Skip to main content
SpringerLink
Log in

A Note on Teleparallel Killing Symmetries in Three Dimensional Circularly Symmetric Static Spacetime

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

Abstract

In this article we investigate Killing vectors in three dimensional Lorentzian manifold for circularly symmetric static spacetime in the presence of torsion. Teleparallel Killing equations are obtained and then solved by using some algebraic and direct integration techniques. This study reveals that the above spacetime admit two, three, four, five or six teleparallel Killing vectors. We compare our results with the available results in general relativity where the same spacetime admit two, three, four or six Killing vectors. It turns out that the teleparallel Killing vectors are different from Killing vectors in general relativity for the same spacetime.

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. Bokhari, A.H., Qadir, A.: Symmetries of static spherically symmetric space-times. J. Math. Phys. 28, 1019 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  2. Feroze, T., Qadir, A., Ziad, M.: The classification of plane symmetric space-times by isometries. J. Math. Phys. 42, 4947 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  3. Hall, G.S., Steele, J.D.: Homothety groups in space-time. Gen. Relativ. Gravit. 22, 457 (1990)

    MathSciNet  ADS  Google Scholar 

  4. Qadir, A., Sharif, M., Ziad, M.: Homotheties of cylindrically symmetric static manifolds and their global extension. Class. Quantum Gravity 17, 345 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  5. Shabbir, G., Ramzan, M.: Classification of cylindrically symmetric static space-times according to their proper homothetic vector fields. Appl. Sci. 9, 148 (2007)

    MathSciNet  Google Scholar 

  6. Maartens, R., Maharaj, S.D., Tupper, B.O.J.: General solution and classification of conformal motions in static spherical space-times. Class. Quantum Gravity 12, 2577 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  7. Shabbir, G., Ramzan, M., Ali, A.: Classification of non-static spherically symmetric space-times according to their proper conformal vector fields, University of Politehnica Bucharest Scientific Bulletin Series A. Appl. Math. Phys. 71, 3 (2009)

    MathSciNet  Google Scholar 

  8. Shabbir, G., Khan, S.: A note on self similar vector fields in plane symmetric static space-times. TWMS J. Pure Appl. Math. 1, 252 (2010)

    MathSciNet  Google Scholar 

  9. Shabbir, G., Khan, S.: A note on self-similar vector fields in static spherically symmetric space-times, University of Politehnica Bucharest Scientific Bulletin Series A. Appl. Math. Phys. 74, 177 (2012)

    MathSciNet  Google Scholar 

  10. Sharif, M., Aziz, S.: On physical properties of cylindrically symmetric self similar solutions. Int. J. Mod. Phys. A 20, 7579 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  11. Petrov, A.Z., spaces, Einstein: Pergamon. Oxford University Press (1969)

  12. Hall, G.S.: Symmetries and Curvature Structure in General Relativity, World Scientific (2004)

  13. Stephani, H., Kramer, D., Maccallum, M., Hoenselaers, C., Herlt, E.: Exact solutions of einstein’s field equations, 2nd edn. Cambridge University Press (2003)

  14. de Berredo-Peixoto, G.: On the static solutions in gravity with massive scalar field in three dimensions. Class. Quantum Gravity 20, 4305 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  15. Banâdos, M., Teiteloim, C., Zanelli, J.: The black holes in three dimensional spacetime. Phys. Rev. Lett. 69, 1849 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  16. Clêment, G., Fabbari, A.: The gravitating δ model in 2 + 1 dimensions, black hole solutions. Class. Quantum Gravity 16, 323 (1999)

    Article  ADS  Google Scholar 

  17. Bokhari, A. H., Karim, M., Al-Sheikh, D.N., Zaman, F.D. Int. J. Theor. Phys. 47, 2672 (2008)

    Article  MathSciNet  Google Scholar 

  18. Gracia, A.A., Hehl, F.W., Heinicle, C., Macias, A.: Exact vacuum solution of a (2 + 1) dimensional Poincarê gauge theory: BTZ solution with torsion. Preprint. arXiv:0302097 [gr-qc] (2003)

  19. Sousa, A.A., Maluf, J.W.: Black holes in (2 + 1) teleparallel theories of gravity. Preprint. arXiv:0301079 [gr-qc] (2003)

  20. Sharif, M., Amir, M.J.: Teleparallel Killing vectors of the Einstein Universe. Mod. Phys. Lett. A 23, 963 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  21. Shabbir, G., Khan, S., Ali, A.: A note on classification of spatially homogeneous rotating space-times according to their teleparallel Killing vector fields in teleparallel theory of gravitation. Commun. Theor Phys. 55, 268 (2011)

    Article  MathSciNet  Google Scholar 

  22. Shabbir, G., Ali, A., Khan, S., Chin. Phys. B: A note on teleparallel killing vector fields in Bianchi type VIII and IX space-times in teleparallel theory of gravitation. Chin. Phys. B 20, 070401 (2011)

    Article  Google Scholar 

  23. 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 (2011)

    Article  ADS  Google Scholar 

  24. Khan, S., Hussain, T., Khan, G.A.: A note on teleparallel Lie symmetries using non diagonal tetrad. Rom. J. Phys. 59, 488 (2014)

    Google Scholar 

  25. Khan, S., Gohar, Khan, G.A., Amir, M.J.: Teleparallel killing motions of Bianchi type V spacetimes, to be appear in Rom. Rep. Phys. (2015)

  26. Sharif, M., Majeed, B.: Teleparallel Killing vectors of spherically symmetric space-times. Commun. Theor. Phys. 52, 435 (2009)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Peshawar, Peshawar, Pakistan

    Suhail Khan, Tahir Hussain & Gulzar Ali Khan

  2. Department of Basic Sciences, University of Engineering and Technology Peshawar, Peshawar, Pakistan

    Amjad Ali

Authors
  1. Suhail Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tahir Hussain
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gulzar Ali Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Amjad Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Suhail Khan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khan, S., Hussain, T., Ali Khan, G. et al. A Note on Teleparallel Killing Symmetries in Three Dimensional Circularly Symmetric Static Spacetime. Int J Theor Phys 54, 2969–2976 (2015). https://doi.org/10.1007/s10773-015-2535-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-015-2535-0

Keywords

Search

Navigation