Does time slow down in a black hole merger?

Here’s a great question I saw recently. I’m wondering if anyone has a good answer for this:

I just watched a video of two black holes merging. I read about how time slows down near a black holes surface. If that’s true, shouldn’t the black holes slow down as they get close to each other, so that they never actually merge?

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I guess this question is not completely well posed as it does not tell in what frame time is being measured. Where is the observer ?

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@ecm that’s a great point!

Since we can only observe black hole mergers from earth, it probably makes sense to think about an observer that is very far (millions of light years away!) from the merger.

We know that a test particle falling into a black hole, as observed by a distant observer, would appear to “freeze” near the event horizon, as time seems to slow down neat the event horizon from the perspective of the distant observer.

However, with black hole mergers, this doesn’t seem to happen. Instead, LIGO and Virgo observe black hole mergers, and they merge in finite time as observed from earth. As best I can tell, this means that the “test particle” approximation for time dilation doesn’t work for two black holes merging, and instead we need to understand them in a more holistic context.

I meant to reply to this earlier, but didn’t have the time. Even with a point particle falling into a black hole, the ringdown signal comes primarily from when the particle passes the light ring, not when it goes all the way to the horizon (see, e.g., Cardoso, Franzin, and Pani), so there are no concerns with the merger signal being infinitely redshifted.

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