Geometrically defined asymptotic coordinates in General Relativity

TL;DR

This paper reviews recent advances in understanding the asymptotic structure of relativistic initial data sets in General Relativity, focusing on geometric invariants and foliations at infinity.

Contribution

It introduces a geometric framework for asymptotic flatness and relates various physical invariants to specific geometric foliations.

Findings

Geometrization of asymptotic flatness and invariants

Relations between mass, energy, momentum, and foliations

Analysis of CMC- and STCMC-foliations at infinity

Abstract

We review and announce recent results on the asymptotic behavior of asymptotically Euclidean relativistic initial data sets and asymptotic foliations thereof. In particular, we discuss the geometrization of asymptotic flatness and of asymptotic geometric (in-)\-variants such as mass, energy, linear momentum, angular momentum and center of mass as well as their relations to certain geometric asymptotic foliations such as the CMC- and STCMC-foliations.