Advertisement

International Journal of Theoretical Physics

, Volume 53, Issue 5, pp 1483–1494 | Cite as

Invariances and Conservation Laws Based on Some FRW Universes

  • U. Camci
  • S. Jamal
  • A. H. Kara
Article

Abstract

A symmetry analysis of some special classes of Friedmann-Robertson-Walker (FRW) universe and nonlinear wave equations in this geometry are performed. Conserved forms for the wave equation are constructed by the application of Noether’s theorem. We illustrate how the symmetry structure is used to reduce the wave equation leading to some exact solutions.

Keywords

FRW metric Conservation laws Noether symmetries 

Notes

Acknowledgements

This work was supported by Akdeniz University, Scientific Research Projects Unit. S. Jamal would like to thank the National Research Foundation of South Africa for financial support.

References

  1. 1.
    Friedman, A.: Gen. Relativ. Gravit. 31, 1991–2000 (1999) ADSCrossRefMATHGoogle Scholar
  2. 2.
    Noether, E.: Invariante variationsprobleme. Nachr. Akad. Wiss. Gött. Math.-Phys. Kl., 2B 2, 235 (1918). English translation: Transp. Theory Stat. Phys. 1, 186 (1971) Google Scholar
  3. 3.
    Anco, S., Bluman, G.: Eur. J. Appl. Math. 13, 545 (2002) MATHMathSciNetGoogle Scholar
  4. 4.
    Olver, P.: Application of Lie Groups to Differential Equations. Springer, New York (1993) CrossRefGoogle Scholar
  5. 5.
    Ibragimov, N.H.: CRC Handbook of Lie Group Analysis of Differential Equations: Symmetries, Exact Solutions and Conservation Laws. CRC Press, Boca Raton (1994) MATHGoogle Scholar
  6. 6.
    Bokhari, A.H., Al-Dweik, A.Y., Kara, A.H., Karim, M., Zaman, F.D.: J. Math. Phys. 52, 063511 (2011) ADSCrossRefMathSciNetGoogle Scholar
  7. 7.
    Bokhari, A.H., Kara, A.H.: Gen. Relativ. Gravit. 39, 2053 (2007) ADSCrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Bokhari, A.H., Kara, A.H., Kashif, A.R., Zaman, F.D.: Int. J. Theor. Phys. 45, 1029 (2006) CrossRefMathSciNetGoogle Scholar
  9. 9.
    Tsamparlis, M., Paliathanasis, A.: Gen. Relativ. Gravit. 42, 2957 (2010) ADSCrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Tsamparlis, M., Paliathanasis, A.: Gen. Relativ. Gravit. 43, 1861 (2011) ADSCrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Eardley, D., Isenberg, J., Marsden, J., Moncrief, V.: Commun. Math. Phys. 106, 137 (1986) ADSCrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Sharma, S.: J. Math. Phys. 46, 042502 (2005) ADSCrossRefMathSciNetGoogle Scholar
  13. 13.
    Maartens, R., Maharaj, S.D.: Class. Quantum Gravity 3, 1005 (1986) ADSCrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Maartens, R.: J. Math. Phys. 28, 2051 (1987) ADSCrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Ibragimov, N.H., Kara, A.H., Mahomed, F.M.: Nonlinear Dyn. 15, 115 (1998) CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Kara, A.H., Mahomed, F.M.: Int. J. Theor. Phys. 39(1), 23 (2000) CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Stephani, H.: Differential Equations: Their Solution Using Symmetries. Cambridge University Press, Cambridge (1989) MATHGoogle Scholar
  18. 18.
    Hall, G.S., Shabbir, G.: Class. Quantum Gravity 18, 907 (2001) ADSCrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Shabbir, G.: Il Nuovo Cimento B 119, 433 (2004) ADSMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of PhysicsAkdeniz UniversityAntalyaTurkey
  2. 2.School of Mathematics and Centre for Differential Equations, Continuum Mechanics and ApplicationsUniversity of the WitwatersrandJohannesburgSouth Africa

Personalised recommendations