[jeffreyH (OP)]

Since time slows down at the event horizon of each black hole shouldn't it take an infinite amount of time for the process to conclude?

[yor_on]

Depends on where you are If you're at, or near, the event horizon, your clock will tell you that you're passing it. For someone far away you will just hang there waiting. Locally defined all clocks have a same 'beat' as I think of it, the proof of it is in joining a same frame of reference and then measure that 'beat'. If you by it mean that it won't happen according to a 'far away observer'? I think so too, and in a same manner it then may be possible to argue that 'c' 'slows down' if you think of it as equivalent to a 'clock'. But you, and everything else, can't exist any way other than 'locally', and locally measured 'c' must be 'c', and nothing stops that beat.

[yor_on]

What I'm saying there is that if I make 'c' equivalent to a clock, I do it 'locally', not by referring to comparisons between 'frames of reference'. But it makes it weird, doesn't it Because assuming that all 'black holes' have a 'event horizon' for a observer, then where won't it hold true, if so? How could they ever come to be from a far observer, no difference at what scale.
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Actually I think I'm stating something more by it, but I need to think about that one. What it ends in though, if it would be correct, is that this 'beat' is local, and equivalent, meaning that it is something more than just a result of scaling up. A origin instead of a result of SpaceTime. And I'm not sure on that one at all
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What one has to remember thinking of it is that matter will 'move', adding to the mass of that Black hole, although, possibly, never pass that event horizon, from a 'far away observer'. So it will add mass at that location any which way.
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I keep getting stuck on that one Jeffrey, if now 'c' is equivalent to a perfect 'local clock', which is how I see it. Either 'time' is a result of SpaceTime existing, or SpaceTime exist due to 'c'. If you define it locally then 'time' as we see it comparing a local clock to this far away 'black hole' is our artifact, existing as a result of ones comparison. 'Locally' though it then must be the same, at some, or several, scales. It's about equilibriums.

[yor_on]

It turns SpaceTime upside down if it is seen this way, SpaceTime as we see it becoming one thing, but what holds it together being totally 'equivalent'. The same physical laws everywhere, it has to be so if that is right, a Big Bang at every location, you just have to be in the right position to see that it will be so.

[jeffreyH (OP)]

At the detector the waves are measured in fractions of a second. No time dilation recorded at the detector.

[yor_on]

Yep. the question then becomes, how 'local' is local? And what about being in a same frame of reference, as us here on Earth. can you use QM, or should it be loops and strings? And if you can accept that you might find 'equivalences' at all scales, aka 'same frames of reference', what does it state?

[Bill S]

By the same token; if black holes have singularities at the centre, from a remote RF, there are no black holes, because it would take infinitly long for material to become infinitly compacted/curved, so they are all still forming.

[Janus]

Since time slows down at the event horizon of each black hole shouldn't it take an infinite amount of time for the process to conclude?

Imagine you have two 100 solar masses black holes, they will have event horizons radii of 295 km.  When their centers are 590 km apart, their event horizons touch. Keep in mind that the event horizon is not a physical thing, but a boundary.   But, the event horizon radius is directly proportional to the mass and the total mass of the two BH's is 200 solar masses and the thus event horizon of the new black hole will be 590 km, or equal to the distance the centers are now apart.   In other words, the event horizon for the combined mass of the original two black hole expands to include the singularities of both black holes before the singularities get as close as the original event horizon radii.

Here's a diagram showing a pair of black holes merging. the circles are the extent of the event horizons.

[jeffreyH (OP)]

By the same token; if black holes have singularities at the centre, from a remote RF, there are no black holes, because it would take infinitly long for material to become infinitly compacted/curved, so they are all still forming.

That I very much doubt. Black holes should form very quickly. It is our view of time dilation/length contraction that is in error.

[Bill S]

Imagine you have two 100 solar masses black holes, they will have event horizons radii of 295 km.  When their centers are 590 km apart, their event horizons touch.

Is it as simple as that? Muller says:

Imagine that you and I are a few feet apart, in space”.....“our proper frames are identical, so in that frame we are both at rest. Now, get a small primordial (completely formed) black hole,”……..”Plunk it right in between you and me.”……..”When the black hole is in place, the straight line distance between you and me becomes infinite.”…..”The distance between us has changed.  Yet our locations have not.”

Don’t ask where I’m going with this.  I’m just wondering if this is valid thinking, and, if so, whether it would mean that the centres of your black holes would be infinitely far apart.

[Bill S]

That I very much doubt. Black holes should form very quickly. It is our view of time Would the dilation/length contraction that is in error.

If the formation process involves an approach to infinity, wouldn’t it be asymptotic?

[jeffreyH (OP)]

If we get an infinity in the mathematics then there is something wrong with the thinking behind the mathematics.

[evan_au]

The original gravitational wave detection lasted about 10ms.
See: https://en.wikipedia.org/wiki/File:LIGO_measurement_of_gravitational_waves.svg

This consisted of a "chirp" with increasing frequency as the two black holes orbited faster and closer, followed by a ringdown phase as the new combined black hole settled into a more symmetrical spheroidal shape.

The "echoes" mentioned in the recent Nature article were in multiples of 100ms after the original merger. These echoes occur long after the original merger occurred.  If confirmed, these would be significantly time-delayed echoes, since the speed of light across an object 500km across is about 25us in "flat" space.

[jeffreyH (OP)]

So in fact we have a finite amount of time dilation. Therefore the merger cannot have taken an infinite time period to complete. The original question of the thread was provocative and did not reflect a personal viewpoint. Now we have something new to discuss.

[Bill S]

If we get an infinity in the mathematics then there is something wrong with the thinking behind the mathematics

I agree, absolutely; but you knew that. []

It just seems a shame that so many experts use "infinity" as though this were not the case, when it suits them.

[jeffreyH (OP)]

If that is the case then I would have to question their expertise. Infinities arise in calculus, for example, and are considered a real problem. Limits and rules such as L'Hopital's are used to rectify this situation.

[evan_au]

Since time slows down at the event horizon of each black hole shouldn't it take an infinite amount of time for the process to conclude?

Let's have a look at the amount of time dilation expected as two black holes merge (simple approximation*):
t_r/t=SQRT(1-r_s/r), where:
- t_r represents the amount of time, as experienced by an object close to a black hole (at radius r)
- t represents the time as experienced by a distant observer (us)
- r_s is the Schwarzchild radius of the black hole (the point where the escape velocity exceeds c)
- r is the distance of the object from the center of the black hole

If you were going to see a 1000-fold slowdown in time (10ms stretches out to 10s),  the object would need to be within 0.0001% of the Schwarzchild radius of the black hole (but just outside of the Schwarzchild radius).

However, when two black holes of similar size merge, the center of the other black hole is at twice the Schwarzchild radius, so events will occur at about 70% of the rate that it would in flat space.

In other words, the black hole inspiral will be observed to occur, at a rate about 70% of what Newton might have predicted, rather than infinitely slowed.

For a stellar-mass black hole merging with a supermassive black hole, more extreme time dilation will occur. A 1000-fold time dilation could occur if a stellar-mass black hole merged with a galactic-center black hole with a mass 1 million times larger.

See: https://en.wikipedia.org/wiki/Schwarzschild_radius#In_gravitational_time_dilation

*This formula assumes that the object approaching the black hole is "small". Another black hole of similar size is not "small", so it wouldn't surprise me if events unfolded at half the rate Newton would have predicted. But this is still a big difference from "infinitely delayed".