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I have read this question:

Therefore there is nothing (except things travelling towards the singularity) inside the event horizon of a black hole.

Does anything exist between singularity and the event horizon of a black hole

Now imagine particles moving towards the singularity inside two black holes, that are actually merging. Until the horizons do not overlap, all particles are moving towards the singularity of their own black hole, that is understandable.

Now let's see what happens when the horizons start overlapping. How do particles that are already on the way towards their own singularity, "know" that they need to change course (either towards the other singularity or to a new common one)?

Here is what I do not understand: information inside a black hole can only travel towards the singularity (decreasing r), there is no way for information to travel backwards. Now when the black holes' event horizons start overlapping, naively thinking, the "travel towards the singularity" has to change direction, whatever that direction means, because on this site it is often mentioned that moving towards the singularity is like moving towards tomorrow (so travel in time not space).

Now information can only travel towards a decreasing r, that is equivalently, changes in the gravitational field can only propagate at the speed of light towards a decreasing r. But if that is true, then the particles that are moving towards their own singularity would have to receive information from other regions inside the new common black hole, so that information would need to travel outwards, that is increasing r. But that is not possible, and changes in the gravitational field cannot propagate outwards (increasing r).

So there are two things coming to mind:

  1. particles moving towards their own singularity would need to make a change in direction moving in time as soon as the event horizons start overlapping

  2. to do that, particles would need to receive information (changes in the gravitational field) that is propagating outwards (increasing r) in the new common black hole

Question:

  1. How do particles in merging black holes "know" they need to change direction in time towards a new singularity?
Árpád Szendrei
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  • Possible duplicates: https://physics.stackexchange.com/q/237144/50583, https://physics.stackexchange.com/q/237433/50583 – ACuriousMind Dec 27 '21 at 23:47
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    I'm also unsure why you imagine the particles having to switch suddenly to a "new" singularity. Most processes in physics are smooth, why is the naive picture here not just that the two singularities just get closer to each other and then merge (i.e. the "worldline" of the singularities is a Y-shape)? – ACuriousMind Dec 27 '21 at 23:49
  • @ACuriousMind these are not duplicates, as they do not answer my specific question. I do not state that anything would be suddenly. I am just saying they need to change direction in time. Even if as you say they (two singularities) get closer, information (changes in the gravitational field) have to travel in some situations towards an increasing r (in the new common black hole). My question is about this. – Árpád Szendrei Dec 28 '21 at 00:20
  • @ACuriousMind The Y-shape doesn’t refer to two singularities merging. Note that the drawing by Penrose: https://cdn.sanity.io/images/vgvol637/production/e6df9ab2b236828ad973c45c996177bda1e217aa-1600x1981.jpg - is essentially in the null coordinates showing that the singular region forms only “after” the eternity of time in the coordinates of an external observer. Yet the merger of two black holes (or rather collapsed stars) happens in a finite coordinate time. Thus only the bottom (future) part of the Y-shape refers to a singular region. There are no “merging singularities” in this picture. – safesphere Dec 29 '21 at 06:21
  • @safesphere I understand thank you. Though, I have read on this site somewhere that because black holes form from collapsed stars, some matter has to already be inside the horizon, and I thought those particles move towards the singularity. – Árpád Szendrei Dec 29 '21 at 06:38
  • @safesphere I think I understand, so from our external view, the inside of the black hole is basically frozen (in time)? And since inside the temporal coordinate is the one that we move along towards the future singularity (decreasing r), things inside are not moving towards anything (from our external view)? – Árpád Szendrei Dec 29 '21 at 21:52
  • When you jump out of an airplane, how does your body know which way to fall? If you can tell us what you'd consider a good answer to the airplane question, it will help clarify what you're asking for. – WillO Dec 29 '21 at 23:46
  • @safesphere correct, from an external view all this is correct. I just don't understand, from the falling matter's view. In that (the falling matter itself) view, the singularities did form as far as I understand. So from an infalling matter's frame, the singularities should be there and the matter should move towards (in time) the singularity, then the horizons combine, and the matter should change direction (in time) towards a new common singularity? – Árpád Szendrei Dec 30 '21 at 00:20
  • @WillO there is a distinction between your airplane example, and a black hole. The black hole is an extreme example, where the curvature is so extreme, that no information can propagate outwards (increasing r). The person jumping from an airplane, if the Earth was to collide with another planet while the person is in freefall, the trajectory of the freefall would change. We can simply say, that while the collision happens, the gravitational field changes, and those changes propagate towards the person in freefall. But in the black hole the changes can only propagate to decreasing r. – Árpád Szendrei Dec 30 '21 at 00:24
  • @WillO now when the horizons combine, the changes in the gravitational field should sometimes propagate towards an increasing r (in the new common black hole) towards the infalling matter. That is not possible, because no information can propagate towards increasing r (outwards). How will the infalling matter's trajectory (in time) be changed towards the new common singularity? – Árpád Szendrei Dec 30 '21 at 00:25

1 Answers1

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In General Relativity, gravitation and the structure of spacetime are one and the same. When the two black holes merge, the gravitational field is already encoding the information of "where is the future", and in fact this is precisely why things fall.

You are correct that the "wiggles", so to speak, in the gravitational field take some time to be carried around. For example, when two black holes merge, the information of the merger is carried at the speed of light before it reaches the gravitational wave detectors at Earth. However, if a particle is in a region where the two black holes are touching, then by construction it is in a region of spacetime where this information is already present. Both black holes are distorting spacetime in that direction and their gravity is defining where the future points to.

Intuitively, we can think that the direction of time changed due to the gravitational influence of the new black hole that approached the original system comprised of particle and black hole. As the new black hole comes nearby, it warps spacetime differently and changes the way the particle will move. In terms of the (correct) statement that falling down the singularity is going to the future, the new black hole warps spacetime as to change "where the future is". At sufficiently late times, the black holes will have merged completely and set down to an stationary state, when a single singularity will be present.

Two side comments are in order to avoid misunderstandings:

  1. I should point out that once the two black holes touch we can no longer distinguish them, since the event horizon possesses no local effect. In other words, one can't tell where one black hole starts and the other one ends. To think of two touching black holes as an analogy to get a better understanding of the process can be pedagogical, but it shouldn't be taken too seriously.

  2. As mentioned by safesphere on the comments, we must also recall that an external observer never sees anything falling down the black hole. This includes the star itself. Hence, an external observer will never really see the black hole forming, much less see two singularities merging. As a consequence, an external observer will see the two black holes merging before they see any singularity forming, so they don't really see any singularities merging or anything of the sort. If the observer falls down the black hole, when they finally see a singularity there will already be a single one.

Notice that, in any case, the problem of "how does a particle knows the direction of time?" does not depend on spacetime having singularities at all, and the very same problem could be posed on other spacetimes. For example, the very same question would hold if one were to ask "If a star enters the solar system and passes close to the Sun, how would the Earth 'know' where it should fall to, given it was already falling towards the Sun?".

For a bit more on "an external observer never sees a black hole forming", see, e.g., this answer.

Níckolas Alves
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