Communications in Mathematical Physics

, Volume 14, Issue 4, pp 329–335 | Cite as

Global aspects of the Cauchy problem in general relativity

  • Yvonne Choquet-Bruhat
  • Robert Geroch
Article

Abstract

It is shown that, given any set of initial data for Einstein's equations which satisfy the constraint conditions, there exists a development of that data which is maximal in the sense that it is an extension of every other development. These maximal developments form a well-defined class of solutions of Einstein's equations. Any solution of Einstein's equations which has a Cauchy surface may be embedded in exactly one such maximal development.

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References

  1. 1.
    Choquet-Bruhat, Y.: Acta Math., 1952. See also a review article in: Gravitation: an introduction to current research, L. Witten (Ed.). New York: J. Wiley 1962.Google Scholar
  2. 2.
    Lichnerowicz, A.: Theories relativistes de la gravition et de l'electromagnétisme. Paris: Masson 1955.Google Scholar
  3. 3.
    Wheeler, J. A.: Article in: Relativity, groups and topology. New York: Gordon-Breach 1964.Google Scholar
  4. 4.
    Choquet-Bruhat, Y.: Article in: Batelle seattle recontres. New York: Benjamin 1968.Google Scholar
  5. 5.
    Leray, J.: Hyperbolic differential equations. Preprint, Princeton, 1952.Google Scholar
  6. 6.
    Penrose, R.: Phys. Rev. Letters14, 57 (1965).Google Scholar
  7. 7.
    Hawking, S. W.: Proc. Roy. Soc.294 A, 511 (1966).Google Scholar
  8. 8.
    Geroch, R.: The domain of dependence. J. Math. Phys. (to be published).Google Scholar
  9. 9.
    Choquet-Bruhat, Y.: Bull. Soc. Math.96, 181–192 (1968).Google Scholar
  10. 10.
    See, for example: Kelly, J. L.: General topology. New York: Van Nostrand 1955.Google Scholar

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • Yvonne Choquet-Bruhat
    • 1
  • Robert Geroch
    • 2
  1. 1.Département de MathématiquesFaculté des SciencesParis
  2. 2.Department of MathematicsBirbeck CollegeLondon

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