  A natural one codimension isometric embedding of each $(n+1)$-dimensional
spherical Robertson-Walker (RW) spacetime $I\times_f \mathbb{S}^n$ in
$(n+2)$-dimensional Lorentz-Minkowski spacetime $\mathbb{L}^{n+2}$ permits to
contemplate $I\times_f \mathbb{S}^n$ as a rotation Lorentzian hypersurface of
$\mathbb{L}^{n+2}$. After a detailed study of such Lorentzian hypersurfaces,
any $k$-dimensional spacelike submanifold of such an RW spacetime can be
contemplated as a spacelike submanifold of $\mathbb{L}^{n+2}$. Then, we use
that situation to study $k$-dimensional stationary (i.e., of zero mean
curvature vector field) spacelike submanifolds of the RW spacetime. In
particular, we prove a wide extension of the Lorentzian version of the
classical Takahashi theorem, giving a characterization of stationary spacelike
submanifolds of $I\times_f \mathbb{S}^n$ when contemplating them as spacelike
submanifolds of $\mathbb{L}^{n+2}$.
