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.
Asymptotically de Sitter metrics from scattering data in all dimensions
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abstract
In spacetime dimensions $n+1\geq 4$, we show the existence of solutions of the Einstein vacuum equations which describe asymptotically de Sitter spacetimes with prescribed smooth data at the conformal boundary. This provides a short alternative proof of a special case of a result by Shlapentokh-Rothman and Rodnianski, and generalizes earlier results by Friedrich and Anderson to all dimensions.
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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.