The Rindler Coordinate Theory's Expansion and Problem

In the general relativity theory, the Rindler coordinate theory’s mathematics modernizes and the Rindler coordinate theory expands to be the Rindler coordinate theory of the accelerated observer that have the initial velocity. First, find the Rindler coordinate theory with initial velocity that used the tetrad on the new method and discover the new inverse-coordinate transformation of the Rindler coordinate theory with the initial velocity. Specially, if , this theory treats that the observer with the initial velocity does slowdown by the constant negative acceleration in the Rindler’s time-space.And according to the accelerated system or the decelerated system, consider the Doppler effect.