be any one–parameter subgroup of ${\mbox{SO$_0(2,n\!-\!1)$}}$ such that $t \mapsto \lambda(t) x_O$ is an orthochronous curve. (Note that AdS is time orientable.) We interpret this curve as the worldline of some observer. Among these observers will be those moving along a geodesic (henceforth, geodesic observers) and those experiencing a constant acceleration (uniformly accelerated observers). Points in a neighborhood of $x_O$ will, in general, also give rise to orthochronous curves under the action of the chosen subgroup of ${\mbox{SO$_0(2,n\!-\!1)$}}$, and we denote by $W$ the connected neighborhood of $x_O$ in consisting of all such curves. Typically, $W$ is the causal completion of the originally specified worldline. We view the region $W$ as the maximal possible localization for any laboratory within the purview of the given observer. The associated dynamics are given by $e^{\, itM} \doteq U(\lambda(t))$ with suitable generator $M$. Since we are choosing a fixed parametrization of the pertinent subgroups of , the proper time of the observer is obtained by rescaling $t$ with $((\dot{\lambda}(0) \, x_O)^2){}^{1/2}$.

To become more precise, the geodesics of are conic sections by two–planes containing the origin of the ambient space $\RR^{n+1}$. So, one-parameter subgroups[^2] $\lambda(t)$, $t \in \RR$, of ${\mbox{SO$_0(2,n\!-\!1)$}}$ of the form $\lambda 