In four-dimensional Lambda-vacuum spacetimes, algebraic specialness plus local conformal flatness of null infinity forces the asymptotic Weyl data into the Kerr-de Sitter-like class.
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Classification of $\Lambda \neq 0$-vacuum algebraically special spacetimes with conformally flat $\mathscr I$ from Weyl tensor expansion
In four-dimensional Lambda-vacuum spacetimes, algebraic specialness plus local conformal flatness of null infinity forces the asymptotic Weyl data into the Kerr-de Sitter-like class.