Asymptotia of Kerr-de Sitter Black Holes

Exterior geometries of physical black holes are believed to asymptotically approach the Kerr--de Sitter spacetime at late times. A characteristic feature of that vacuum Einstein solution is the presence of a hidden symmetry generated by a closed conformal Killing--Yano tensor. Using this symmetry and modern conformal geometry technology, we find necessary conditions for generic solutions to asymptotically approach the Kerr--de Sitter metric. Further, we constrain the admissible form of the geometric free data on the conformal infinity giving rise to this family of spacetimes and constrain it in terms of the stress-energy tensor.