Rindler coordinates

In relativistic physics, the Rindler coordinate chart is an important and useful coordinate chart representing part of flat spacetime, also called Minkowski spacetime. The Rindler coordinate system or frame describes a uniformly accelerating frame of reference in Minkowski space. In special relativity, a uniformly accelerating particle undergoes hyperbolic motion. For each such particle, a Rindler frame can be chosen in which it is at rest.The Rindler chart is named after Wolfgang Rindler who popularised its use, although it was already "well known" in 1935, according to a paper by Albert Einstein and Nathan Rosen. For general overview as well as history of the application of accelerations in flat spacetime, see Acceleration (special relativity).

To obtain the Rindler chart, start with the Cartesian chart (an inertial frame) with the metric (c=1 is assumed)

In the region ${\displaystyle \scriptstyle 0\,<\,X\,<\,\infty ,\;-X\,<\,T\,<\,X}$, which is often called the Rindler wedge, if g represents the proper acceleration (along the hyperbola x=1) of the Rindler observer whose proper time is defined to be equal to Rindler coordinate time (see below), the new chart is defined using the coordinate transformation

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