A thought crossed my mind that I realized was hard to conceptualize so I decided to simplify the question by putting it in terms of event horizons.
If I am an observer approaching black hole "A", and I track another blackhole "B" in the distance, as I fall toward A's event horizon would blackhole B's event horizon appear to:
- grow
- shrink
- grow then shrink
- shrink then grow
- almost no change
And in choosing one, which factors would be affecting this observation? Some thoughts I was having was the issue of never seeing something fall into a black hole due to time dilation. As you got closer to A's event horizon more of the objects around B would appear to speed up so essentially at least the horizon would get..."sharper"? But then, everything is speeding up relative to you so time is passing much quicker at blackhole B and....
I dunno. My head starts getting in a twist when I start to parse out the different phenomena happening.
Any insights would probably help! Thanks!