Annali di Matematica Pura ed Applicata

, Volume 96, Issue 1, pp 175–183 | Cite as

On the theorems of Levine and Zund

  • G. S. Hall
Article
  • 29 Downloads

Summary

Some results of Levine and Zund are extended and applied to Maxwell's theory. It is deduced that a null Maxwell field in a conformally flat space-time is necessarily expansion free and twistfree as well as shearfree. An analogous result is given for null Maxwell fields which are type N in the Petrov classification.

Keywords

Analogous Result Maxwell Field Petrov Classification 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Lichnerowicz, Ann. di Mat. pura e appl.,50 (1960), pp. 1–95.MATHMathSciNetGoogle Scholar
  2. [2]
    A. Lichnerowicz, C.R. Acad. Sci. Paris,246 (1958), pp. 893–896.MATHMathSciNetGoogle Scholar
  3. [3]
    H. Levine -J. Zund, Ann. di Mat. pura e appl.,80 (1968), pp. 373–386.MathSciNetGoogle Scholar
  4. [4]
    J. Zund C.R. Acad. Sci. Paris,262 (1966), pp. 1081–1083.MathSciNetGoogle Scholar
  5. [5]
    H. Levine -J. Zund, C.R. Acad. Sci. Paris,264 (1967), pp. 1029–1032.MathSciNetGoogle Scholar
  6. [6]
    F. A. E. Pirani, inLectures on General Relativity, Brandeis Summer Institute in Theoretical Physics, vol. 1, Prentice Hall, 1964, Chapters 4 and 5.Google Scholar
  7. [7]
    I. Robinson, Journ. Math. Phys.,2 (1961), pp. 290–291.CrossRefGoogle Scholar
  8. [8]
    R. Debever, C.R. Acad. Sci. Paris,249 (1959), pp. 1744–1746.MATHMathSciNetGoogle Scholar
  9. [9]
    J. N. Goldberg -R. K. Sachs, Acta Phys. Polon (Supplementum),22 (1962), pp. 13–23.MathSciNetGoogle Scholar
  10. [10]
    R. K. Sachs, Proc. Roy. Soc., A264 (1961), pp. 309–338.MATHMathSciNetGoogle Scholar
  11. [11]
    L. Mariot, C.R. Acad. Sci. Paris,239 (1954), pp. 1189–1190.MATHMathSciNetGoogle Scholar
  12. [12]
    L. Mariot, C.R. Acad. Sci. Paris,241 (1955), pp. 175–176.MATHMathSciNetGoogle Scholar

Copyright information

© Nicola Zanichelli Editore 1973

Authors and Affiliations

  • G. S. Hall
    • 1
  1. 1.NewcastleEngland

Personalised recommendations