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arXiv · 1610.09846

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

Marc Mars·Tim-Torben Paetz·José M. M. Senovilla
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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.

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Marc Mars, Tim-Torben Paetz, José M. M. Senovilla. 2016-10-31. Classification of Kerr-de Sitter-like spacetimes with conformally flat Scri. https://doi.org/10.1088/1361-6382%2Faa5dc2

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