How did black holes merge in finite time?

[adrian_m]

This question is in context of the recent gravitational wave detection by aLigo. Apparently aLigo has detected the entire process, including the before merger, during merger, and aftermath of the completed merger.

My understanding is that two black holes should not be seen to be merging in finite time, as observed by a distant observer. Since nothing can reach a black hole's event horizon in finite time (as observed from outside), how did the two black holes cross each others' event horizons and form a merged black hole in finite time?

 

[PeterDonis]

My understanding is that two black holes should not be seen to be merging in finite time, as observed by a distant observer.

Your understanding is wrong. See below.

Since nothing can reach a black hole's event horizon in finite time (as observed from outside)

No; a distant observer cannot see an object reach the event horizon of a static, isolated black hole in finite time. But if you have two black holes merging, neither one is static and isolated.

There is also a further point: the GWs we detected from the merger came from outside the horizon of the merged black hole; they were fluctuations in spacetime curvature that propagated from outside the merged horizon outward to the rest of the universe. So seeing them is not the same as seeing an object fall to the horizon.

 

[pervect]

This question is in context of the recent gravitational wave detection by aLigo. Apparently aLigo has detected the entire process, including the before merger, during merger, and aftermath of the completed merger.

My understanding is that two black holes should not be seen to be merging in finite time, as observed by a distant observer. Since nothing can reach a black hole's event horizon in finite time (as observed from outside), how did the two black holes cross each others' event horizons and form a merged black hole in finite time?

I'll have to agree with your understanding as stated. While the black holes merge in a finite proper time, we are observing them from a distance and hence in this case we are interested in the appropriate coordinate time rather than proper time. There is a large gravitational redshift from anything emitted close enough to the newly formed black hole, one that increases without bound.

My understanding of what we actually see is that as the inspiral starts, the emission of gravitational waves increases, increasing the signal, and that this increase overcomes any initially small gravitational redshift that occurs.

However, the gravitational redshift becomes more and more important as the inspiral proceeds, and eventually it dominates. So the signal reaches a peak, and then fades due to the redshift, and that's what we observe.

 

[PAllen]

I'll have to agree with your understanding as stated. While the black holes merge in a finite proper time, we are observing them from a distance and hence in this case we are interested in the appropriate coordinate time rather than proper time.
...

But which coordinate time?

What is an invariant description of the situation is that after a finite time for a distant observer, the merger and ringdown of the merged horizon ceases to be in the causal future, and shifts to spacelike relation, which means it can be treated as coordinate now, then coordinate past. The only thing prevented by the causal geometry is that the merged horizon never becomes part of the distant observer's causal past. However, all the events e.g. a millionth of a Planck length outside the merged horizon do eventually become in the causal past of a distant observer.

 

[PeterDonis]

There is a large gravitational redshift from anything emitted close enough to the newly formed black hole, one that increases without bound.

This is true once the newly formed black hole is reasonably stationary. But it's not even close to being reasonably stationary during the period when the gravitational waves are being emitted. The region of spacetime in which the GWs are generated is highly dynamic (it has to be to generate the GWs). So I don't think we can use our intuitions about gravitational time dilation the same way we would for a stationary black hole.

(Note also that the newly formed black hole in this case was spinning fairly rapidly, so it has to be modeled, even in its final stationary state, as a Kerr hole, not a Schwarzschild hole. That changes somewhat the behavior of gravitational time dilation anyway.)

 

[adrian_m]

OK, sounds like the event will be completed in finite time even for a distant observer, though the distant observer may not be able to see it happen fully. If it was a smaller neutron star and a much larger black hole scenario (though between them enough to have detectable GWs), would the observations and conclusion be the same?

 

[PeterDonis]

sounds like the event will be completed in finite time even for a distant observer

There is no absolute meaning to the "time" the merge happens for the distant observer; it depends on what simultaneity convention he adopts. (This is true for the case of an isolated static black hole as well, and is a key reason why people like me object when others talk about "the" time when events near or at the hole's horizon happen "for the distant observer" as if that had some absolute meaning.)

though the distant observer may not be able to see it happen fully

In principle there could be portions of the GW emission from the merger that would not be visible to distant observers until much later than the main signal. However, in practice it does not appear that this is significant; any such portion of the signal is too weak to be detectable anyway (because it comes from such a late part of the merger that the emitted waves are very faint).

If it was a smaller neutron star and a much larger black hole scenario (though between them enough to have detectable GWs), would the observations and conclusion be the same?

I'm not sure how strong the GWs emitted from a neutron star-BH merger would be. What makes the GWs from a BH-BH merger so strong is that both objects are made of spacetime curvature. If only one object in the merger is made of spacetime curvature, the GW emission is (I think) likely to be a lot weaker. But I don't know how much this case has been explored in the literature.

 

[adrian_m]

LIGO has template for NS-BH mergers also in place for detecting such events, so I am assuming such events are expected to be detectable as well. Large mass NS would also have considerable spactime curvature near them.