Study of the de Sitter space-time and its behavior at infinity

TL;DR

This paper reviews the properties of de Sitter space-time, its null infinity, and asymptotic symmetries, comparing it with asymptotically flat space-times, and discusses mathematical formalisms like Fefferman-Graham and Penrose-Newman.

Contribution

It provides a comprehensive review of de Sitter space-time, its null infinity, and the associated symmetry groups, highlighting formal approaches used in the field.

Findings

Clarification of de Sitter space-time properties

Comparison of null infinities in different space-times

Discussion of symmetry groups and formal frameworks

Abstract

The aim of this manuscript is to review the studies about de Sitter solution and the null infinity of asymptotically flat and de Sitter space-times. Thus, after introducing the de Sitter space-time, the symmetry group is described. Also precise definitions of asymptotically flat and de Sitter space-times are reviewed. Henceforth, the null infinities and the asymptotic symmetry groups of these two space-times are considered, which lead to the Fefferman-Graham approach and the Penrose-Newman formalism.