  In this paper, we consider the boundary rigidity problem on a cylindrical
domain in $\mathbb R^{1+n}$, $n\geq 2$, equipped with a stationary
(time-invariant) Lorentzian metric. We show that the time separation function
between pairs of points on the boundary of the cylindrical domain determines
the stationary spacetime, up to some time-invariant diffeomorphism, assuming
that the metric satisfies some a-priori conditions.
