All the stationary vacuum states of de Sitter space

We obtain all the stationary vacua of de Sitter space by classifying the inequivalent timelike isometries of the de Sitter group. Besides the static vacuum, de Sitter space also admits a family of rotating vacua, which we use to obtain Kerr--de Sitter solutions in three, four, and five dimensions. By writing the metric in a coordinate system adapted to the rotating Hamiltonian, we show that empty de Sitter space admits not only an observer-dependent horizon but also an observer-dependent ergosphere.