Abstract
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] KeywordsEinstein EquationNonlinear StabilityIsometry GroupCorrected EnergyExtrinsic CurvatureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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