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

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 Möbius 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.

63 pages

References in corpus (2)

• On the uniqueness of smooth, stationary black holes in vacuum
• A set of invariant quality factors measuring the deviation from the Kerr metric

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