Nonlinear Stability of an Expanding Universe with the S1 Isometry Group

  • Yvonne Choquet-Bruhat
  • Vincent Moncrief
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 52)


We prove the existence for an infinite proper time in the expanding direction of spacetimes satisfying the vacuum Einstein equations on a manifold of the form \( \sum { \times {S^1} \times R}\) where Σ is a compact surface of genus G >1. The Cauchy data are supposed to be invariant with respect to the group S1 and sufficiently small, but we do not impose a restrictive hypothesis made in the previous work [1]


Einstein Equation Nonlinear Stability Isometry Group Corrected Energy Extrinsic Curvature 
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  1. 1.
    Y. Choquet-Bruhat and V. MoncriefFuture global einsteinian spacetimes with U(1) isometry groupC.R. Acad. Sci. Paris t. 332 serieI(2001), 137–144; Ann.H.Poincaré2(2001), 1007–1064.MathSciNetzbMATHGoogle Scholar
  2. 2.
    V. MoncriefReduction of Einstein equations for vacuum spacetimes with U(1) spacelike isometry groupAnnals of Physics167(1986), 118–142.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Y. Choquet-Bruhat and V. MoncriefExistence theorem for solutions of Einstein equations with 1 parameter spacelike isometry group (H.Brezis and I.E. Segal, eds.), Proc. Symposia in Pure Math.59(1996), 67–80.Google Scholar
  4. 4.
    L. Andersson, V. Moncrief and A. TrombaOn the global evolution problem in 2+1 gravityJ. Geom. Phys.23no. 3–4 (1997), (1991), 205.Google Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Yvonne Choquet-Bruhat
    • 1
  • Vincent Moncrief
    • 2
  1. 1.YCB Université Paris 6ParisFrance
  2. 2.Department of PhysicsYale UniversityNew HavenUSA

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