For , these coordinates cover a wedge of Minkowski spacetime and give in two dimensions. A constant- observer has proper acceleration and the Unruh effect temperature in natural units. The apparent degeneration at is a coordinate horizon.
Static observers at positive Rindler radii follow hyperbolae . Their proper clock rates scale with at fixed Rindler time, so light received at smaller radius is blueshifted by the ratio of emitter to receiver radii. A direct Doppler calculation at emission and reception gives the same result.
For in a patch with , the null paths solve , giving with . They are geodesics after choosing an affine parameter. The Rindler coordinates , give and . Thus each exponential path is a straight inertial null line. A literal curve is outside this degenerate coordinate chart, not an extra null geodesic within it.
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Rindler coordinates are a specific set of coordinates used in the context of special relativity and general relativity to describe the perspective of an observer undergoing constant proper acceleration. They are particularly useful for analyzing scenarios involving accelerated frames of reference. In Minkowski space (the spacetime of special relativity), Rindler coordinates are derived from the usual Cartesian coordinates by performing a change of coordinates that reflects the experience of an observer who is accelerating with respect to an inertial observer.