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Hypothetical question based on my understanding that two event horizons that overlap (touch) can't ever separate again:

Imagine a 1 billion solar mass black hole (so the event horizon is massive and very gravitationally weak) is travelling at a velocity of 0.9c through empty flat intergalactic space; now imagine an identical 1 billion solar mass black hole travelling at 0.9c but in exactly the opposite direction so the two are heading roughly towards each other. The black holes' paths, once all the space time warping is taken into account, aren't on a direct collision but the outermost edges of the event horizons will just 'clip' each other, ordinarily only overlap for a fraction of a nanosecond as these two bodies are travelling at such incredibly fast velocities and in opposite directions to each other.

So firstly, am I right in thinking that if two event horizons overlap they can never 'unlap'?

Secondly, what would happen to this incredible amount of momentum of each other the black holes? Would it just get instantly turned into gravitational energy? Bearing in mind when black holes normally merge, it happens very slowly as black holes slowly move closer and closer together over millions of years giving off gravitational energy as that happens, so not in a fraction of a nanosecond as in this case.

And thirdly, what would this look like? Would the event horizons remain fairly spherical and the radiated energy just insane or would they stretch and warp into a kind of long thin elastic event horizon as they shoot past each other and then over time slow down and snap back to each other?

Toby Speight
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Loadwick
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2 Answers2

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You have already got some good answers, but I'll just try to provide one more intuitive solution on why the event horizons will never separate again if overlapping each other:
First, imagine a speck of dust that comes inside the EH of a black hole. I believe we'll agree this speck can never escape the black hole, because nothing can come back from behind the event horizon.
Now, imagine the same speck of dust, but inside the overlapping parts of the EH of two black holes passing each other. This speck of dust will never escape any of those two black holes, because it is inside the EH of them both. If these black holes would be able to separate again, the speck caught between them would obviously escape at least one of the black holes, after being behind it's event horizon.
Since this can not happen, the two black holes will be united from the point their event horizons are overlapping, no matter their speed.

Mads Aggerholm
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    As a layman browsing casually, this is a great intuitive explanation! – Daniel B Jun 25 '19 at 17:05
  • I do like this visualisation, i assume it is still possible to escape using quantum tunnelling. But largely irrelevant unless we learn to control quantum tunnelling for instantiations travel.

    Anyway, I agree with you and it is this reason I think the EH would stretch and warp like an elastic band. It can't separate but it can't stop instantly either.

     – Loadwick Jun 25 '19 at 22:11
  • This is pretty much the argument in the Stephen Hawking paper. – Steve Linton Jun 26 '19 at 15:41
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    You don't even need a speck of dust. Any particle will do the same thing--even a virtual particle. And there are always virtual particles. – Loren Pechtel Jun 26 '19 at 16:36
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    @Loren Pechtel, the speck of dust was just an example. There does not need to be anything at all, it is not the presence of eventual matter that keep the black holes event horizons together. The event horizons do not 'know' if there is matter inside them or not: IF there is one speck of dust inside both EH's then it is obvious why they can not separate again. Therefore, dust or no dust, event horizons that overlap can never separate again. – Mads Aggerholm Jun 27 '19 at 19:35
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    This does not occur to me as an intuitive explanation; the logic seems rigorous and irrefutable. Intelligible != intuitive ;-). – Peter - Reinstate Monica Jun 27 '19 at 20:57
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    This is a fantastic argument reminiscent of proofs from Set Theory. Spec "X" is a member of both sets of dark black holes. Rad, dude. – RoboBear Jul 03 '19 at 17:17
  • There's no such thing as "the overlapping parts of the EH of two black holes". There's one event horizon for the whole system. This whole argument seems to be rooted in an entirely incorrect picture of black holes as force-field spheres in a Euclidean background space. – benrg Aug 27 '20 at 18:50
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If the event horizons ever touch and become one continuous surface, their fate is sealed - the two black holes will merge all the way in. They can never separate again, no matter what.

There are several possible ways to explain it, with varying degrees of rigorousness.

An intuitive explanation is that escape velocity at the event horizon equals the speed of light. But nothing can move as fast as light, not even a black hole. In order for the two black holes to separate, parts of one would have to "escape" the other, or move faster than light, which is impossible.

EDIT: Another intuitive "explanation" (a.k.a. lots of handwaving) - inside the event horizon, all trajectories lead to the center. There is no possible path from any place within the horizon to the outside. Whichever way you turn, you're looking at the center. Whichever way you move, you move towards the center. If the event horizons have merged, for the black holes to split up again, parts of them would have to move "away from center" (or away from one of the centers), which is not possible.

All of the above is about as "rigorous" as "explaining" general relativity with steel balls on a rubber sheet. It's just metaphor.

More rigorously, see this paper by Stephen Hawking:

Black holes in general relativity

As time increases, black holes may merge together and new black holes may be created by further bodies collapsing but a black hole can never bifurcate. (page 156)

EDIT: Event horizons don't really "just clip each other". Perfectly spherical event horizons are a theoretical abstraction (a non-rotating black hole in an otherwise empty universe). In reality, anything near a BH will deform the event horizon, which will "reach out" towards that mass. If it's a small mass, the effect is negligible.

But if two black holes get close to each other, the EHs become egg-shaped, as if trying to touch each other. If they're close enough, then eventually a very narrow bridge will form in between, and the EHs will merge. At that moment, the full merger is decreed and will procede with absolute certainty until it's complete. Nothing can stop it.

See this answer:

Are black holes spherical during merger?

what would happen to this incredible amount of momentum of each other the black holes?

The resulting black hole after the merger is going to have a heck of a lot of spin, if the collision is not perfectly frontal. Whatever energy cannot be stuffed into spin, is probably going to be radiated away as gravitational waves (as others have indicated already in comments to your question).

Florin Andrei
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    If the two EHs touch, the centers of the blackholes are still not inside each other's event horizon. Depending on their sizes, the centers may be quite a long way away from the other's event horizon... so surely if they're going fast enough, they can escape even after the event horizons merge? – Rob Jun 25 '19 at 06:10
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    For example, in this picture: https://i.stack.imgur.com/Kgkhy.png - If each blackhole was travelling at 0.999c in opposite directions, surely the centers here would be able to escape the other event horizon? And as an additional question: in the overlapping region, would there not be an area which was not part of either event horizon, due to the gravitational fields of both blackholes 'cancelling' out? – Rob Jun 25 '19 at 06:14
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    @Rob The center is not privileged. Forget the center. Once the bridge has been created, for all intents and purposes it's one black hole. There is no "overlap", your image is wrong - the two entities have merged already, there's a single event horizon, not two (see the answer I've linked at the end). And you cannot split chunks off an event horizon, no matter what you do. Forget the 0.999c, that's nothing. Most people don't realize how truly scrambled is the spacetime within the event horizon. There really is no way out, it's not a figure of speech. – Florin Andrei Jun 25 '19 at 07:42
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    I guess what's difficult for me to reconcile in my head is that if the singularity (assuming all the matter is located at a single point) doesn't cross another event horizon - why should it be unable to escape? I understand the event horizons merge, however, if we think of the two singularities (surely they don't instantaneously merge?) having their own schwarzschild radius, why should their intersections spell doom for their respective singularities? If a sun partially crossed an event horizon, I would imagine only the part of the sun that crossed the event horizon would be trapped forever – Rob Jun 25 '19 at 07:56
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    @Rob It seems like your mental model basically has the mass and the event horizon having locations in space just like normal objects. That's not how it is. Both the singularity and the event horizon are aspects of extremely curved space-time and their behaviour can only be understood, even approximately, in that curved space time. Look at https://www.youtube.com/user/SXSCollaboration for some simulations that take this into account – Steve Linton Jun 25 '19 at 08:53
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    Interesting. The egg-shaped event horizons are quite unintuitive. I would have thought that the space in the middle between two equally powerful attractors would allow any matter travelling perpendicularly to escape with ease, i.e. the event horizons would repel one another and be squashed. Why is the opposite the case? – Fax Jun 25 '19 at 12:21
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    I do not understand that answer. If two event horizons touch, there is nothing to trap there. It's too virtual frontiers intersecting. I thought the only thing that counts is if one of the black hole matter is in the other black hole's EH. Like so: https://i.imgur.com/Zsj3two.png – Guimoute Jun 25 '19 at 14:31
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    @Fax https://images.vice.com/motherboard/content-images/article/no-id/1461736705855188.jpg gives a bit of an idea. Each black hole is a region of very low gravitational potential. Their combined effect makes the potential low in the region between them. – Steve Linton Jun 25 '19 at 14:52
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    @Rob Increasing the relative speed of the BHs doesn't help them escape each other. In fact, it has the opposite effect.The source of the gravitational field in the Einstein field equations of GR is the stress-energy-momentum tensor. So the additional KE & momentum increases the gravity in the region where the BHs meet. – PM 2Ring Jun 25 '19 at 15:22
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    @Guimoute Black holes aren't full of matter like your diagram depicts. GR says that any matter inside the EH (event horizon) must rapidly fall to the centre of the BH, and once it crosses the EH it's causally disconnected from the outside universe. (We don't know exactly what happens at the very core of a BH, we need a proper theory of Quantum Gravity for that). So we only need to consider the gravitational field outside the EH. Please see How does the gravity get out of a black hole? – PM 2Ring Jun 25 '19 at 15:39
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    @Fax The egg-shaped regions prevent things from leaving too. Anything "moving perpendicular" to the "boundary" between the two black holes still needs enough momentum to overcome the combined gravity pulling it back towards the Lagrangian point between the two black holes (remember, you need to fight against both, even if you could escape if there was only one of them). If the escape velocity at the Lagrange point exceeds the speed of light, then the Lagrange point is, itself, inside the combined event horizon and the black holes merge. – Draco18s no longer trusts SE Jun 25 '19 at 18:23
  • @Draco18s Does that mean that in theory something moving in that exact direction (would that be practically impossible, because the center of mass of the two black holes is not stationary) would become a third black hole at the center of mass of the two black holes, eventually causing three black holes to merge at the same time? – Paul Jun 25 '19 at 20:28
  • @Paulpro No, that's the point where the "bridge" between the two egg-shaped-protrusions from the original two black holes touch and combine their event horizons and become "one" blackhole. – Draco18s no longer trusts SE Jun 25 '19 at 23:48
  • @Draco18s and SteveLinton - thank you both very much. The explanation about the lagrange point between the holes and the image finally made this 'click' for me! – Rob Jun 26 '19 at 01:48
  • @PM2Ring Rapidly? According to, who, specifically where. :P – Aron Jun 26 '19 at 08:54
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    @Aron According to the proper time of the infalling matter. That is, if an indestructible clock is inside the EH, it won't tick for long before it reaches the centre of the BH. – PM 2Ring Jun 26 '19 at 09:33
  • Comments are not for extended discussion; this conversation has been moved to chat. – called2voyage Jun 26 '19 at 13:24
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    @Rob Another way of looking at the merger problem: In a simplistic world the space grabbed is entirely empty, but in the real world it's certain to contain particles (if nothing was falling in you still have virtual particles.) Imagine one particle in the overlap zone. It's part of A and can never be pulled away. It's also part of B and can never be pulled away. You have a real world example of an infinitely strong object--even a yank that makes the Death Star look like a candle can't break it. – Loren Pechtel Jun 26 '19 at 16:34
  • @LorenPechtel That is a truly fascinating explanation - basically even a single virtual particle getting trapped in the overlap of two event horizons would be enough of a fixed point of sorts to "lasso" both black holes and irrevocably bind them together. It's not the interaction of anything we would normally think of as "real" (matter, energy, etc.) but more like both holes are getting snagged on the overlapping spacetime itself. – Michael Jun 26 '19 at 23:22
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    @Michael No particle is needed for the merger to complete once it has started. All of the above are just intuitive models. – Florin Andrei Jun 27 '19 at 01:23
  • Can you explain how evaporation figures into this? If the black holes are shrinking - and small ones shrink fast - couldn't they shrink apart? Particles caught in both would be destroyed or go wherever it is everything else in a black hole goes when it evaporates. – Robert Jun 27 '19 at 06:42
  • Cleaner details on why touching EHs merge both blackholes into a single blackhole may help this answer be easier to understand. - IE, why is it considered a single EH as soon as they deform enough to 'touch', rather than one EH where anything goes to Blackhole A, EH where anything goes to BH-B, and an 'overlapping zone' of both EHs where 'extremely weird stuff probably happens...' | Confusion may arise from thinking like "EH is 'an area of space', and black holes can shrink, which suggests space can 'escape' a blackhole, so why can't one EH 'escape' another EH?" – TheLuckless Jun 27 '19 at 16:55
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    @TheLuckless A college-level class in relativity would provide the definitive answers to all those questions and more. And those would be true answers, not pop-sci metaphors. – Florin Andrei Jun 27 '19 at 17:02