gravitational waves - So Black Holes Actually Merge! In 1/5th of a Second - How?

I've read a lot of conflicting answers in these forums. However, today saw the awesome announcement of gravitational waves. Two black holes merged: http://www.slate.com/blogs/bad_astronomy/2016/02/11/gravitational_waves_finally_detected_at_ligo.html

Not only that, they merged FAST. In 1/5th of a second revolving around each other 250 times a second. The entire event was quicker than a heartbeat. Moreover, we observed this happening as distant outsiders. So now we can say for sure:

1. Objects approaching the event horizon DO NOT appear to slow down


2. Black holes CAN merge in a finite (and quick) amount of time


3. And all this is wrt a frame of reference far, far away

To quote the NYTimes article:

One of them was 36 times as massive as the sun, the other 29. As they approached the end, at half the speed of light, they were circling each other 250 times a second.

And then the ringing stopped as the two holes coalesced into a single black hole, a trapdoor in space with the equivalent mass of 62 suns. All in a fifth of a second, Earth time.

However, everything I've read so far has let me to believe that an outside observer should never be able to measure the collision happening in a finite time. So what exactly is happening here? I must have read at lest 5 different versions of this so far everywhere in these forums over the past several years.

Answer

This presumably stems from the fact that in the coordinate system of an external observer nothing can ever cross the event horizon of a black hole.

This is perfectly true, but if you were watching an object fall onto a stellar mass black hole it would red shift to invisibility in a few microseconds and it would look to you just like it crossed the horizon. More precisely, no matter how sensitive your measuring equipment there would be a time after which you could no longer detect that the object had not crossed the horizon, and for any physically reasonable equipment this time is extremely short.

The same principle applies to the merging black holes. We have two objects that can't actually be real black holes because in any finite universe we know real black holes cannot exist. However they are experimentally indistinguishable from real black holes. As these two objects approach each other the spacetime geometry changes and approaches that of a single rotating black hole - the Kerr metric. We know the geometry can never actually become Kerr because that would take an infinite time. However the geometry approaches the Kerr geometry so quickly that after a fifth of a second it is experimentally indistinguishable from the Kerr geometry.

Whether the black holes have merged or not depends on exactly what you mean by merged. They are certainly no longer two separate objects, and that happens in a short time and is observable. In this sense it seems reasonable to me to describe tham as having merged. If you insist the merger is complete only when the transition to the Kerr geometry is complete then this will take an infinite time so they will never merge.

tl;dr - in any sensible meaning of the term merge the two black holes do indeed merge in a finite, and very short, time.