Travel Time Tomography in Stationary Spacetimes

In this paper, we consider the boundary rigidity problem on a cylindrical domain in $${\mathbb {R}}^{1+n}$$ , $$n\ge 2$$ , 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.