Variation of the velocity and the frequency of a periodic signal along   the world line of the emitter
  The variation of the velocity of a periodic signal and its frequency along the world line of a standard emitter (at rest with an observer) are considered in a space with affine connections and metrics. It is shown that the frequency of the emitted periodic signal is depending on the kinematic characteristics of the motion of the emitter in space-time related to its shear and expansion velocities. The same conclusions are valid for a standard clock moving with an observer. 
Sawa Manoff