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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?

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    $\begingroup$ FWIW, If they were heading exactly towards each other, their relative speed would be 180c/181, about .9945c. According to vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator their EH radius is about 9853 light-seconds. And don't forget they have a huge relative angular momentum too. $\endgroup$
    – PM 2Ring
    Commented Jun 24, 2019 at 21:57
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    $\begingroup$ To also spice things up further lets say they are already rotating at the Kerr's limit in opposite directions to each other so when they touch its very messy from an angular momentum conservation point of view. $\endgroup$
    – Loadwick
    Commented Jun 24, 2019 at 22:37
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    $\begingroup$ Well, SMBHs do tend to be rotating fairly close to the limit anyway, so that's not unrealistic, unlike the relative speed you've given them. ;) But it's going to make an already difficult calculation even harder. There's no analytical solution to the general 2 body problem in GR, so you have to resort to numerical methods, and trying to handle a pair of SMBHs at relativistic speed will require some very heavy number crunching just to get an estimate that's vaguely trustworthy. $\endgroup$
    – PM 2Ring
    Commented Jun 24, 2019 at 22:51
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    $\begingroup$ Possible duplicate of highspeed black holes or neutron stars on (almost) head-on collision course and kinetic energy $\endgroup$
    – eirikdaude
    Commented Jun 25, 2019 at 7:14
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    $\begingroup$ FWIW, there was a thread on xkcd a month or two ago related to this topic: Is it possible to escape from a black hole using another black hole? $\endgroup$
    – PM 2Ring
    Commented Jun 25, 2019 at 16:12

2 Answers 2

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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.

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    $\begingroup$ As a layman browsing casually, this is a great intuitive explanation! $\endgroup$
    – Daniel B
    Commented Jun 25, 2019 at 17:05
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    $\begingroup$ 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. $\endgroup$
    – Loren Pechtel
    Commented Jun 26, 2019 at 16:36
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    $\begingroup$ @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. $\endgroup$
    – Mads Aggerholm
    Commented Jun 27, 2019 at 19:35
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    $\begingroup$ This does not occur to me as an intuitive explanation; the logic seems rigorous and irrefutable. Intelligible != intuitive ;-). $\endgroup$
    – Peter - Reinstate Monica
    Commented Jun 27, 2019 at 20:57
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    $\begingroup$ 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. $\endgroup$
    – RoboBear
    Commented Jul 3, 2019 at 17:17
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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).

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    $\begingroup$ 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? $\endgroup$
    – Rob
    Commented Jun 25, 2019 at 6:10
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    $\begingroup$ @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. $\endgroup$
    – Florin Andrei
    Commented Jun 25, 2019 at 7:42
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    $\begingroup$ 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 $\endgroup$
    – Rob
    Commented Jun 25, 2019 at 7:56
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    $\begingroup$ @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 youtube.com/user/SXSCollaboration for some simulations that take this into account $\endgroup$
    – Steve Linton
    Commented Jun 25, 2019 at 8:53
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    $\begingroup$ @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. $\endgroup$
    – Draco18s no longer trusts SE
    Commented Jun 25, 2019 at 18:23

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