Skip to main content
SpringerLink
Log in

Noether versus Killing symmetry of conformally flat Friedmann metric

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

In a recent study Noether symmetries of some static spacetime metrics in comparison with Killing vectors of corresponding spacetimes were studied. It was shown that Noether symmetries provide additional conservation laws that are not given by Killing vectors. In an attempt to understand how Noether symmetries compare with conformal Killing vectors, we find the Noether symmetries of the flat Friedmann cosmological model. We show that the conformally transformed flat Friedman model admits additional conservation laws not given by the Killing or conformal Killing vectors. Inter alia, these additional conserved quantities provide a mechanism to twice reduce the geodesic equations via the associated Noether symmetries.

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. Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation Benjamin, New York (1973)

  2. Petrov A.Z. (1969). Einstein Spaces. Pergamon, Oxford

    MATH  Google Scholar 

  3. Stephani H., Kramer D., MacCallum M.A.H., Hoenselaers C. (2003). Exact solutions of Einstein Field Equations. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  4. Katzin, G.H., Levine, J.: Coloq. Math. 26, (21) (1972)

  5. Hall, G.S.: Symmetries and curvature structure in general relativity. World Scientific, (2004)

  6. Bokhari A.H., Kashif A.R. (1996). J. Math. Phys. 37(7): 3496

    Article  ADS  MathSciNet  Google Scholar 

  7. Giachetta, G., Sardanashvily, G.: Stree-energy-momentum tensors in Lagrangian field theory, arXiv:gr-qc/9510061

  8. Camci U., Barnes A. (2002). Class. Quantum Grav. 19: 393

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. Nunez L.A., Percoco U., Villalba V.M. (1990). J. Math. Phys. 31: 137

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. Bokhari A.H. (1992). Int. J. Th. Phys. 31: 2091

    Article  MATH  MathSciNet  Google Scholar 

  11. Amer M.J., Bokhari A.H., Qadir A. (1994). J. Math. Phys. 35(6): 3005

    Article  ADS  MathSciNet  Google Scholar 

  12. Marteen, R., Maharaj, S.D.: Class. Quantum Grav., 3, 1005 (1986)

  13. Fatibene L., Ferraris M., Francaviglia M., McLenaghan R.G. (2002). J. Math. Phys. 43(6): 3147

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. Mangiarotti L., Sardanashvily G. (2000). Connections in classical and quantum field theory. World Scientific, Singapore

    MATH  Google Scholar 

  15. Bokhari A.H., Kara A.H., Kashif A.R., Zaman F.D. (2006). Int. J. Th. Phys. 45(6): 1063

    Article  MATH  MathSciNet  Google Scholar 

  16. Wolf, T.: Crack, LiePDE, ApplySym and ConLaw, section 4.3.5 and computer program on CD-ROM. In: Grabmeier, J., Kaltofen, E., Weispfenning, V. (eds.) Computer Algebra Handbook, vol. 465. Springer, Heidelberg (2002)

  17. Wolf T. (2004). Applications of CRACK in the classification of integrable systems. CRM Proc. Lect. Notes 37: 283

    Google Scholar 

  18. Bokhari, A.H.: Conformal extension of Pseudo-Newtonian Formalis, PhD Thesis, Quaid-i-Azam University (1985)

  19. Kara A.H., Mahomed F.M., Vawda F.E. (1994). Lie groups and their applications 2: 27

    MathSciNet  Google Scholar 

  20. Kara A.H., Khalique C.M. (2005). J. Phys. A 38: 4629

    Article  MATH  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Ashfaque H. Bokhari

  2. School of Mathematics and Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa

    A. H. Kara

Authors
  1. Ashfaque H. Bokhari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. H. Kara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ashfaque H. Bokhari.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bokhari, A.H., Kara, A.H. Noether versus Killing symmetry of conformally flat Friedmann metric. Gen Relativ Gravit 39, 2053–2059 (2007). https://doi.org/10.1007/s10714-007-0501-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10714-007-0501-8

Keywords

Search

Navigation