Question

Observer a is an inertial observer, and b is an observer in a uniformly-accelerating frame of reference, with a constant proper acceleration g. Therefore the coordinate transformation between a and b is the rindler transformation. Start by assuming the minkowski met- ric for a, and show the metric used by b's coordinate system is the rindler metric (5)

Answer 1

In relativistic physics, the coordinates of a hyperbolically accelerated reference frame[H 1][1] constitute an important and useful coordinate chart representing part of flat Minkowski spacetime.[2][3][4][5] In special relativity, a uniformly accelerating particle undergoes hyperbolic motion, for which a uniformly accelerating frame of reference in which it is at rest can be chosen as its proper reference frame. The phenomena in this hyperbolically accelerated frame can be compared to effects arising in a homogeneous gravitational field. For general overview of accelerations in flat spacetime, see Acceleration (special relativity) and Proper reference frame (flat spacetime).