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Using asymptotic characterization results of spacetimes at conformalinfinity, we prove that Kerr-Schild-de Sitter spacetimes are in one-to-onecorrespondence with spacetimes in the Kerr-de Sitter-like class withconformally flat $\mathscr{I}$. Kerr-Schild-de Sitter are spacetimes ofKerr-Schild form with de Sitter background that solve the $(\Lambda>0)$-vacuumEinstein equations and admit a smooth conformal compactification sharing$\mathscr{I}$ with the background metric. Kerr-de Sitter-like metrics withconformally flat $\mathscr{I}$ are a generalization of the Kerr-de Sittermetrics, defined originally in four spacetime dimensions and extended here toall dimensions in terms of their initial data at null infinity. We explicitlyconstruct all metrics in this class as limits or analytic extensions of Kerr-deSitter. The structure of limits is inferred from corresponding limits of theasymptotic data, which appear to be hard to guess from the spacetime metrics.

Classification of Kerr-de Sitter-like spacetimes with conformally flat $\mathscr{I}$ in all dimensions