  Two different forms of time dilation, namely, the kinematical time dilation
of special relativity and gravitational red shift are coupled during
observations of systems moving through a gravitational field. In the particular
situation of free fall in a Schwarzschild geometry these two effects are
decoupled and in consequence the time dilation, as observed by a distant
observer, factorises. Such a factorization is not a universal feature. We
define here a necessary and sufficient criterion for time dilation and
gravitational red-shift decoupling. This property is manifested in a particular
form of the Doppler shift in Schwarzschild geometry.
