General existence proof for rest frame systems in asymptotically flat space-time

We report a new result on the nice section construction used in the definition of rest frame systems in general relativity. This construction is needed in the study of non trivial gravitational radiating systems. We prove existence, regularity and non-self-crossing property of solutions of the nice section equation for general asymptotically flat space times. This proves a conjecture enunciated in a previous work.