Can event horizons cross for passing black holes at high speed

[deanbrown3d]

Scenario:

You have two black holes approaching, one from the left (A), one from the right (B), each at speed S.
They are offset vertically. S is sufficiently high that they will deflect passed each other without merging.

Question:

Suppose the speed S is high enough so that the event horizons can overlap for a short time. I assume this is possible because there is no limit to the theoretical kinetic energy of each black hole.

Can a particle in the gravitational balance point exist unmoved during this collision, and enter both event horizons while they overlap?

If the answer is yes, then has the particle not escaped from within an event horizon?

 

[DennisN]

Can a particle in the gravitational balance point exist unmoved during this collision, and enter both event horizons while they overlap? If the answer is yes, then has the particle not escaped from within an event horizon?

I like this scenario a lot, it's a thoughtful one!
I was about to say that I have a hunch what happens, but that I refrain from answering because I don't know enough about general relativity and black holes. But I thought some more, and I feel bold enough to make a guess: I think the two event horizons merge into one event horizon, but what happens after that, I don't know at the moment. It will be interesting to hear from PF experts on this scenario...

 

[Orodruin]

I assume this is possible because there is no limit to the theoretical kinetic energy of each black hole.

You assume wrong.

 

[Andrea Panza]

In my understanding the individual event horizons cannot cross but instead they recede from each other, but if the black holes are close enough they will be surrounded by a bigger horizon given by both masses (so an external observer will see a merge)

 

[Vanadium 50]

What does it mean for event horizons to overlap if not that the BHs merge?

 

[deanbrown3d]

In my understanding the individual event horizons cannot cross but instead they recede from each other, but if the black holes are close enough they will be surrounded by a bigger horizon given by both masses (so an external observer will see a merge)

Is the bigger horizon an 'event horizon'?

 

[deanbrown3d]

What does it mean for event horizons to overlap if not that the BHs merge?

Yeah that is what I'm trying to think figure out. The question is - temporarily can they merge but then separate again because of their momentum?

 

[Orodruin]

Yeah that is what I'm trying to think figure out. The question is - temporarily can they merge but then separate again because of their momentum?

No.

 

[DennisN]

No.

So does this mean that two black holes BH₁ and BH₂ will always merge if one point on the event horizon of (let's say) BH₁ passes the event horizon of BH₂?
Edit: And, on a second thought, maybe the conditions of black holes merges are looser than that?

 

[Vanadium 50]

Yeah that is what I'm trying to think figure out.

It's not really fair to us to write something and then ask us what you mean.

GR says black holes whose EHs intersect merge. You say they don't. Who are we to believe?

 

[deanbrown3d]

GR says black holes whose EHs intersect merge.

I understand that, but that is for black holes that merge. The specific question here is a dynamic meeting where they don't merge. The idea being that a particle within the EH of one black hole could be pulled out by the dynamic influence of another. I've never read any discussions about this particular scenario where they don't merge.

An similar analogue might be the the escape of a star from a galaxy by the collision with another galaxy. Normally it could not escape, but with an external influence can it be different?

With enough kinetic energy KE, the singularities can get any distance together and still separate. The attraction between them is not infinite, and there is a finite amount of energy E needed to pull them apart. If KE > E, then a particle can be within the event horizon of one black hole and be released.

 

[davenn]

I understand that, but that is for black holes that merge. The specific question here is a dynamic meeting where they don't merge.

You were told that if they intersect, they merge.
If they don't merge, then the EH's didn't intersect, OK ?

 

[Vanadium 50]

I'm sorry. I thought you were asking a question. It appears that you instead are making a statement. Unfortunately, it's not correct.

 

[deanbrown3d]

You were told that if they intersect, they merge.
If they don't merge, then the EH's didn't intersect, OK ?

No, just stating that is not enough. You're just saying that, at any kinetic energy, no matter it's magnitude, the two masses MUST merge, just because the event horizons overlap. The event horizon being nothing more than the boundary where the escape velocity is c. It is not a physical entity with mass, it is a field. And a field is not constrained to the laws of motion in general relativity.

 

[davenn]

No, just stating that is not enough. You're just saying that, at any kinetic energy, no matter it's magnitude, the two masses MUST merge, just because the event horizons overlap. The event horizon being nothing more than the boundary where the escape velocity is c. It is not a physical entity with mass, it is a field. And a field is not constrained to the laws of motion in general relativity.

well, what can I say ...
If you think that V50 and I are wrong, go and find a credible research paper that states otherwise and link to it here

there's your mission for the day

 

[deanbrown3d]

well, what can I say ...
If you think that V50 and I are wrong, go and find a credible research paper that states otherwise and link to it here

there's your mission for the day

I am asking on here to get an answer, so that someone might be able to point me to a good paper/book/paragraph. Is that not what this forum is for?

Would you respond to my question with some backup discussion? It is a very specific scenario, and gets hardly any coverage online. What I have read so far has not provided me with a satisfying answer.

 

[Orodruin]

I am asking on here to get an answer, so that someone might be able to point me to a good paper/book/paragraph. Is that not what this forum is for?

No you are not asking. You are repeating the same wrong statement again and again after being told repeatedly that it is wrong. You are trying to think in a Newtonian way about something inherently relativistic.
I suggest learning GR. Currently it seems as if all your ideas come from reading popular science. This is not a good way to learn actual physics. I would recommend the new texbook by Guidry, but note that textbooks are going to have prerequisites.

What I have read so far has not provided me with a satisfying answer.

This means that you have not read any of the answers in this thread or you are not satisfied by the correct answer.

You're just saying that, at any kinetic energy, no matter it's magnitude, the two masses MUST merge, just because the event horizons overlap.

Yes!

The event horizon being nothing more than the boundary where the escape velocity is c. It is not a physical entity with mass, it is a field.

No! It is a popularised misunderstanding that ”the escape velocity is c”. It is the boundary a region from which there is no possibility to reach spatial infinity by a future directed non-spacelike curve. You cannot apply classical mechanics to something that is fundamentally based on GR. The notions of time and space fron Newtonian physics are simply not applicable

It is not a ”field”. A ”field” in physics is a quantity that has a value in every point, such as the electromagnetic field or pressure.

And a field is not constrained to the laws of motion in general relativity.

Also wrong, given that we use the appropriate definition of field and not a made up popsci or scifi concept, which we should not if we want to discuss actual science.

With enough kinetic energy KE, the singularities can get any distance together and still separate.

This is a statement, not a question. It is just repeating the same wrong idea that you started with. That is not going to make it true and that is why people are now getting irritated. It is one thing to, after being told (in some cases by experienced physicists) that your assumption is wrong, say ”oh, I did not know that, interesting, if it does not work like that then how does it work?” It is another thing to choose not to believe the experts and continue to press on with the same wrong statement and demand a different answer. You seem to have chosen the latter path to which the answer is irrelevant. If you are not going to accept the correct answers, we might as well answer ”orange”.

 

[Andrea Panza]

Hi,
As black hole horizon radius grows linearly with the mass, a black hole with mass M1 will have a radius R1,a black hole with twice that mass ( M2=2M1) will have an horizon with twice the radius R2=2R1.
For the two horizons to touch (not even to intersect, just to be tangent) the center of the black holes have to be at maximum at a distance R1+R2 that is equivalent to 3R1, but putting 3 times the mass of R1 in a sphere of radius R3 is exactly the mass you need to create a black hole of mass R3.
As I mentioned in a previous post I am convinced that the horizon of each black hole recedes from the incoming one, but as soon as the two masses are close enough to each other they are surrounded by a new event horizon whose radius is derived from the mass of the two (and an external observer will see that the two black hole merge).

I hope it helps

 

[deanbrown3d]

As I mentioned in a previous post I am convinced that the horizon of each black hole recedes from the incoming one, but as soon as the two masses are close enough to each other they are surrounded by a new event horizon whose radius is derived from the mass of the two (and an external observer will see that the two black hole merge).
I hope it helps

Yes it does help! Can we ask a bit further though about the kinetic energy, and if you increase further and further, is there a point where it becomes so dominant that the EHs can overlap for some time?

 

[berkeman]

Thread closed for Moderation and to clean up misinformation...

 

[PeterDonis]

As black hole horizon radius grows linearly with the mass, a black hole with mass M1 will have a radius R1,a black hole with twice that mass ( M2=2M1) will have an horizon with twice the radius R2=2R1.

You appear to have a mistaken understanding of what the "radius" of a black hole's horizon is. It is not "distance to the center"; the "center" of a black hole (meaning the locus $r = 0$) is not a place in space at all, it's a moment of time that's to the future of all other moments in the hole's interior.

The "radius" of a black hole's horizon is actually $\sqrt{A / 4 \pi}$, where $A$ is the area of the horizon.

For the two horizons to touch (not even to intersect, just to be tangent) the center of the black holes have to be at maximum at a distance R1+R2

This is incorrect because, as above, the "center" of the holes is not a place in space to begin with, and the radius of the horizon is not "distance from the center".

Also, this description implies that the horizons are also "places in space". They're not. They are outgoing null surfaces, i.e., they are made up of light rays that are radially outgoing. So falling through a black hole's horizon is not like "passing a point in space". It's like floating in space while a blast of light rays flies past you.

I am convinced that the horizon of each black hole recedes from the incoming one

This is wrong. I have no idea why you would think this.

 

[PeterDonis]

Yes it does help!

It shouldn't; pretty much everything in that post was wrong (see my previous post).

Can we ask a bit further though about the kinetic energy, and if you increase further and further, is there a point where it becomes so dominant that the EHs can overlap for some time?

Kinetic energy is frame-dependent, and the kinetic energy of a black hole in a particular frame has nothing to do with the size or behavior of the hole's horizon.

In other words, these two conditions from your OP...

S is sufficiently high that they will deflect passed each other without merging.

Suppose the speed S is high enough so that the event horizons can overlap for a short time.

...are inconsistent with each other. Either the holes merge, or they don't.

Also, black holes merging is not a matter of their event horizons "overlapping". In a spacetime in which two black holes merge into one, there is only one event horizon: it just is shaped like a pair of trousers rather than like a cylinder (heuristically speaking).

 

[PeterDonis]

So does this mean that two black holes BH1 and BH2 will always merge if one point on the event horizon of (let's say) BH1 passes the event horizon of BH2?

Event horizons are not made up of "points"; they are made up of outgoing light rays (per one of my previous posts a little bit ago). Two black holes merging means, as I said in my previous post, that there is only one event horizon, but it's shaped like a pair of trousers rather than a cylinder, heuristically speaking. But even this viewpoint requires choosing coordinates in which radially outgoing light rays have a constant radial coordinate, so your usual intuitions about how coordinates work and what they mean do not work.

 

[PeterDonis]

The idea being that a particle within the EH of one black hole could be pulled out by the dynamic influence of another.

It can't.

With enough kinetic energy KE, the singularities can get any distance together and still separate.

No, they can't. Black holes are not like ordinary objects. Your mental model of them is wrong.

You're just saying that, at any kinetic energy, no matter it's magnitude, the two masses MUST merge, just because the event horizons overlap.

More precisely, because if they merge, there is only one horizon, not two, and it is shaped like a pair of trousers, not a cylinder, as I said in a previous post. If the holes are moving very fast relative to one another, the pair of trousers will have "legs" that are not parallel, but twisted relative to one another, heuristically speaking.

The event horizon being nothing more than the boundary where the escape velocity is c. It is not a physical entity with mass, it is a field.

No, it is neither of those things. It is an outgoing null surface--a surface made up of radially outgoing light rays (or the worldlines that such rays would follow if they were present--no actual light rays need to be present). In other words, in suitable global coordinates, an event horizon is a surface in which radially outgoing light rays stay at the same radial coordinate. Which, as I said in a previous post, means that your usual intuitions about how coordinates work are not valid. The radial coordinate at the horizon is no longer a "spatial" coordinate: it no longer labels a "place in space". It's a null coordinate, labeling the path of an outgoing light ray (or family of such rays). And the reason nothing can escape from an event horizon is that nothing can outrun a light ray, so if radially outgoing light rays stay at the same radial coordinate, anything else must fall inward, to smaller radial coordinates.

All of this applies just as well when two black holes merge: you just have to apply it along the surface of the trousers instead of a cylinder.

 

[PeterDonis]

Would you respond to my question with some backup discussion?

I think I've covered the key points on which you and other posters were mistaken.

The thread will remain closed.