Classification of Kerr–de Sitter-like spacetimes with conformally flat **Preprint UWThPh-2016-20.

Abstract

We provide a classification of -vacuum spacetimes which admit a Killing vector field with respect to which the associated ‘Mars–Simon tensor’ (MST) vanishes and have a conformally flat (or ). To that end, we also give a complete classification of conformal Killing vector fields on the 3-sphere 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 is determined in every case, and a characterization result at of the Kerr–de Sitter family presented.