Classification of Kerr-de Sitter-like spacetimes with conformally flat Scri

TL;DR

This paper classifies certain positive cosmological constant vacuum spacetimes with specific symmetries and conformal properties, revealing fundamental invariants and the topology of their conformal boundaries.

Contribution

It provides a complete classification of Kerr-de Sitter-like spacetimes with conformally flat Scri and characterizes their fundamental geometric invariants.

Findings

Classification of $ abla$-vacuum spacetimes with vanishing MST

Complete classification of conformal Killing vectors on $S^3$

Determination of the topology of $J$ in each case

Abstract

We provide a classification of $\Lambda>0$-vacuum spacetimes which admit a Killing vector field with respect to which the associated "Mars-Simon tensor" (MST) vanishes and having a conformally flat $\mathcal{J}^-$ (or $\mathcal{J}^+$). To that end, we also give a complete classification of conformal Killing vector fields on the $3$-sphere $\mathbb{S}^3$ up to M\"obius transformations shedding light on the two fundamental constants that characterize the family of Kerr-de Sitter-like spacetimes, which turn out to be well-defined geometrical invariants. The topology of $\mathcal{J}$ is determined in every case, and a characterization result at $\mathcal{J}$ of the Kerr-de Sitter family presented.