But why fast forward? Doesn’t SR predict slower perceived time for objects moving relative to the observer?
If a hypervelocity star passed by us, we would see them in slow motion because they are moving at high speed relative to us. At the same time, they would see us in slow motion because we would be moving at high speed relative to them. The effect of “the other clock is slower” is reciprocal.
The weirder and non-reciprocal effects would occur when the hypervelocity star is first slingshotted out to high speed. At that point they would be close to a black hole (deep in a gravitational well) and accelerating (non-inertial frame of reference). Under those conditions, their clock would run slower than our clock for observers on both sides — i.e., we would see them in slow motion and they would see us in fast forward.
You may be confusing it with red shift.