Two different forms of time dilation, namely, the kinematical time dilation of special relativity and gravitational red shift are coupled together during observations of a system travelling through a gravitational field. In the case of a Schwarzschild geometry these two effects are decoupled and in consequence they factorise. 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 frequency shift in a Schwarzschild geometry.

PACS numbers: 03.30.+p, 04.20.Cv