Expansion of Rindler Coordinate Theory and Light's Doppler Effect

In the general theory of relativity the Rindler coordinate theory has been extended to the Rindler coordinate theory of accelerated observer that has already some initial velocity. In this paper, we present this extended theory that uses the tetrad as the new method, and discover the new inverse-coordinate transformation. Specially, if, 0 0 a < , this theory treats the observer with the initial velocity that does slowdown by the constant negative acceleration in the Rindler’s time-space. We consider the light’s Doppler Effect in the accelerated system as well as the decelerated system.