  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 various 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.
