Advertisement

Annali di Matematica Pura ed Applicata

, Volume 80, Issue 1, pp 373–386 | Cite as

States of total pure radiation in general relativity

  • Jack Levine
  • J. D. Zund
Article

Summary

In this paper we investigate and exhibit space-times which admit states of pure radiation in the sense of Lichnerowicz. In § 1 the notion of special total pure radiation is introduced, and in § 2 we derive the canonical line element for this type of radiation. An additional type of spacetime admitting radiation is considered in § 3. A class of singular integrable electromagnetic fields for the space-times of § 2 are constructed in § 4. The final section is concerned with the radiation condition proposed by Zakharov.

Keywords

General Relativity Electromagnetic Field Final Section Radiation Condition Line Element 
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.

Bibliography

  1. [1]
    J. Levine,Groups of motions in conformally flat spaces, I., Bull. Amer. Soc. Math. 42(1937), pp. 418–422.CrossRefGoogle Scholar
  2. [2]
    —— ——,Fields of parallel vectors in conformally flat spaces, Duke Math. Jonr. 17 (1950) pp. 15–20.CrossRefzbMATHGoogle Scholar
  3. [3]
    J. Levine andG. H. Katzin,Conformally flat spaces admitting special quadratic first iutegrals, I. (Symmetric spaces), Tensor (to appear).Google Scholar
  4. [4]
    -- --, and -- --,Conformally flat spaces admitting special quadratic first integrals, II. (Recurrent spaces), Tensor, (to appear).Google Scholar
  5. [5]
    A. Lichnerowicz,Théorie relativistes de la gravitation et de l'electromagnétisme, Masson et Cie, Paris (1955).Google Scholar
  6. [6]
    —— ——,Ondes et radiations electromagnétiques et gravitationnelles en relativite générale, Ann. di Mat. Pura ed Appl. 50 (1960), pp. 1–95.CrossRefzbMATHMathSciNetGoogle Scholar
  7. [7]
    H. S. Ruse, A. G. Walker, T. J. Willmore,Harmonic spaces, Edizione Cremonese, Roma (1961).zbMATHGoogle Scholar
  8. [8]
    A. G. Walker,On Ruse's spaces of recurrent curvature, Proc. of the London Math. Soc. Ser. 2, 52 (1950), pp. 36–44.zbMATHGoogle Scholar
  9. [9]
    V. D. Zakharov,A physicalcharacteristic of Einsteinian spaces of the second degenerate type in the Petrov classification, Dokl. Akad. Nauk SSR 161 (1965), pp. 563–595 (translation: Sov. Phys. Dok. 10 (1965), pp. 242–243).zbMATHGoogle Scholar
  10. [10]
    J. Zund,Sur la radiation gravitationnelle, C. R. Acad. Sci. Paris. 262 Sér. A (1966) p. 1081.MathSciNetGoogle Scholar
  11. [11]
    J. D. Zund andJ. Levine,Sur la radiation gravitationnelle, C. R. Acad. Sci. Paris 264, Sér. A (1967), pp. 1029–1032.MathSciNetzbMATHGoogle Scholar
  12. [12]
    —— ——, and —— ——,A class of nonintegrable singular electromagnetic fields, Il Nuovo Cimente, Ser. X, 51 A (1967), pp. 687–695.Google Scholar
  13. [13]
    J. D. Zund andW. F. Maher, Jr.,A spinor approach to some problems in Lorentzian geometry, Rend. del Circ. Mat. Di Palermo (to appear).Google Scholar

Copyright information

© Nicola Zanichelli Editore 1968

Authors and Affiliations

  • Jack Levine
    • 1
  • J. D. Zund
    • 1
  1. 1.Raleigh

Personalised recommendations