Under compatibility conditions on both horizons, every smooth stationary vacuum solution with positive cosmological constant is claimed to be isometric to Kerr-de Sitter in its stationary region.
M.A Spacetime Characterization of the Kerr-NUT- (A)de Sitter and Related Metrics
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On the uniqueness of Kerr-de Sitter spacetimes
Under compatibility conditions on both horizons, every smooth stationary vacuum solution with positive cosmological constant is claimed to be isometric to Kerr-de Sitter in its stationary region.