Applications of theorems of Jean Leray to the Einstein-scalar field equations

  • Yvonne Choquet-Bruhat
  • James Isenberg
  • Daniel Pollack


The Einstein-scalar field theory can be used to model gravitational physics with scalar field sources. We discuss the initial value formulation of this field theory, and show that the ideas of Leray can be used to show that the Einstein-scalar field system of partial differential equations is well-posed as an evolutionary system. We also show that one can generate solutions of the Einstein-scalar field constraint equations using conformal methods.

Mathematics Subject Classification (2000).

Primary 83C05 


Partial differential equations Einstein’s equations 


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Copyright information

© Birkhäuser Verlag, Basel/Switzerland 2007

Authors and Affiliations

  • Yvonne Choquet-Bruhat
    • 1
  • James Isenberg
    • 2
  • Daniel Pollack
    • 3
  1. 1.Académie des SciencesParis Cedex 06France
  2. 2.Department of MathematicsUniversity of OregonEugeneUSA
  3. 3.Department of MathematicsUniversity of WashingtonSeattleUSA

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