Time-Dependent Generalized Relativistic Transformation and its Compatibility with General Relativity

With the recent proposal of the Generalized Relativistic Transformation (GRT) [1-6] — which describes any orientation of information, of velocity, and observer position in inertial relativistic events — it becomes natural to incorporate time dependence into the GRT approach. By doing so, we demonstrate that GRT not only reproduces General Relativity’s prediction for satellite time correction by reinterpreting the Doppler effect as a purely relativistic phenomenon but also yields a general solution for arbitrarily accelerated reference frames. Furthermore, although resulting in a metric that differs in form from the traditionally accepted Schwarzschild solution, but their results align perfectly with those of the Schwarzschild formulation for gravitational time correction while providing novel corrections to generic accelerated system.