Relativistic Doppler Effect near a Black Hole

[appot89]

TL;DR

Relativistic Doppler Effect near a blackhole

Hey everyone, if I were to view a shining person rotating near a black hole at near the speed of light there would be 2 kinds of redshifts: gravitational redshift and relativistic doppler effect redshift. Right?

But, say at some point, the person is traveling towards me, then the doppler effect would result in a blueshift while the gravitational redshift would remain. Is it possible that if the doppler effect blueshift and the gravitational redshift were equal, would I view the light shining at its original frequency?

 

[Orodruin]

Yes.

 

[Ibix]

You can always adjust your speed relative to a nearby hovering observer so that your kinematic blueshift cancels the gravitational redshift, yes. It'll happen naturally at some point for an object in a circular orbit (and probably any other), if my algebra is correct.