Future Global in time einsteinian spacetimes with U(1) isometry group

Abstract

We prove that spacetimes satisfying the vacuum Einstein equations on a manifold of the form $\Sigma \times U(1)\times R$ where $\Sigma$ is a compact surface of genus $G>1$ and where the Cauchy data is invariant with respect to U(1) and sufficiently small exist for an infinite proper time in the expanding direction.

Accepted for publication in Annales Henri Poincare

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