Mass distribution behavior of the singularities during black hole mergers

  • #1

Summary:

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

Main Question or Discussion Point

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. :smile:
 

Answers and Replies

  • #2
PeterDonis
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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.
 
  • #3
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?
 
  • #4
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 (Schwarzchild) 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.
 
  • #5
PeterDonis
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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.
 
  • #6
PeterDonis
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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.
 
  • #7
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?
 
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  • #8
PeterDonis
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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.
 
  • #9
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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.
 
  • #10
PeterDonis
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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.
 
  • #11
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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?
 
  • #12
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 blackholes 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...
 
  • #13
GalileosTelescope, thanks for the help and descriptions. That is what i was asking about. It's definitely an interesting instant in time.
 
  • #15
PeterDonis
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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 blackholes 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.
 
  • #16
PeterDonis
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thanks for the help and descriptions
You shouldn't be thanking him since pretty much all of what he said was wrong.
 
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  • #17
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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.
 
  • #18
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.
 
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  • #19
PeterDonis
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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.
 
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  • #20
PAllen
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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.
 
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  • #21
……..
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 ?
 
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  • #22
Ibix
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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.
 
  • #23
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.
 
  • #24
PeterDonis
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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.
 
  • #25
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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?
 

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