Skip to main content
SpringerLink
Log in

A Note on Classification of Cylindrically Symmetric Non-static Space–Times According to Their Teleparallel Killing Vector Fields in the Teleparallel Theory of Gravitation

  • Particles and Fields
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

Abstract

In this paper, we explored the conservation laws of cylindrically symmetric non-static space–times by using direct integration technique. This classification also covers non-static plane symmetric space–times, static cylindrically symmetric space–times and plane symmetric static space–times. In this paper, we will only present the results of non-static cylindrically symmetric and non-static plane symmetric space–times. The results of static cylindrically symmetric space–times and plane static space–times can be found in Shabbir and Khan (Mod Phys Lett A 25:525, 2010). It turns out that the non-static cylindrically symmetric space–times admit four, five, or seven conservation laws. It is important to note that the above space–times admit at least one or at the most four extra conservation laws.

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. Harvey, E. Schucking, E.J. Surowitz, Am. J. Phys. 74, 1017 (2006)

    Article  ADS  Google Scholar 

  2. J.P. Krisch, E.N. Glass, Phy. Rev. D 80, 044001 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  3. A.Z. Petrov, Physics Einstein Spaces (Oxford University Press, Pergamon, 1969)

    Google Scholar 

  4. R. Aldrovandi, J.G. Pereira, An Introduction to Geometrical Physics (World Scientific, Singapore, 1995)

    Book  MATH  Google Scholar 

  5. J.G. Pereira, T. Vargas, C.M. Zhang, Class. Quantum Gravity 18, 833 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. V.C. de Andrade, J.G. Pereira, Phy. Rev. D 56, 4689 (1997)

    Article  ADS  Google Scholar 

  7. M. Sharif, M.J. Amir, Mod. Physics Lett. A 23, 963 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. G. Shabbir, S. Khan, Mod. Physics Lett. A 25, 55 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. G. Shabbir, S. Khan, Mod. Physics Lett. A 25, 1733 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. G. Shabbir, S. Khan, Commun. Theor. Physics 54, 469 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. G. Shabbir, S. Khan, Commun. Theor. Phys. 55, 268 (2011)

    Article  MathSciNet  Google Scholar 

  12. G. Shabbir, S. Khan, Mod. Physics Lett. A 25, 525 (2010)

    Article  ADS  MATH  Google Scholar 

  13. G.G.L. Nashed, Chin. Phys. B 19, 020401 (2010)

    Article  ADS  Google Scholar 

  14. R. Aldrovandi, J.G. Pereira, An Introduction to Gravitation Theory (lecture notes) (2001).

  15. V.C. de Andrade, L.C.T. Guillen, J.G. Pereira, In Proceedings of the Ninth Marcel Grossmann Meeting (World Scientific, Singapore, 2000), p. 1022.

  16. H. Stephani, D. Kramer, M.A.H. MacCallum, C. Hoenselears, E. Herlt, Exact Solutions of Einstein’s Field Equations (Cambridge University Press, Cambridge, 2003)

    Book  MATH  Google Scholar 

  17. G.G.L. Nashed, Astrophys Space Sci. 333, 317 (2011)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering Sciences, GIK Institute of Engineering Sciences and Technology, Topi, Swabi, Khyber Pukhtoonkhwa, Pakistan

    Ghulam Shabbir & Suhail Khan

  2. Department of Mathematics, University of Sargodha, Sargodha, 40100, Pakistan

    M. Jamil Amir

Authors
  1. Ghulam Shabbir
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Suhail Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Jamil Amir
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ghulam Shabbir.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shabbir, G., Khan, S. & Amir, M.J. A Note on Classification of Cylindrically Symmetric Non-static Space–Times According to Their Teleparallel Killing Vector Fields in the Teleparallel Theory of Gravitation. Braz J Phys 41, 184–194 (2011). https://doi.org/10.1007/s13538-011-0032-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-011-0032-3

Keywords

Search

Navigation