Consider the case of two black holes approaching each other in preparation for a merger.
As they get closer they each approach the event horizon of the other black hole.
My Question: Why are we able to actually witness the merger?
After all, at the event horizon of each black hole the rate of time change is zero.
Shouldn't we see them getting slowly closer but the time dilation takes over so we should never be able to witness the final merger itself? (i.e., measure any gravitational waves at the start of the merger).
My thinking is that the generated gravitational waves should be infinitely red-shifted (make them not measurable by our LIGO instruments) when the event horizons touch.
What am I missing here?
