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


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.


Radiation Manifold Axial Symmetry Differential Geometry Radiation Field 
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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

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