General Relativity and Gravitation

, Volume 25, Issue 1, pp 95–100 | Cite as

Trapping and completeness of a spherical light-cone

  • Sean A. Hayward
Research Articles

Abstract

This article concerns an outgoing spherically symmetric light-cone evolving according to the Einstein equations. The relevant equations are solved explicitly as integrals of the Mailing matter, which is unspecified apart from energy conditions and a consistency condition. A condition on the matter is derived which is necessary and sufficient for the cone to be trapped. If the cone is not trapped it is complete, and if it is trapped it will recollapse to a point. In either case, the asymptotic behaviour of the matter is consequently constrained.

Keywords

Asymptotic Behaviour Energy Condition Differential Geometry Einstein Equation Consistency Condition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Schoen, R., and Yau, S.-T. (1983).Commun. Math. Phys. 90, 575.Google Scholar
  2. 2.
    Bizon, P., Malec, E., and Ó Murchadha, N. (1988).Phys. Rev. Lett. 61, 1147.Google Scholar
  3. 3.
    Bizon, P., Malec, E., and Ó Murchadha, N. (1989).Class. Quant. Grav. 6, 961.Google Scholar
  4. 4.
    Brauer, U., and Malec, E. (1992).Class. Quant. Grav. 9, 905.Google Scholar
  5. 5.
    Hawking, S. W., and Ellis, G. F. R. (1973).The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge).Google Scholar
  6. 6.
    Müller zum Hagen, H., and Seifert, H.-J. (1977).Gen. Rel. Grav. 8, 259.Google Scholar
  7. 7.
    Friedrich, H. (1981).Proc. Roy. Soc. Lond. A378, 401.Google Scholar
  8. 8.
    Rendall, A. D. (1990).Proc. Roy. Soc. Lond. A427, 221.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • Sean A. Hayward
    • 1
  1. 1.Max-Planck-Institut für AstrophysikGarchingbei-MünchenGermany

Personalised recommendations