General existence proof for rest frame systems in asymptotically flat spacetime

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 the existence, regularity and non-self-crossing property of solutions of the nice section equation for general asymptotically flat spacetimes. This proves a conjecture given in a previous work.