On de Sitter-like and Minkowski-like space-times

TL;DR

This paper re-examines Friedrich's proofs on the global existence of de Sitter-like and Minkowski-like space-times using extended conformal field equations and a conformal geodesic gauge, simplifying the analysis of their conformal boundaries.

Contribution

It introduces a gauge based on conformal geodesics that makes the location of the conformal boundary known beforehand, simplifying the proof structure.

Findings

Simplified analysis of conformal boundaries for de Sitter-like and Minkowski-like space-times.

Clarified the role of conformal geodesic gauge in global existence proofs.

Provided a more accessible framework for studying space-time boundaries.

Abstract

Friedrich's proofs for the global existence results of de Sitter-like space-times and of semi-global existence of Minkowski-like space-times [Comm. Math. Phys. \textbf{107}, 587 (1986)] are re-examined and discussed, making use of the extended conformal field equations and a gauge based on conformal geodesics. In this gauge the location of the conformal boundary of the space-times is known \emph{a priori} once the initial data has been prescribed. Thus it provides an analysis which is conceptually and calculationally simpler.