Communications in Mathematical Physics

, Volume 14, Issue 4, pp 329–335

Global aspects of the Cauchy problem in general relativity

  • Yvonne Choquet-Bruhat
  • Robert Geroch

DOI: 10.1007/BF01645389

Cite this article as:
Choquet-Bruhat, Y. & Geroch, R. Commun.Math. Phys. (1969) 14: 329. doi:10.1007/BF01645389


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.

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
  3. 3.Dept. of PhysicsSyracuse UniversitySyracuse