Decoupling of kinematical time dilation and gravitational time dilation in particular geometries

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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.
4 pages

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