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Annales Henri Poincaré

, Volume 4, Issue 1, pp 1–34 | Cite as

Elliptic-Hyperbolic Systems and the Einstein Equations

  • L. Andersson
  • V. Moncrief
Original article

Abstract.

The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasi-linear elliptic-hyperbolic system of evolution equations. We prove that the Cauchy problem is locally strongly well posed and that a continuation principle holds.¶For initial data satisfying the Einstein constraint and gauge conditions, the solutions to the elliptic-hyperbolic system defined by the gauge fixed Einstein evolution equations are shown to give vacuum space-times.

Keywords

Initial Data Cauchy Problem Evolution Equation Einstein Equation Gauge Condition 

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Copyright information

© Birkhäuser Verlag Basel, 2003

Authors and Affiliations

  • L. Andersson
    • 1
  • V. Moncrief
    • 2
  1. 1.Department of Mathematics, University of Miami, Coral Gables, FL 33124, USA, e-mail: larsa@math.miami.eduUSA
  2. 2.Department of Physics, Yale University, P.O. Box 208120, New Haven, CT 06520, USA, e-mail: vincent.moncrief@yale.eduUSA

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