Initial data for solutions of Einstein’s gravitational field equations cannot be chosen freely: the data must satisfy the four Einstein constraint equations. We first discuss the geometric origins of the Einstein constraints and the role the constraint equations play in generating solutions of the full system. We then discuss various ways of obtaining solutions of the Einstein constraint equations, and the nature of the space of solutions.


constraint equations Einstein equations conformal method quasi-spherical thin sandwich 


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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Robert Bartnik
    • 1
  • Jim Isenberg
    • 2
  1. 1.School of Mathematics and StatisticsUniversity of CanberraAustralia
  2. 2.Department of Mathematics and Institute for Theoretical ScienceUniversity of OregonEugeneUSA

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