Symmetries of the asymptotically de Sitter spacetimes

TL;DR

This paper systematically investigates the isometries of asymptotically de Sitter spacetimes, classifying possible symmetry algebras and showing that only the de Sitter universe has a Killing horizon intersecting null infinity.

Contribution

It reformulates the Killing equation as conformal equations at null infinity, enabling classification of symmetry algebras and identifying conditions for maximal symmetries.

Findings

Possible symmetry algebras are at most 4-dimensional.

Only the de Sitter universe has a Killing horizon intersecting null infinity.

Provides examples illustrating the classification.

Abstract

We start a systematic investigation of possible isometries of the asymptotically de Sitter solutions to Einstein equations. We reformulate the Killing equation as conformal equations for the initial data at $\mathcal{I}^+$. This allows for partial classification of possible symmetry algebras. In particular, if they are not maximal, they may be at most $4$-dimensional. We provide several examples. As a simple collorary it is shown that the only spacetime in which the Killing horizon intersects $\mathcal{I}^+$ (after a conformal completion) is locally the de Sitter universe.