Final answer:
With a relative velocity of zero, there is no relativistic Doppler effect, since it requires relative motion between the source and the observer to change the observed frequency of light.
Step-by-step explanation:
What happens to the relativistic Doppler effect when relative velocity is zero? The answer is that there is no Doppler effect. This is because the relativistic Doppler effect depends only on the relative velocity of the source and the observer.
When the relative velocity is zero, there will be no measured change in wavelength or frequency, and thus no shift in the observed frequency or color of light (no red shift or blue shift). Since there is no relative motion, this absence of the Doppler effect is indeed expected.