|MadSci Network: Physics|
This is an interesting question, but I think that some of your underlying assumptions are wrong. The first assumption is that the black hole has some momentum. My question back to you is "relative to what?" For something to be moving, it needs to have a reference frame. So if we have a reference frame, relative to what is the motion of the black hole occurring? Now, given a large enough reference frame (i.e. when you consider large enough distances), then yes, everything is moving. But why would the particle/antiparticle pairs popping out of the vacuum not have the same momentum distribution? But to be honest, the only way that the proposition you make would have an impact is if the black hole had a momentum relative to the local space that was a significant fraction of the speed of light.
I hope this helps!
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