  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.
