General Relativity and Gravitation

, Volume 9, Issue 9, pp 779–782 | Cite as

The shear-free condition in Robinson's theorem

  • Franco Bampi
Research Articles

Abstract

A geometrical interpretation of the shear-free condition, required by Robinson's theorem, is given. In particular it is proved that the shear-free condition for a (geodesic) null congruence is necessary and sufficient in order that the null conditions be preserved along the rays.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Robinson, I. (1961).J. Math. Phys.,2, 290.Google Scholar
  2. 2.
    Pirani, F. A. E. (1965). “Introduction to Gravitational Radiation Theory,” in Trautman, A., Pirani, F. A. E., and Bondi, H., Lectures in General Relativity, Brandies 1964 Summer Institute of Theoretical Physics, Vol. I. Prentice-Hall, Englewood Cliffs, New Jersey.Google Scholar
  3. 3.
    Synge, J. L. (1956).Relativity: The Special Theory, (North-Holland, Amsterdam).Google Scholar
  4. 4.
    Mariot, L. (1954).C. R. Acad. Sci.,238, 2055.Google Scholar
  5. 5.
    Bampi, F., and Jacassi, P. (1977).Boll. Unione Mat. Ital.,16, 286.Google Scholar
  6. 6.
    Cattaneo, C. (1958).Nuovo Cimento,10, 318.Google Scholar
  7. 7.
    Cattaneo, C. (1959).Ann. Math.,48, 361.Google Scholar
  8. 8.
    Massa, E. (1974).Gen. Rel. Grav.,5, 555.Google Scholar
  9. 9.
    Massa, E. (1974).Gen. Rel. Grav.,5, 573.Google Scholar
  10. 10.
    Zwanziger, D. (1964).Phys. Rev.,133, B1036 (see Appendix).Google Scholar
  11. 11.
    Newman, E., and Penrose, R. (1962).J. Math. Phys.,3, 566.Google Scholar
  12. 12.
    Massa, E. (1977).Ann. Mat. Pura et Appl., (in print).Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • Franco Bampi
    • 1
  1. 1.Istituto Matematico dell'Università di GenovaGenovaItaly

Personalised recommendations