General Relativity and Gravitation

, Volume 12, Issue 2, pp 99–108 | Cite as

Singularities at real points of ℋ space

  • K. P. Tod
  • J. Winicour
Research Articles

Abstract

In the presence of gravitational radiation, there are ordinarily no shear-free slices of null infinity. A four-complex-dimensional set of shear-free slices of complexified null infinity do exist. They comprise the manifold ℋ space. In general, there are no preferred real subspaces of space associated with slices of real null infinity. However, for radiation fields possessing a twist-free axial symmetry, a two-parameter family of shear-free slices of real null infinity exist and therefore pick out a preferred two-dimensional real subspace of space. In this paper, we study the geometry of these 2-spaces for the particular case of quadrupole radiation fields for which determination of the shear-free slices reduces to the standard problem of determining orbits of a particle moving in a potential. Our principal interest is the investigation of possible singularities caused by sufficiently intense radiation fields. We find that such singularities do occur for radiation fields having the characteristic powerc5/G.

Keywords

Radiation Manifold Axial Symmetry Differential Geometry Radiation Field 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dubisch, R., and Winicour, J. (1978).Gen Rel. Grav.,9, 637.Google Scholar
  2. 2.
    Newman, E. T. (1975). InGeneral Relativity and Gravitation, eds. G. Shaviv and J. Rosen (J. Wiley and Sons, New York).Google Scholar
  3. 3.
    Hansen, R. O., Newman, E. T., Penrose, R., and Tod, K. P. (1978), “The Metric and Curvature Properties of-space,”Proc. R. Soc., London,A363, 445.Google Scholar
  4. 4.
    Bondi, H., van der Burg, M. G. J., and Metzner, A. W. K. (1962).Proc. R. Soc., London,A269, 21.Google Scholar
  5. 5.
    Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973).Gravitation (Freeman, San Francisco), p. 980.Google Scholar
  6. 6.
    Penrose, R. (1976).Gen. Rel. Grav.,7, 31.Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • K. P. Tod
    • 1
  • J. Winicour
    • 2
  1. 1.Mathematical InstituteUniversity of OxfordOxford
  2. 2.Department of Physics and AstronomyUniversity of PittsburghPittsburgh

Personalised recommendations