This defines a local Lorentz frame in the tangent space at each event (in the region covered by our Rindler chart, namely the Rindler wedge). The integral curves of the timelike unit vector field e → → 0 give a timelike congruence, consisting of the world lines of a family of observers called the Rindler observers. In the Rindler chart, these world lines appear as the vertical coordinate lines x = x 0 , y = y 0 , z = z 0 . Using the coordinate transformation above, we find that these correspond to hyperbolic arcs in the original Cartesian chart.