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Suppose that there are two (non rotating, un-charged, bog standard) black holes of dissimilar masses heading for a head-on collision. They will accelerate towards each other. The larger one will accelerate at a lesser rate than the smaller one, but the acceleration of both towards each other can be observed.

As they merge, will a distant observer see a change in the acceleration of the bodies, and when the smaller black hole just disappears beneath the the event horizon of the larger black hole (admittedly creating a much larger event horizon for the combined masses), will there still be a perceived acceleration of the combination for some interval? If so, for how long might this observable acceleration persist?

Just curious.