Skip to main content

Causally continuous spacetimes


Causally continuous general relativistic spacetimes are defined and analyzed. In a causally continuous spacetime, the past and future of a local observer behave continuously under small perturbations of the metric or small changes in his location. Causally simple spacetimes are causally continuous; causally continuous spacetimes are causally stable. Possible reasons for taking causal continuity as a basic postulate in macrophysics are briefly discussed.

This is a preview of subscription content, access via your institution.


  1. 1.

    Bishop, R.L., Goldberg, S.I.: Tensor analysis on manifolds, New York: MacMillan 1968

    Google Scholar 

  2. 2.

    Budic, R., Sachs, R. K.: Set causality in general relativity (preprint, 1973)

  3. 3.

    Carter, B.: Phys. Rev.174, 1559 (1968)

    Google Scholar 

  4. 4.

    Carter, B.: Gen. Rel. Grav.1, 349 (1971)

    Google Scholar 

  5. 5.

    Geroch, R.: J. Math. Phys.11, 437 (1970)

    Google Scholar 

  6. 6.

    Geroch, R., Kronheimer, E.H., Penrose, R.: Proc. Roy. Soc. A327, 545 (1972)

    Google Scholar 

  7. 7.

    Hawking, S.: Proc. Roy. Soc. A308, 433 (1968)

    Google Scholar 

  8. 8.

    Hawking, S., Penrose, R.: Proc. Roy. Soc. A314, 529 (1970)

    Google Scholar 

  9. 9.

    Hawking, S., Ellis, G.F.R.: The large scale structure of space-time. Cambridge University Press, 1973

  10. 10.

    Kronheimer, E.H., Penrose, R.: Proc. Cambridge Phil. Soc.63, 481 (1967)

    Google Scholar 

  11. 11.

    Penrose, R.: Proc. Roy. Soc. A284, 159 (1965)

    Google Scholar 

  12. 12.

    Penrose, R.: The Structure of Spacetime. In: de Witt, C.M., Wheeler, J.A. (Eds.): Batelle recontres. New York: Benjamin, 1968

    Google Scholar 

  13. 13.

    Penrose, R.: Techniques of differential topology in general relativity. Am. Math. Soc. Colloq. Publ., 1973

  14. 14.

    Seifert, H.: Gen. Rel. Grav.1, 3, 247 (1971)

    Google Scholar 

  15. 15.

    Woodhouse, N.M.J.: J. Math. Phys.14, 4, 495 (1973)

    Google Scholar 

Download references

Author information



Additional information

Supported by grants from the NSF, SRC, and Guggenheim foundation.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hawking, S.W., Sachs, R.K. Causally continuous spacetimes. Commun.Math. Phys. 35, 287–296 (1974).

Download citation


  • Neural Network
  • Statistical Physic
  • Complex System
  • Nonlinear Dynamics
  • Small Perturbation