Future complete Einsteinian space times with U(1) symmetry, the unpolarized case

TL;DR

This paper proves the existence of certain expanding vacuum Einstein spacetimes with U(1) symmetry and unpolarized conditions, extending previous work by removing the orthogonality assumption on the orbits.

Contribution

It establishes the existence of unpolarized, U(1) symmetric Einstein spacetimes that are complete in the expanding direction without orthogonality assumptions.

Findings

Existence of vacuum U(1) symmetric Einstein spacetimes

Completeness in the expanding direction for small initial data

Removal of orthogonality condition on orbits

Abstract

I prove the existence of vacuum $S^{1}$ symmetric Einsteinian, unpolarized, space times which are complete in the direction of the expansion, for small initial data, without supposing that the $S^{1}$ orbits are orthogonal to the 3-manifolds, as was done in previous work in collaboration with V. Moncrief.