Rest Frame System for Asymptotically Flat Spacetimes

TL;DR

This paper generalizes the existence proofs of nice sections, a concept for defining the center of mass in asymptotically flat spacetimes, by relaxing conditions and establishing global solutions.

Contribution

It provides a generalized and formalized proof of the existence of nice sections, including local and global solutions, with relaxed radiation conditions and properties analysis.

Findings

Existence of solutions to the linearized nice sections equation is established.

Nice sections can be constructed without strict radiation conditions.

The family of solutions exhibits differentiability and non-self-crossing properties.

Abstract

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.