The structure of the space of solutions of Einstein's equations. I. One Killing field.

Abstract

This paper deals with globally hyperbolic solutions of the vacuum Einstein equations in a neighborhood of spacetimes that have a compact Cauchy surface of constant mean curvature. The first part of paper deal with solutions which have a single Killing vector field. Part II of the paper will then deal with the case of several Killing fields and general applications to mechanics.

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