I Mass distribution behavior of the singularities during black hole mergers

[DarkMattrHole]

TL;DR Summary

mass distribution and behavior of the dual singularities during black hole collisions?

When two BHs collide the resulting single BH bulges and contorts until it settles down to a stable state.

1) Does this mean that during this 'settling' period the mass internal to the merged BH is not (yet) a singularity, but instead two 'singularities' spinning down around each other in irregular fashion due to a wobbling spacetime, or distributed matter in the internal space in the form of a blob or blobs?

2) We know what happens externally, and how fast it happens. What would this settling process 'look' (what does the math say) like from an internal observer's point of view? Or from a 'magic eye's point of view? How fast would the settling take from internal reference, say of an imaginary weather man reporting from within the collision event.

 

[PeterDonis]

Does this mean that during this 'settling' period the mass internal to the merged BH is not (yet) a singularity, but instead two 'singularities' spinning down around each other in irregular fashion due to a wobbling spacetime, or distributed matter in the internal space in the form of a blob or blobs?

No. If two black holes merge, there is only one singularity. The singularity is in the future; it's a moment of time, not a place in space.

In fact, saying "two black holes merge" is not precisely correct. Strictly speaking, there is only one black hole--only one connected region of spacetime that can't send light signals to infinity. The black hole region of spacetime just looks like a pair of trousers instead of a cylinder, if we picture a (reduced dimension) spacetime diagram of the scenario. The legs of the trousers are the "two black holes" before the merger, and the upper part is the "one black hole" after the merger. The singularity in this viewpoint would be at the top, inside the trousers.

Also, black holes are made of vacuum, not matter, so there doesn't need to be any matter involved at all in a black hole merger.

What would this settling process 'look' (what does the math say) like from an internal observer's point of view?

We don't have a closed form analytical solution for this case, so the only "math" we have is computer simulations.

Basically, the simulations say that an observer falling in during the merge process would see increasingly chaotic oscillations in the spacetime curvature, i.e., tidal gravity, in his vicinity, similar in general nature to the gravitational waves that get emitted outward by the merger process, but growing stronger and stronger as he falls. These oscillations would probably tear him apart well before he reached the singularity. (The technical name for the oscillations the simulations show is "BKL oscillations", after Belinsky, Khalatnikov, and Lifschitz, the three Russian physicists who discovered this general pattern of oscillations.)

If the observer waits a long time after the merger before falling in (and is able to survive the strongly oscillating tidal gravity of the wave front of gravitational waves emitted outward by the merger), he would observe much more gentle oscillations in spacetime curvature, since the hole would have had time to "settle down" in its interior. In this case, the observer might get close enough to the singularity for quantum gravity effects to become significant, and we have no way of knowing at this point what would happen then, since we have no good theory of quantum gravity.

 

[DarkMattrHole]

Oh, great description. Thanks, PeterDonis. So to better understand, from your description using trousers, during the time before the merger each BH has a singularity, right? And after merging there is only one singularity, is that right so far? If so, might that mean that all three singularities are actually the one and the same singularity? Or, in what manner do two singularities become one?

 

[GalileosTelescope]

Very interesting question. I don't think this will fully answer it, but here is a little thought experiment.

Before the black holes merge, the math says an observer inside one of the holes, cannot move in the outward radial direction, only towards the singularity. This is because according to the math the radial dimension and the time dimension flip once you cross the event horizon. So just like outside you can only travel in one directing in time, inside you can only travel in one direction in "radius". Ok so this is happening in both black holes. Then right when they merge, if you have two singularities, then which way is an observer inside between the two singularities allowed to travel? If he travels towards one singularity, then he will be traveling away from the other, which is forbidden. So the only way to simultaneously move toward both, is to move perpendicularly towards the line connecting the two singularities. So it would seem that effectively, what you have is a "line singularity" connecting the original two singularities that is created once the two event horizons touch. As the black hole settles to a static spherical (Schwarzschild) black hole, the line shrinks (and maybe spins?) down to a point.

All this assumes of course that the metric is the same outside and inside a black hole, which no one knows. I tend to think that prediction of a singularity, is a sign that the metric is not valid inside. I hope this helps. Good question though.

 

[PeterDonis]

during the time before the merger each BH has a singularity, right?

No. Remember what I said: the singularity ("the", only one) is a moment of time. It is not a place in space. So thinking of it as "inside" the black hole, or of one being inside each hole before they merge, is wrong; it's like asking if next Tuesday is inside the Earth. The singularity is in the future for any event inside the black hole region of spacetime; there is only one such region, the trousers, and the singularity, as I said, is at the top of the trousers.

in what manner do two singularities become one?

No such thing happens. See above.

 

[PeterDonis]

Before the black holes merge, the math says an observer inside one of the holes, cannot move in the outward radial direction, only towards the singularity.

That's not quite what the math says, because your statement implies that "the outward radial direction" and "towards the singularity" are opposite directions. They're not. The singularity is in the future; it's a moment of time, not a place in space.

according to the math the radial dimension and the time dimension flip once you cross the event horizon.

This is an artifact of a particular set of coordinates and is not telling you anything physical. See my series of Insights articles on the Schwarzschild geometry (the link is to the first of four):

https://www.physicsforums.com/insights/schwarzschild-geometry-part-1/

This series clears up many common misconceptions, of which your statement is one.

right when they merge, if you have two singularities

You don't. There is only one singularity in this scenario. Please see my responses to @DarkMattrHole .

I tend to think that prediction of a singularity, is a sign that the metric is not valid inside.

More precisely, it's a sign, at least to many physicists, that the Schwarzschild metric, and more generally the treatment of spacetime in GR as a continuum with a single well-defined geometry, stops being valid close enough to the singularity (which might still be well inside the black hole horizon), and quantum gravity becomes the relevant physics in that regime. We don't have a good theory of quantum gravity, so we have no way of knowing at this point.

 

[DarkMattrHole]

Thanks GalileosTelescope, PeterDonis.

PeterDonis, thanks for the clarifications, i'll look for the trousers analogy, thanks. So I'm still on track, prior to merging with the other another, each BH does have a singularity though, right?, each has an end of time, before they merge? Each singularity is not a place, but each is an end of time, correct?

 

[PeterDonis]

each BH does have a singularity though, right?

I have already answered this question (with "no") several times now.

each has an end of time, before they merge?

No. Read what I said about the trousers, and where the singularity is in the "trousers" picture, again.

 

[kent davidge]

I'd just like to add that...

This is because according to the math the radial dimension and the time dimension flip once you cross the event horizon

I don't think that this is the reason that a massive particle falls towards r = 0 because this is just a coordinate system dependent explanation. I think the real reason is the popular one, that one needs "imaginary" or "more than infinite" acceleration to even be at rest once inside the hole, which besides being shown to you by the math, is a physical explanation and thus "free" of coordinate systems.

 

[PeterDonis]

I think the real reason is the popular one, that one needs "imaginary" or "more than infinite" acceleration to even be at rest once inside the hole

This isn't really a good reason either, since it doesn't explain why "not being able to be at rest" requires one to move towards the singularity. (Nor does it explain why one needs "imaginary" or "more than infinite" acceleration to be at rest.)

The correct explanation is the statement I have made several times now in this thread, that the singularity is in the future of any event inside the hole's horizon. You can no more avoid moving towards it than you can avoid moving towards tomorrow.

 

[kent davidge]

the singularity is in the future of any event inside the hole's horizon

But wouldn't this amount to just what @GalileosTelescope said, with the difference that you stated it in a coordinate independent way?

 

[GalileosTelescope]

I suppose I wasn't clear enough. Yes the schwarzchild radial direction becomes a time coordinate, in the sense that it gets the negative sign in the spacetime interval. So like many have said, falling towards the singularity is a time location in that sense. But ultimately what the original question was asking (as I understand it) is that if each black hole has singularity (call it time or schwarzchild radial coordinate singularity) that everything inside must move towards, what direction is that just as the black holes merge prior to settling down to a static black hole? Which is what my thought experiment was trying to address in a geometric sense. Or maybe I misunderstood the specifics of the question...

 

[DarkMattrHole]

GalileosTelescope, thanks for the help and descriptions. That is what i was asking about. It's definitely an interesting instant in time.

 

[PeterDonis]

wouldn't this amount to just what @GalileosTelescope said

No.

 

[PeterDonis]

the schwarzchild radial direction becomes a time coordinate

No. There are still spacelike vectors that point in the radial direction.

in the sense that it gets the negative sign in the spacetime interval

Only for one particular choice of coordinates.

falling towards the singularity is a time location in that sense

No. You don't "fall toward" the singularity. The singularity is in the future. Would you say you are "falling toward" tomorrow?

if each black hole has singularity

No. There is only one singularity.

Please do not post again until you have actually read what I actually wrote. You keep repeating the same misstatement even after I have corrected it.

what direction is that just as the black holes merge prior to settling down to a static black hole?

The singularity (the only one) is always in the future of any event inside the (there is only one of these too) horizon. You need to stop and take a while and think very carefully about what that means. Read my previous posts in the thread again, particularly the ones about the "pair of trousers" and where the singularity is in that analogy.

 

[PeterDonis]

thanks for the help and descriptions

You shouldn't be thanking him since pretty much all of what he said was wrong.

 

[Nugatory]

to even be at rest once inside the hole,

And what does “at rest” mean in this context? “Not moving” just invites the “relative to what?” question, and the difficulty answering that is a hint as to how little you can trust your intuition inside the horizon.

 

[GalileosTelescope]

No. There are still spacelike vectors that point in the radial direction.
Only for one particular choice of coordinates.
No. You don't "fall toward" the singularity. The singularity is in the future. Would you say you are "falling toward" tomorrow?
No. There is only one singularity.

Please do not post again until you have actually read what I actually wrote. You keep repeating the same misstatement even after I have corrected it.
The singularity (the only one) is always in the future of any event inside the (there is only one of these too) horizon. You need to stop and take a while and think very carefully about what that means. Read my previous posts in the thread again, particularly the ones about the "pair of trousers" and where the singularity is in that analogy.

While I admit I was maybe a bit too loose with my language, I think your disagreement with me is mostly a matter of linguistic preferences and semantics.

I think I would say I'm falling towards tomorrow. It's got a nice poetic ring to it. I'm certainly not falling towards yesterday.

How can I "keep repeating" something when I had only posted twice? At best I could have repeated it only once.

Anyway, you got unnecessarily hostile pretty fast... so I have lost interest in this thread.

 

[PeterDonis]

I think your disagreement with me is mostly a matter of linguistic preferences and semantics.

No, it's mostly a matter of you making incorrect statements and me correcting them.

I think I would say I'm falling towards tomorrow. It's got a nice poetic ring to it.

Physics is not poetry. "Falling" implies that there is a "down" direction, distinguished from other spatial directions. That's not the case inside a black hole.

How can I "keep repeating" something when I had only posted twice?

And in both posts you made the same incorrect statement that I had already corrected before your first post, in response to someone else.

you got unnecessarily hostile pretty fast

Correcting incorrect statements is not hostility.

Also bear in mind that you did not start this thread. You are responding to other people's posts. You haven't asked any questions, so the only purpose your responses could serve is to help other people understand something better. That purpose is not served if you post incorrect statements. It's particularly not served if you post incorrect statements that were already made by someone else before you started posting, and which had already been corrected before you started posting.

 

[PAllen]

I'll add to @PeterDonis excellent points, the following:

Shcwarzschild coordinates inside the horizon are completely disconnected from those outside. In differential geometry terms, they are disconnected coordinate patches. There is no switching of anything at the horizon, because the horizon is not covered by either coordinate patch. For Schwarzschild interior coordinates, it makes sense to relabel the coordinate usually presented as 't' to be 'z' since it is the axial coordinate of a hypercylinder (S2XR). It also makes sense to relabel "r" as "-t" since decreasing r represents a future timelike direction. But, again, nothing has switched - it is just that the standard letters used for interior Shwarzschild coordinates are misleading.

 

[Tomas Vencl]

……..
Basically, the simulations say that an observer falling in during the merge process would see increasingly chaotic oscillations in the spacetime curvature, ……..

If the observer waits a long time after the merger before falling in, he would observe much more gentle oscillations in spacetime curvature, since the hole would have had time to "settle down" in its interior. ….

Shcwarzschild coordinates inside the horizon are completely disconnected from those outside. In differential geometry terms, they are disconnected coordinate patches. There is no switching of anything at the horizon, because the horizon is not covered by either coordinate patch. For Schwarzschild interior coordinates, it makes sense to relabel the coordinate usually presented as 't' to be 'z' since it is the axial coordinate of a hypercylinder (S2XR). It also makes sense to relabel "r" as "-t" since decreasing r represents a future timelike direction. But, again, nothing has switched - it is just that the standard letters used for interior Shwarzschild coordinates are misleading.

What if the observer jumps into BH a long time before merge process ? In what singularity he ends ? The merged one, as "there is only one singularity" ? does he see the merge process ?

Is not strange (in the sense of writed above), that "long time after the merger" for external observer also means long time after the merge for black hole internal spacetime (as "the hole would have had time to "settle down" in its interior") ?
Does it mean, that at least time coordinates of exterior and interior of BH are somehow transformable ?

 

[Ibix]

Does it mean, that at least time coordinates of exterior and interior of BH are somehow transformable ?

You can create coordinates that work through the event horizon, yes. Painleve, Eddington-Finkelstein and Kruskal-Szekeres coordinates all work fine (for isolated black holes anyway - as Peter points out we don't have a closed form solution for merging black holes). It's just Schwarzschild coordinates that are discontinuous over the horizon.

 

[Tomas Vencl]

You can create coordinates that work through the event horizon, yes. Painleve, Eddington-Finkelstein and Kruskal-Szekeres coordinates all work fine (for isolated black holes anyway - as Peter points out we don't have a closed form solution for merging black holes). It's just Schwarzschild coordinates that are discontinuous over the horizon.

Yes, I know. But It seems that we can (which should not be correct) also connect time of exterior Schwarzschild coordinate with time (or z coordinate) of interior Schwarzschild coordinate through merging process. Time of merging we can describe in exterior Schw.coo. Can we do this also in interior Schw. coordinates ?
Yes, maybe the point is (as you both said) that the Schwarzschild (static eternal) solution is not valid for merging process.

 

[PeterDonis]

In what singularity he ends ?

There is only one singularity, so obviously there is only one singularity he can end on.

Why do people keep failing to read what I have written multiple times now?

does he see the merge process ?

He will see incoming light rays that could in principle tell him about the merge process, yes.

Is not strange (in the sense of writed above), that "long time after the merger" for external observer also means long time after the merge for black hole internal spacetime

No, it's not strange because it's not true.

(as "the hole would have had time to "settle down" in its interior") ?

Careful. I did not say it took a long time by the clock of someone in the interior of the hole for the hole's interior to settle down. I only said that if an observer outside the hole waited a long time by his clock before falling in, he would see the interior settled down.

In fact, it's not even meaningful to ask how long it takes by the clock of an observer inside the hole for the hole's interior to settle down after a merger, because there is no way for an observer inside the hole to sit "at the same point in space" and watch the settling down process and measure how long it takes.

 

[Vanadium 50]

Why do people keep failing to read what I have written multiple times now?

They read it. They just don't believe it.

Somewhere - probably from popularizations - people get the idea that "singularlity" means "tiny superhard superheavy marble in the middle of the otherwise empty black hole region". And who is some random guy on the internet to say otherwise?

 

[Tomas Vencl]

There is only one singularity, so obviously there is only one singularity he can end on.
Why do people keep failing to read what I have written multiple times now?

It is quite simple. Because most people imagine singularity of black hole by popular pictures (it is also in Kip Thornes books and many others.)

In case of merging it seems that 2 of those pictures connects together to form a trousers shape. In those pictures singularities are lines (connected). And it is not obvious that it is only one.
Can you pleale show a picture how the merging of 2 BH looks in Kruskal-Szekeres spacetime diagram, which is proobably what you mean with trousers and singularity at the top ?

He will see incoming light rays that could in principle tell him about the merge process, yes.

OK it makes sense.

Careful. I did not say it took a long time by the clock of someone in the interior of the hole for the hole's interior to settle down. I only said that if an observer outside the hole waited a long time by his clock before falling in, he would see the interior settled down.

Sorry, I do not see a difference yet. Actually I see the first follow from second. If hole interior settle down it must do so at some specific spacetime point (it is an event). Another event is to settle down even more. What interval is between those events? (inside probably spacelike, but still it can be measured or calculated at least, no?)

In fact, it's not even meaningful to ask how long it takes by the clock of an observer inside the hole for the hole's interior to settle down after a merger, because there is no way for an observer inside the hole to sit "at the same point in space" and watch the settling down process and measure how long it takes.

Yes this may be answer. I will think about it. Really helpfull would be this spacetime diagram of merging black holes. Thanks.

 

[PeterDonis]

most people imagine singularity of black hole by popular pictures

Yes, but you're not looking at popular pictures in this thread. You're reading my posts. Or you're supposed to be. And if I say something that seems to be inconsistent with the popular pictures (such as that there is only one singularity in the scenario under discussion), particularly if I say it with such high confidence, you need to not just keep repeating what the popular pictures say, which is what several people in this thread have done. You need to ask me why I am saying something that seems to be inconsistent with the popular pictures you've seen.

Also, popular pictures are not valid sources and you shouldn't be trying to learn the actual science from them anyway. See below.

In case of merging it seems that 2 of those pictures connects together to form a trousers shape. In those pictures singularities are lines (connected). And it is not obvious that it is only one.

Note carefully that Kip Thorne did not draw a picture of a black hole merger such as you describe. He only drew a picture of one black hole in the form you show (even though he discusses black hole mergers in his book, assuming that you are referring to Black Holes and Time Warps, which is where I remember seeing the picture you refer to). There's a reason for that--if he had drawn a picture of a merger of two black holes as you describe, with a trousers shape and singularity lines inside each leg of the trousers, it would have been wrong. You cannot model a merger of two black holes using the same mathematical machinery that lies behind the picture of one black hole that Thorne drew in the book you refer to. It doesn't work.

So the mental picture of trousers with two singularity lines inside each leg, that then merge into one singularity line in the upper part, does not come from "popular pictures". It comes from you incorrectly taking a popular picture and doing something with it that the underlying math and physics does not justify. This illustrates why you can't learn science from popular pictures: you don't know how those pictures relate to the actual physics, or what the limitations of the pictures are, or in what ways they can or cannot be extended to other scenarios besides the specific one shown in the picture. The person who drew the pictures knows that, but he can't possibly distill all his underlying knowledge of the physics into a popular book, or tell you about all the things you cannot do with the pictures he draws. You simply have to accept that you cannot learn science from popular pictures.

Can you pleale show a picture how the merging of 2 BH looks in Kruskal-Szekeres spacetime diagram

No, because a Kruskal-Szekeres spacetime diagram only works for a single black hole. It doesn't work for a merger of two black holes.

which is proobably what you mean with trousers and singularity at the top ?

Not really, no. I purposely was very vague about how the inside of the "trousers" works geometrically, except for the simple statement that the singularity is at the top (which must be the case since the singularity is to the future of every event inside the horizon). That's because, as I said, we don't have a closed form solution for this case, we only have numerical simulations, so we don't have a good way to draw a diagram the way we can draw various diagrams of a single black hole, such as a Kruskal diagram, or an Eddington-Finkelstein diagram (which is the basis for the picture of the single black hole in Thorne's book that you referred to). The best we can do is to generally describe the shape of the horizon as it would seem to observers outside the merger (which is what the "trousers" shape describes, heuristically) and to infer how the singularity has to be placed relative to the inside of the trousers from the fact that it is to the future of all events inside the horizon.

 

[PeterDonis]

an Eddington-Finkelstein diagram (which is the basis for the picture of the single black hole in Thorne's book that you referred to)

It might be worth expanding on this some. Take a look at the diagram shown in the Wikipedia entry on Eddington-Finkelstein coordinates:

https://en.wikipedia.org/wiki/Eddington–Finkelstein_coordinates#Metric

The picture Thorne put in his book is basically a representation of this same diagram, with one angular coordinate put back (so each point in the diagram corresponds to a circle in Thorne's picture--in particular, the line going straight up in the diagram that marks the horizon corresponds to the cylinder in Thorne's picture that marks the horizon).

It's natural to think of the "up" direction in the diagram as pointing towards the future, i.e., in the future timelike direction; but that is only true outside the horizon. The horizon itself is null, yet it goes straight up in the diagram. And inside the horizon, straight up in the diagram is a spacelike direction! So the singularity line at the left of the diagram (which corresponds to the singularity line at the center of the cylinder in Thorne's picture) is a spacelike line, not a timelike one; it represents a moment in time, not a place in space.

Now consider two black holes merging, where the horizon now has the "pair of trousers" shape I described. The problem now is, if each leg of the trousers has a "singularity" line in the center, as in Thorne's diagram, that line has to be spacelike (since the singularity is). But the two lines would also have to merge into one in the upper part of the trousers, and the one line would have to keep on going up, so the merged hole looks like the single hole in Thorne's picture. But that's not possible; spacelike lines can't work that way. You can't have two moments of time that merge into one, but that's what two spacelike lines merging into one would describe.

 

[PeterDonis]

If hole interior settle down it must do so at some specific spacetime point (it is an event). Another event is to settle down even more.

More precisely, the "settling down" is a process that occupies a particular region of spacetime.

What interval is between those events?

Undefined, because, as above, it's a region of spacetime that's involved, and there will be pairs of events within that region that have all three possible relationships to each other: timelike, null, and spacelike.

In the "trousers" picture, heuristically, the "settling down" process occupies a region that starts on each leg a little below where they meet, makes the horizon wiggle from that point on each leg up to a little above where the legs meet on the upper part of the trousers, and then quickly narrows down towards the center of the upper part of the trousers, ending on a narrow part of the singularity at the top (this corresponds to the fluctuations in spacetime curvature caused by the merger--the ones that aren't emitted as gravitational waves--falling into the singularity). So someone who falls in well after the merger will not be able to "catch up" with the narrowing "settling down" region; that person will hit the singularity first (somewhere outside the narrow region where the "settling down" region hits it).

 

[Tomas Vencl]

Yes, but you're not looking ..... You simply have to accept that you cannot learn science from popular pictures.

Agree.

No, because a Kruskal-Szekeres spacetime diagram only works for a single black hole. It doesn't work for a merger of two black holes.

Not really, no. I purposely was very vague about how the inside of the "trousers" works geometrically, except for the simple statement that the singularity is at the top (which must be the case since the singularity is to the future of every event inside the horizon). That's because, as I said, we don't have a closed form solution for this case, we only have numerical simulations, so we don't have a good way to draw a diagram the way we can draw various diagrams of a single black hole, such as a Kruskal diagram, or an Eddington-Finkelstein diagram (which is the basis for the picture of the single black hole in Thorne's book that you referred to). The best we can do is to generally describe the shape of the horizon as it would seem to observers outside the merger (which is what the "trousers" shape describes, heuristically) and to infer how the singularity has to be placed relative to the inside of the trousers from the fact that it is to the future of all events inside the horizon.

I am disappointed a little. I understand that we don't have final solution. But I though that we can transform our general idea how merging process looks like into some general shape diagram (it can have more dimensions).

 

[PeterDonis]

I though that we can transform our general idea how merging process looks like into some general shape diagram (it can have more dimensions).

We can for the region at and outside the horizon; that's what the "pair of trousers" picture is conveying (in a very oversimplified way--a more realistic picture would have the legs of the trousers twisting around each other, to reflect the fact that black hole mergers usually involve two holes in orbits spiraling inward about each other, not just falling straight in).

The region inside the horizon is the problem; we don't have a good way of picturing that (beyond "inside the trousers"), unfortunately.

 

[Tomas Vencl]

It might be worth expanding on this some. Take a look at the diagram shown in the Wikipedia entry on Eddington-Finkelstein coordinates:

https://en.wikipedia.org/wiki/Eddington–Finkelstein_coordinates#Metric

The picture Thorne put in his book is basically a representation of this same diagram, with one angular coordinate put back (so each point in the diagram corresponds to a circle in Thorne's picture--in particular, the line going straight up in the diagram that marks the horizon corresponds to the cylinder in Thorne's picture that marks the horizon).

It's natural to think of the "up" direction in the diagram as pointing towards the future, i.e., in the future timelike direction; but that is only true outside the horizon. The horizon itself is null, yet it goes straight up in the diagram. And inside the horizon, straight up in the diagram is a spacelike direction! So the singularity line at the left of the diagram (which corresponds to the singularity line at the center of the cylinder in Thorne's picture) is a spacelike line, not a timelike one; it represents a moment in time, not a place in space.

This is clear

Now consider two black holes merging, where the horizon now has the "pair of trousers" shape I described. The problem now is, if each leg of the trousers has a "singularity" line in the center, as in Thorne's diagram, that line has to be spacelike (since the singularity is). But the two lines would also have to merge into one in the upper part of the trousers, and the one line would have to keep on going up, so the merged hole looks like the single hole in Thorne's picture. But that's not possible; spacelike lines can't work that way. You can't have two moments of time that merge into one, but that's what two spacelike lines merging into one would describe.

This is interesting, Thank you, I will think about it. (Maybe this tell us something important about contradiction of idea of BH interior and merging (or forming) BH process. But this not belong to this fofum, sorry.)

 

[Tomas Vencl]

More precisely, the "settling down" is a process that occupies a particular region of spacetime.

OK,yes

Undefined, because, as above, it's a region of spacetime that's involved, and there will be pairs of events within that region that have all three possible relationships to each other: timelike, null, and spacelike.

very interesting,will think...

In the "trousers" picture, heuristically, the "settling down" process occupies a region that starts on each leg a little below where they meet, makes the horizon wiggle from that point on each leg up to a little above where the legs meet on the upper part of the trousers, and then quickly narrows down towards the center of the upper part of the trousers, ending on a narrow part of the singularity at the top (this corresponds to the fluctuations in spacetime curvature caused by the merger--the ones that aren't emitted as gravitational waves--falling into the singularity). So someone who falls in well after the merger will not be able to "catch up" with the narrowing "settling down" region; that person will hit the singularity first (somewhere outside the narrow region where the "settling down" region hits it).

So, this is almost picture

 

[PeterDonis]

this is almost picture

It's the best I can do at describing what I understand the numerical simulations to be saying, without making any commitments about the details of the geometry inside the "trousers". Note, in particular, that, while in general the "up" direction in what I've described is the future direction of time, the distortion involved has to be extreme in some parts of the picture.

 

[Tomas Vencl]

It's the best I can do at describing what I understand the numerical simulations to be saying, without making any commitments about the details of the geometry inside the "trousers". Note, in particular, that, while in general the "up" direction in what I've described is the future direction of time, the distortion involved has to be extreme in some parts of the picture.

OK, thank you Peter for interesting discussion.

 

[DarkMattrHole]

Thanks all. I've looked at a number of trousers diagrams now and will dig deeper. The impression I'm getting from this discussion is that there is essentially nothing inside the horizon at all to an outside observer, not even space, space is not part of the inside of a BH, the horizon is a barrier (from outside view) - like an edge in space, but an edge that recedes as you approach it, and any time that is ticking and marking off change, must be taking place in material at or outside the horizon where spacer exists for things to happen or stop happening. How close is that? Also that lower dimensional drawings of BHs, with central singularity indicated are depicting an end to all futures, not a place, and there's no good way to draw a diagram of two BHs merging the way we can draw various diagrams of a single black hole. Things sure get interesting when all four dimensions including time get into play.

I found an interesting trousers model (trousers with pantaloons) here..
..."suggests a possibility of proving the Penrose inequality mathematically for generic astrophysical binary back hole configurations."
https://www.aei.mpg.de/2420822/what-happens-inside-a-black-hole-merger

 

[PeterDonis]

The impression I'm getting from this discussion is that there is essentially nothing inside the horizon at all to an outside observer, not even space

The fact that the outside observer cannot see inside the horizon does not mean the outside observer thinks there is nothing there.

space is not part of the inside of a BH

This is not correct. Spacetime is still 4-dimensional inside the horizon, and at every event one can still find an orthonormal tetrad of one timelike vector and three spacelike vectors, so one can still split spacetime into "space" and "time" locally. The global behavior is what is highly counterintuitive.

the horizon is a barrier (from outside view)

No, it isn't. It's perfectly possible to fall inside the horizon. You just can't get back out again once you're inside.

like an edge in space, but an edge that recedes as you approach it

I don't know where you are getting all this from, but it's wrong.

any time that is ticking and marking off change, must be taking place in material at or outside the horizon where spacer exists for things to happen or stop happening

This is wrong. Time ticks perfectly normally for an observer falling through the horizon and on inside the hole.

lower dimensional drawings of BHs, with central singularity indicated are depicting an end to all futures, not a place

Yes.

there's no good way to draw a diagram of two BHs merging the way we can draw various diagrams of a single black hole

Yes. To put it another way, even the minimum amount of distortion you can have in a diagram of a BH merger is far more distortion than you need to have in a diagram of a single BH.

 

[PeterDonis]

I found an interesting trousers model (trousers with pantaloons) here

Note that what this paper is calling a "horizon" is not precisely the same as what we have been calling a "horizon" in this thread. We have been using the term "horizon" to mean the event horizon--the boundary of the region in spacetime that cannot send light signals to infinity. When I say there is only one horizon, shaped (heuristically) like a pair of trousers, it is the event horizon I mean.

This paper is using the term "horizon" to mean "Marginally Outer Trapped Surface" (or MOTS), which is also referred to as an "apparent horizon". Heuristically, it is a surface at which a spherical radially outgoing wave front of light does not increase in area. In a stationary black hole (i.e., an idealized black hole that isn't merging with another one, and isn't absorbing any matter, and isn't evaporating), the apparent horizon coincides with the event horizon; but in any dynamic situation, like a merger, or a black hole with matter falling into it, or an evaporating black hole (when we take quantum effects into account), the two kinds of horizon no longer coincide. In the case of a merger, the event horizon will in general be outside of any apparent horizons.

The other key difference with apparent horizons is that there can be more than one of them, and they can even overlap and self-intersect, as the paper describes. So you can't really view them as a single "boundary" of a black hole, the way you can view the event horizon. But they are useful in trying to picture what goes on inside the horizon as the merger proceeds and the final hole settles down.