Rest frame system for asymptotically flat space-times

The notion of center of mass for an isolated system has been previously encoded in the definition of the so-called nice sections. In this article we present a generalization of the proof of existence of solutions to the linearized equation for nice sections, and formalize a local existence proof of nice sections relaxing the radiation condition. We report on the differentiable and non-self-crossing properties of this family of solutions. We also give a proof of the global existence of nice sections.