Annali di Matematica Pura ed Applicata

, Volume 126, Issue 1, pp 379–396 | Cite as

Null electromagnetic fields, total gravitational radiation and collineations in general relativity

  • Zafar Ahsan
  • S. Izhar Husain


The null electromagnetic field, or (F, g, r, S)-structure, and the corresponding Nijenhuis tensor have been studied in an invariant index-free manner. It is seen that the null electromagnetic fields are characterized by the relation F3= 0, and the Nijenhuis tensor plays a very natural role in the study of null electromagnetic fields. The Lichnerowicz contions for the total gravitational radiation have been given in the present setting, and the condition F3=0 has been translated into a corresponding condition on the Ricci tensor. Further, different types of collineations, for (F, g, r, S)-structure, along the propagation and polarization vectors S and T, respectively, have been studied. It is also shown that\(\mathop \pounds\limits_S F_{ij} = 0\) implies\(F_j^k \mathop \pounds\limits_S g_{ik} = 0\). Finally, a covariant conservation law generator has been given for the present structure.


General Relativity Electromagnetic Field Polarization Vector Ricci Tensor Present Setting 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Fondazione Annali di Matematica Pura ed Applicata 1980

Authors and Affiliations

  • Zafar Ahsan
    • 1
  • S. Izhar Husain
    • 1
  1. 1.India

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