of a body in hyperbolic motion measured by a comoving observer. By using the proper time of the observer as the time of the entire hyperbolically accelerated frame by setting , the transformation formulas between the inertial coordinates and the hyperbolic coordinates are consequently: with the inverse Differentiated and inserted into the Minkowski metric , the metric in the hyperbolically accelerated frame follows These transformations define the Rindler observer as an observer that is "at rest" in Rindler coordinates, i.e., maintaining constant x, y, z and only varying t as time passes. The coordinates are valid in the region , which is often called the Rindler wedge, if represents the proper acceleration (along the hyperbola ) of the Rindler observer whose proper time is defined to be equal to Rindler coordinate time. To maintain this world line, the observer must accelerate with a constant proper acceleration, with Rindler observers closer to (the Rindler horizon) having greater proper acceleration. All the Rindler observers are instantaneously at rest at time in the inertial frame, and at this time a Rindler observer with proper acceleration will be at position (really , but we assume units where ), which is also that observer's constant distance from the Rindler horizon in Rindler coordinates. If all Rindler observers set their clocks to zero at , then when defining a Rindler coordinate system we have a choice of which Rindler observer's proper time will be equal to the coordinate time in Rindler coordinates, and this observer's proper acceleration defines the value of above (for other Rindler observers at different distances from the Rindler horizon, the coordinate time will equal some constant multiple of their own proper time). It is a common convention to define the Rindler coordinate system so that the Rindler observer whose proper time matches coordinate time is the one who has proper acceleration , so that can be eliminated from the equations. The above equation has been simplified for . The unsimplified equation is more convenient for finding the Rindler Horizon distance, given an acceleration . The remainder of the article will follow the convention of setting both and , so units for and will be 1 unit . Be mindful that setting light-second/second2 is very different from setting light-year/year2. Even if we pick units where , the magnitude of the proper acceleration will depend on our choice of units: for example, if we