  If the Hamiltonian of a quantum field theory is taken to be a timelike
isometry, the vacuum state remains empty for all time. We search for such
stationary vacua in anti-de Sitter space. By considering conjugacy classes of
the Lorentz group, we find interesting one-parameter families of stationary
vacua in three-dimensional anti-de Sitter space. In particular, there exists a
family of rotating Rindler vacua, labeled by the rotation parameter beta, which
are related to the usual Rindler vacuum by non-trivial Bogolubov
transformations. Rotating Rindler-AdS space possesses not only an
observer-dependent event horizon but even an observer-dependent ergosphere. We
also find rotating vacua in global AdS provided a certain region of spacetime
is excluded.
