Because the Rindler observers are vorticity-free, they are also hypersurface orthogonal. The orthogonal spatial hyperslices are t = t 0 ; these appear as horizontal half-planes in the Rindler chart and as half-planes through T = X = 0 in the Cartesian chart (see the figure above). Setting d t = 0 in the line element, we see that these have the ordinary Euclidean geometry, d σ σ 2 = d x 2 + d y 2 + d z 2 , ∀ ∀ x > 0 , ∀ ∀ y , z . Thus, the spatial coordinates in the Rindler chart have a very simple interpretation consistent with the claim that the Rindler observers are mutually stationary. We will return to this rigidity property of the Rindler observers a bit later in this article.