International Journal of Theoretical Physics

, Volume 54, Issue 5, pp 1397–1407 | Cite as

Symmetries of Type N Pure Radiation Fields

  • Zafar Ahsan
  • Musavvir Ali


The geometrical symmetries corresponding to the continuous groups of collineations and motions generated by a null vector l are considered. These symmetries have been translated into the language of Newman-Penrose formalism for pure radiation (PR) type N fields. It is seen that for such fields, conformal, special conformal and homothetic motions degenerate to motion. The concept of free curvature, matter curvature and matter affine collineations have been discussed and the conditions under which PR type N fields admit such collineations have been obtained. Moreover, it is shown that the projective collineation degenerate to matter affine, special projective, conformal, special conformal, null geodesic and special null geodesic collineations. It is also seen that type N pure radiation fields admit Maxwell collineation along the propagation vector l.


Type N PR fields NP-formalism Collineations 


  1. 1.
    Ahsan, Z.: A symmetry property of the spacetime of general relativity in terms of the space matter tensor. Braz. J. Phys. 26(3), 572–576 (1996)ADSGoogle Scholar
  2. 2.
    Ahsan, Z.: Interacting radiation field. Indian J. Pure App. Maths. 31(2), 215–225 (2000)MATHMathSciNetGoogle Scholar
  3. 3.
    Ahsan, Z.: On a geometrical symmetry of the spacetime of genearal relativity. Bull. Cal. Math. Soc. 97(3), 191–200 (2005)MATHMathSciNetGoogle Scholar
  4. 4.
    Davis, W.R., Green, L.H., Norris, L.K.: Relativistic matter fields admitting Ricci collineations and elated conservation laws. Il Nuovo Cimento 34B, 256–280 (1976)CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Davis, W.R., Moss, M.K.: Conservation laws in the general theory of relativity. Il Nuovo Cimento 65B, 19–32 (1970)CrossRefADSMathSciNetGoogle Scholar
  6. 6.
    Debney, G.C., Zund, J.D.: A note on the classification of electromagnetic fields. Tensor(N.S.) 22, 333–340 (1971)MATHMathSciNetGoogle Scholar
  7. 7.
    Duggal, K.L.: Relativistic fluids with shear and timelike conformal collineations. J. Math. Phys. 28, 2700–2705 (1987)CrossRefADSMATHMathSciNetGoogle Scholar
  8. 8.
    Duggal, K.L., Sharma, R.: Conformal collineations and anisotropic fluids in general relativity. J. Math. Phys. 27, 2511–2514 (1986)CrossRefADSMATHMathSciNetGoogle Scholar
  9. 9.
    Garcia Diaz, A., Plebanski, J.F.: All nontwisting N’s with cosmological constant. J. Math. Phys. 22, 2655–2659 (1981)CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    Katzin, G.H., Levine, J.: Applications of Lie derivatives to symmetries, geodesic mappings, and first integrals in Riemannian spaces. J. Colloq. Math. 26, 21–38 (1972)MATHMathSciNetGoogle Scholar
  11. 11.
    Katzin, G.H., Levine, J., Davis, W.R.: Curvature collineations: A fundamental symmetry property of the space-times of general relativity defined by the vanishing lie derivative of the Riemann curvature tensor. J. Math. Phys. 10, 617–630 (1969)CrossRefADSMATHMathSciNetGoogle Scholar
  12. 12.
    Newman, E.T., Penrose, R.: An approach to gravitational radiation by a method of spin coefficients. J. Math. Phys. 3, 566–579 (1962)CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    Norris, L.K., Green, L.H., Davis, W.R.: Fluid space-times including electromagnetic fields admitting symmetry mappings belonging to the family of contracted Ricci collineations. J. Math. Phys. 18, 1305–1312 (1977)CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    Oliver, D.R., Davis, W.R.: On certain timelike symmetry properties and the evolution of matter field space-times that admit them. Gen. Rel. Grav. 8, 905–914 (1977)CrossRefADSMATHMathSciNetGoogle Scholar
  15. 15.
    Stephani, H., Krammer, D., McCallum, M., Herlt, E.: Exact Solutions of Einstein’s Field Equations. Cambridge University Press, Cambridge (2003)CrossRefMATHGoogle Scholar
  16. 16.
    Zakharov, V.D.: Gravitational Waves in Einstein Theory. Halsted Press, Wiley, New York (1973)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia

Personalised recommendations