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

TL;DR

This paper proves the existence and properties of rest frame systems in asymptotically flat space-times, crucial for analyzing gravitational radiation in general relativity.

Contribution

It provides the first rigorous proof of the existence, regularity, and non-self-crossing of solutions to the nice section equation in general asymptotically flat space-times.

Findings

Proved existence of solutions to the nice section equation.

Established regularity and non-self-crossing properties.

Confirmed a previously conjectured property in the field.

Abstract

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.