General Relativity and Gravitation

, Volume 1, Issue 3, pp 269–280 | Cite as

A new definition of singular points in general relativity

  • B. G. Schmidt


To any space time a boundary is attached on which incomplete geodesics terminate as well as inextensible timelike curves of finite length and bounded acceleration. The construction is free ofad hoc assumptions concerning the topology of the boundary and the identification of curves defining the same boundary point. Moreover it is a direct generalization of the Cauchy completion of positive definite Riemannian spaces.


General Relativity Singular Point Boundary Point Differential Geometry Space Time 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Geroch, R. (1968).Ann. Phys.,48, 526.Google Scholar
  2. 2.
    Geroch, R. (1968).J. Math. Phys.,9, 450.Google Scholar
  3. 3.
    Hawking, S. W.Singularities and the Geometry of Space-Time. (Unpublished essay submitted for the Adams Prize, Cambridge University, December, 1966.)Google Scholar
  4. 4.
    Kobayashi, S. and Nomizu, K. (1963).Foundations of Differential Geometry, Vol. I, Interscience, New York.Google Scholar
  5. 5.
    Hicks, N. J. (1965).Notes on Differential Geometry, D. van Nostrand Company, Inc., Princeton, New Jersey.Google Scholar
  6. 6.
    Bishop, R. L. and Crittenden, R. J. (1964).Geometry of Manifolds, Academic Press, New York.Google Scholar
  7. 7.
    Penrose, R. (1968).Battelle Rencontres (ed. DeWitt, C. M. and Wheeler, J. A.), W. A. Benjamin, Inc., New York.Google Scholar
  8. 8.
    Hocking, J. G. and Young, G. S. (1961).Topology, Addison-Wesley Publishing Company, Inc.Google Scholar
  9. 9.
    Dieudonné, I. (1960).Foundations of Modern Analysis, Academic Press, New York.Google Scholar
  10. 10.
    Schubert, H. (1964).Topologie, B. G. Teubner Verlagsgesellschaft, Stuttgart.Google Scholar
  11. 11.
    Kelley, J. L. (1955).General Topology, D. van Nostrand Company, Inc., Princeton, New Jersey.Google Scholar
  12. 12.
    Misner, C. W. (1963).J. Math. Phys.,4, 924.Google Scholar
  13. 13.
    Newman, E. T. and Posadas, R. (1969).The Motion and Structure of Singularities in General Relativity, Pittsburgh.Google Scholar

Copyright information

© Plenum Publishing Company Limited 1971

Authors and Affiliations

  • B. G. Schmidt
    • 1
  1. 1.Institut für Theoretische PhysikUniversität HamburgDeutschland

Personalised recommendations