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It is not about three black holes colliding at the same moment, but about a three massive black holes in three colliding galaxies that one day, in the far futur

It is not about three black holes colliding at the same moment, but about a three massive black holes in three colliding galaxies that one day, in the far future, probably will collide and about a possible effect that two black holes at a close distance might come together sooner in the presence of a third black hole in the vicinity. So, not even discussing the possibility that they may merge at the same moment.

pmiller2 6y ago
> ...at the same moment. As an aside, this is a rather funny phrase to be using about objects so massive that time and space actually switch roles inside their event horizons compared to the normal universe. I don't feel like I can explain it very well, but here is a video that does so: https://www.youtube.com/watch?v=KePNhUJ2reI https://www.youtube.com/watch?v=KePNhUJ2reI (Skip to about 5:15 for the good stuff.)
- pdonis 6y ago
  > time and space actually switch roles inside their event horizons No, they don't. This is a common misconception based on a mathematical artifact of one particular coordinate system. > here is a video that does so This video is actually quite misleading, because in the diagram it shows of a black hole at around 7 minutes ish, it is using coordinates in which the artifact I mentioned above does not occur, but then mislabels the coordinates in the part of the diagram inside the horizon to make it seem as if it does.
  - pmiller2 6y ago
    My understanding of the explanation and the video was that they don't literally switch roles, in the sense that you could then travel backward in time, or couldn't alter your position with respect to the singularity. It's more that, in terms of light cones, inside the event horizon, you can move in space in such a way encountering photons from the past, which is somewhat like travelling back in time. So, in a sense, the "arrow of time" doesn't work inside the black hole. But, since all world lines do eventually end at the singularity, which basically means that no matter what you do, you're always moving toward it, space becomes time-like in the sense that there's then an "arrow of space," analogous to the "arrow of time." I found the mathematical explanation of sign flipping to be fairly easy to understand. One thing in particular that equation makes clear is that at the instant you cross the event horizon, whatever metric you're using is going to become degenerate. That makes some sense, because you're literally crossing over into a different realm there, but, it doesn't seem physical to me, unless it's not actually physically possible for matter to literally fall into a black hole; rather that matter we perceive as falling into it gets smeared out across the event horizon, its information being "painted on" to the event horizon. (This reminds me of the "black hole information paradox," but I'm not sure exactly how it all plays into it. For small enough holes and small enough particles, I would guess there is some interaction between the particle approaching the event horizon and Hawking radiation pushing back on it, kind of like solar wind does. But, that's pure speculation.) Physically, the thing that made the most sense to me was that of the 4 spacetime dimensions, outside of a black hole, the one we have designated as "time" is so designated because it doesn't behave like the other 3, because we can only travel in one direction along it. Inside the event horizon, it's clear that one spatial dimension corresponding to the vector extending outward from the singularity to your position acquires this property. Because they only did the example of a Schwartzchild black hole, I'm sure this all goes out the window in case of a rotating black hole, in which you no longer have a point singularity, but a ring singularity [0]. Since I have never specifically studied GR, all my actual black hole knowledge comes from intuition derived from a differential topology course. But, that intuition is telling me that something similar happens in this general case, except that space never actually becomes time-like. World lines do all still end at some point on the singularity, and you can still get weirdness encountering photons you might think you couldn't, so, my physics layman's intuition is telling me what you have is basically all 4 dimensions acquiring a similar character. That is, spatial dimensions start becoming somewhat time-like, and time starts becoming somewhat space-like. Differential topology gave me a really crude understanding of what goes on here, but, I do understand that black holes are fundamentally simple objects. They only have three properties: mass, charge, and angular momentum; so, you should be able to describe them fully from any reference frame outside the event horizon using those 3 variables plus the spatiotemporal location of the hole. At that point, if you have a universe with nothing in it but your one, lonely black hole, you have a static universe. If you introduce matter, you could theoretically model interactions between all the particles of matter in your toy universe, and the black hole. If you constrain the number of particles enough, you should be able to at least approximate how this idealized universe evolves. Is this a fair interpretation, or am I way off base?
    - pdonis 6y ago
      > It's more that, in terms of light cones, inside the event horizon, you can move in space in such a way encountering photons from the past I'm not sure what you mean by "photons from the past". You can't "move in space" inside the horizon in any way that's fundamentally different from what you can do outside the horizon. And any photons you encounter will, by definition, come from somewhere in the past light cone of the event where you encounter them; that's equally true inside and outside the horizon. > since all world lines do eventually end at the singularity, which basically means that no matter what you do, you're always moving toward it, space becomes time-like No. The singularity itself is not a place in space; it's a moment of time, which is in the future of every event inside the horizon. That is the best, coordinate-independent way of describing what happens inside the horizon: inside the horizon, your future is now limited in duration by the presence of the singularity, a moment of time that marks the end of your future. There is no such moment of time outside the horizon. It has nothing to do with "space" or "space and time switching" at all. It's simply a future limitation on time. > the mathematical explanation of sign flipping Is only true in one particular set of coordinates. As such, it cannot describe anything physically real. That is a general rule in GR: if it's something you can make go away by switching coordinates, it isn't physically real. > at the instant you cross the event horizon, whatever metric you're using is going to become degenerate No. The metric used to draw the diagrams around minute 7 ish in the video is not degenerate anywhere, including on the horizon. The coordinate-independent, physical thing that picks out the horizon is that radially outgoing light rays have zero expansion--that is, a 2-sphere of radially outgoing light rays at the horizon does not increase in area. In fact, the horizon can be said to be a 2-sphere of radially outgoing light rays with constant area. > of the 4 spacetime dimensions, outside of a black hole, the one we have designated as "time" is so designated because it doesn't behave like the other 3, because we can only travel in one direction along it This isn't a property of a "dimension", it's a property of particular curves in spacetime that observers can follow: such curves are called "timelike" to acknowledge this property. The overall property of spacetime that is related to it is that which direction along timelike curves is the "future" direction must be continuous everywhere--i.e., if you continuously move from one timelike curve to another, the "future" direction stays the same everywhere, it never switches. > Inside the event horizon, it's clear that one spatial dimension corresponding to the vector extending outward from the singularity to your position acquires this property. No, it doesn't. Spacelike and timelike vectors and their properties are the same inside the horizon as outside, and the direction towards the singularity that has the property you describe is still the timelike one. It is true that, at any event inside the horizon, there will be spacelike as well as timelike curves that connect that event to the singularity, but that is also true outside the horizon for any moment of time to the future of a given event (since a "moment of time" outside the horizon is a spacelike 3-surface extending through the entire universe, and there will be points on any such 3-surface that are spacelike separated from any chosen event to the past of the surface). > I'm sure this all goes out the window in case of a rotating black hole Some of it does, but some of it is still applicable. You are correct that the singularity in Kerr spacetime is a ring, and it is also timelike, not spacelike, so it can be correctly described as a ring "in space" that "stays at the same place" as time progresses. However, the ring singularity is inside an inner horizon, and it is impossible to reach the ring singularity without passing through the inner horizon; and from the viewpoint of an observer between the horizons (inside the outer horizon/event horizon, and outside the inner horizon), the inner horizon has some of the same properties as the singularity in Schwarzschild spacetime does, including the key property that it's impossible to avoid it once you're inside the outer horizon--it's unavoidably in your future. > Is this a fair interpretation, or am I way off base? I think you are illustrating why I said the video is highly misleading. You are taking some reasonably valid intuitions from differential topology, but combining them with things the video is saying is leading you to incorrect conclusions.

pmiller2 6y ago

> ...at the same moment. As an aside, this is a rather funny phrase to be using about objects so massive that time and space actually switch roles inside their event horizons compared to the normal universe. I don't feel like I can explain it very well, but here is a video that does so: https://www.youtube.com/watch?v=KePNhUJ2reI https://www.youtube.com/watch?v=KePNhUJ2reI (Skip to about 5:15 for the good stuff.)

pdonis 6y ago
> time and space actually switch roles inside their event horizons No, they don't. This is a common misconception based on a mathematical artifact of one particular coordinate system. > here is a video that does so This video is actually quite misleading, because in the diagram it shows of a black hole at around 7 minutes ish, it is using coordinates in which the artifact I mentioned above does not occur, but then mislabels the coordinates in the part of the diagram inside the horizon to make it seem as if it does.
- pmiller2 6y ago
  My understanding of the explanation and the video was that they don't literally switch roles, in the sense that you could then travel backward in time, or couldn't alter your position with respect to the singularity. It's more that, in terms of light cones, inside the event horizon, you can move in space in such a way encountering photons from the past, which is somewhat like travelling back in time. So, in a sense, the "arrow of time" doesn't work inside the black hole. But, since all world lines do eventually end at the singularity, which basically means that no matter what you do, you're always moving toward it, space becomes time-like in the sense that there's then an "arrow of space," analogous to the "arrow of time." I found the mathematical explanation of sign flipping to be fairly easy to understand. One thing in particular that equation makes clear is that at the instant you cross the event horizon, whatever metric you're using is going to become degenerate. That makes some sense, because you're literally crossing over into a different realm there, but, it doesn't seem physical to me, unless it's not actually physically possible for matter to literally fall into a black hole; rather that matter we perceive as falling into it gets smeared out across the event horizon, its information being "painted on" to the event horizon. (This reminds me of the "black hole information paradox," but I'm not sure exactly how it all plays into it. For small enough holes and small enough particles, I would guess there is some interaction between the particle approaching the event horizon and Hawking radiation pushing back on it, kind of like solar wind does. But, that's pure speculation.) Physically, the thing that made the most sense to me was that of the 4 spacetime dimensions, outside of a black hole, the one we have designated as "time" is so designated because it doesn't behave like the other 3, because we can only travel in one direction along it. Inside the event horizon, it's clear that one spatial dimension corresponding to the vector extending outward from the singularity to your position acquires this property. Because they only did the example of a Schwartzchild black hole, I'm sure this all goes out the window in case of a rotating black hole, in which you no longer have a point singularity, but a ring singularity [0]. Since I have never specifically studied GR, all my actual black hole knowledge comes from intuition derived from a differential topology course. But, that intuition is telling me that something similar happens in this general case, except that space never actually becomes time-like. World lines do all still end at some point on the singularity, and you can still get weirdness encountering photons you might think you couldn't, so, my physics layman's intuition is telling me what you have is basically all 4 dimensions acquiring a similar character. That is, spatial dimensions start becoming somewhat time-like, and time starts becoming somewhat space-like. Differential topology gave me a really crude understanding of what goes on here, but, I do understand that black holes are fundamentally simple objects. They only have three properties: mass, charge, and angular momentum; so, you should be able to describe them fully from any reference frame outside the event horizon using those 3 variables plus the spatiotemporal location of the hole. At that point, if you have a universe with nothing in it but your one, lonely black hole, you have a static universe. If you introduce matter, you could theoretically model interactions between all the particles of matter in your toy universe, and the black hole. If you constrain the number of particles enough, you should be able to at least approximate how this idealized universe evolves. Is this a fair interpretation, or am I way off base?
  - pdonis 6y ago
    > It's more that, in terms of light cones, inside the event horizon, you can move in space in such a way encountering photons from the past I'm not sure what you mean by "photons from the past". You can't "move in space" inside the horizon in any way that's fundamentally different from what you can do outside the horizon. And any photons you encounter will, by definition, come from somewhere in the past light cone of the event where you encounter them; that's equally true inside and outside the horizon. > since all world lines do eventually end at the singularity, which basically means that no matter what you do, you're always moving toward it, space becomes time-like No. The singularity itself is not a place in space; it's a moment of time, which is in the future of every event inside the horizon. That is the best, coordinate-independent way of describing what happens inside the horizon: inside the horizon, your future is now limited in duration by the presence of the singularity, a moment of time that marks the end of your future. There is no such moment of time outside the horizon. It has nothing to do with "space" or "space and time switching" at all. It's simply a future limitation on time. > the mathematical explanation of sign flipping Is only true in one particular set of coordinates. As such, it cannot describe anything physically real. That is a general rule in GR: if it's something you can make go away by switching coordinates, it isn't physically real. > at the instant you cross the event horizon, whatever metric you're using is going to become degenerate No. The metric used to draw the diagrams around minute 7 ish in the video is not degenerate anywhere, including on the horizon. The coordinate-independent, physical thing that picks out the horizon is that radially outgoing light rays have zero expansion--that is, a 2-sphere of radially outgoing light rays at the horizon does not increase in area. In fact, the horizon can be said to be a 2-sphere of radially outgoing light rays with constant area. > of the 4 spacetime dimensions, outside of a black hole, the one we have designated as "time" is so designated because it doesn't behave like the other 3, because we can only travel in one direction along it This isn't a property of a "dimension", it's a property of particular curves in spacetime that observers can follow: such curves are called "timelike" to acknowledge this property. The overall property of spacetime that is related to it is that which direction along timelike curves is the "future" direction must be continuous everywhere--i.e., if you continuously move from one timelike curve to another, the "future" direction stays the same everywhere, it never switches. > Inside the event horizon, it's clear that one spatial dimension corresponding to the vector extending outward from the singularity to your position acquires this property. No, it doesn't. Spacelike and timelike vectors and their properties are the same inside the horizon as outside, and the direction towards the singularity that has the property you describe is still the timelike one. It is true that, at any event inside the horizon, there will be spacelike as well as timelike curves that connect that event to the singularity, but that is also true outside the horizon for any moment of time to the future of a given event (since a "moment of time" outside the horizon is a spacelike 3-surface extending through the entire universe, and there will be points on any such 3-surface that are spacelike separated from any chosen event to the past of the surface). > I'm sure this all goes out the window in case of a rotating black hole Some of it does, but some of it is still applicable. You are correct that the singularity in Kerr spacetime is a ring, and it is also timelike, not spacelike, so it can be correctly described as a ring "in space" that "stays at the same place" as time progresses. However, the ring singularity is inside an inner horizon, and it is impossible to reach the ring singularity without passing through the inner horizon; and from the viewpoint of an observer between the horizons (inside the outer horizon/event horizon, and outside the inner horizon), the inner horizon has some of the same properties as the singularity in Schwarzschild spacetime does, including the key property that it's impossible to avoid it once you're inside the outer horizon--it's unavoidably in your future. > Is this a fair interpretation, or am I way off base? I think you are illustrating why I said the video is highly misleading. You are taking some reasonably valid intuitions from differential topology, but combining them with things the video is saying is leading you to incorrect conclusions.