  The aim of this note is to present a unified approach to the results given in
\cite{bb99} and \cite{bs04} which also covers examples of models not presented
in these two papers (e.g. $d$-dimensional Minkowski space-time for $d\geq 3$).
Assuming that a state is passive for an observer travelling along certain
(essential) worldlines, we show that this state is invariant under the isometry
group, is a KMS-state for the observer at a temperature uniquely determined by
the structure constants of the Lie algebra involved and fulfills (a variant of)
the Reeh-Schlieder property. Also the modular objects associated to such a
state and the observable algebra of an observer are computed and a version of
weak locality is examined.
