Non linear stability of einsteinian spacetimes with U(1) isometry group

Yvonne Choquet-Bruhat (1) , Vincent Moncrief

1 UPMC - Université Pierre et Marie Curie - Paris 6

We prove global completeness in the expanding direction of spacetimes satisfying the vacuum Einstein equations on a manifold of the form $\Sigma \times S^{1}\times R$ where $\Sigma $ is a compact surface of genus $G>1.$ The Cauchy data are supposed to be invariant with respect to the group $S^{1}$ and sufficiently small, but we do not impose a restrictive hypothesis made in gr-qc 0112049 on the lowest eigenvalue of a relevant Laplacian. The total energy decay still holds, but its rate depends of the asymptotic value of this eigenvalue.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Yvonne Choquet-Bruhat, Vincent Moncrief. Non linear stability of einsteinian spacetimes with U(1) isometry group. 2003. ⟨hal-00153427⟩