technical University, 06531, Ankara, Turkey

    Mustafa Salti

  3. Department of Physics, Mersin University, 33343, Mersin, Turkey

    Ali Havare

Authors
  1. Murat Korunur
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mustafa Salti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ali Havare
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Korunur, M., Salti, M. & Havare, A. On the relative energy associated with space-times of diagonal metrics. Pramana - J Phys 68, 735–748 (2007). https://doi.org/10.1007/s12043-007-0073-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12043-007-0073-x

Keywords

PACS Nos

Search

Navigation