I'm pretty sure the answer to the question in title is "No". But why?

Below is a naive Newtonian simulation I made. You can see that in the animation, both black hole's horizons seem to "recede" for a moment as the black holes pass each other. The black holes in the animation are NOT MERGING. Therefore any explanation involving merger and subsequent expansion of the new horizon does not cover this situation.

The color of the pixels describes escape velocity at a given point. Black pixels have the value higher than speed of light.

Click here for animation.

enter image description here

What am I illustrating here is, that if two black holes are too close to each other, their gravity must cancel out. Lagrangian point would appear somewhere in between. Yet we know that nothing should be allowed to escape. At the same time, quantum mechanics requires the surface of the black hole to be directly proportional to it's mass. Which is not the case in the simulation we see.

How does event horizon survive distortion caused by another black hole, when two black holes are extremely close to each other?

  • $\begingroup$ More accurate simulation: ligo.caltech.edu/video/ligo20160211v3 $\endgroup$ – Kyle Kanos Oct 2 '18 at 12:14
  • $\begingroup$ @KyleKanos This still shows the same phenomena I observed in my simulation - the horizon decreases in size for a moment. $\endgroup$ – Tomáš Zato - Reinstate Monica Oct 2 '18 at 12:50
  • $\begingroup$ @KyleKanos In my animation, no merging happens. Any lightlike path that would find itself in the merged event horizon in the linked question's scenario has free path in my scenario. $\endgroup$ – Tomáš Zato - Reinstate Monica Oct 2 '18 at 13:10
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    $\begingroup$ You have a simulation that, by your own description, is not GR. You are trying to infer something about physics in exactly the portion of the theory where Newtonian physics breaks down the most. Why do you think this simulation provides any useful information whatsoever? Your animation is completely non-physical for exactly the effects that you want to explore. How you think you got a black hole at all in this simulation is beyond me since black holes do not exist in Newtonian theory. $\endgroup$ – Brick Oct 2 '18 at 13:29
  • $\begingroup$ @Brick The fact that my premise and simulation are wrong does not mean any answer that just says "no" is correct. If I knew how to correctly simulate this or do the proper math, I wouldn't be asking question. I would also not need to ask a question if I just wanted to know whether anything escapes or not - I already did know an answer to that. $\endgroup$ – Tomáš Zato - Reinstate Monica Oct 2 '18 at 13:42

Their gravity would not at all 'cancel out'. For sure, there could be some point precisely between the two black holes where a test particle would remain in its place without being pulled in; however, this point would be very unstable and any fluctuation of the particle would immediately cause it to fall towards one of the black holes.

Of course, provided you have set up the black holes like in the picture, somewhere in the very near future the black holes would also start to sense each others presence and merge. This makes it even more impossible to have a particle accurately residing between the two black holes without falling in.

  • $\begingroup$ This (nor any other answer) does not address the main issue, which is that the volume under the event horizon got smaller as the black holes approached. Any matter frozen at the event horizon would unfreeze from reference frame afar from the black hole's influence. $\endgroup$ – Tomáš Zato - Reinstate Monica Oct 2 '18 at 12:47
  • $\begingroup$ @TomášZato Nothing "unfreezes." I'm not clear what you mean about volume under the event horizon getting smaller, but nothing about these dynamics lets anything out. $\endgroup$ – Brick Oct 2 '18 at 13:02
  • $\begingroup$ @Brick If you watch the animation, you'll see it quite clearly. A great fraction of the circular black hole is "cut out" for a moment. $\endgroup$ – Tomáš Zato - Reinstate Monica Oct 2 '18 at 13:08
  • $\begingroup$ In general relativity, notions of volume and position are not as straightforward as can be seen on a YouTube video, especially not when considering extreme systems like black holes. The geometry of space-time anywhere near the black holes would deform in such a way to prevent anything from escaping the black holes. $\endgroup$ – Stijn B. Oct 2 '18 at 13:58

You seem to misunderstand a bit what it means to be "in a black hole." That is a short-hand way of saying inside the event horizon. The event horizon is really a surface in spacetime, not separately on each spatial slice. But if you do take a spatial slice through it to get a picture "like" your picture (taking into account that, as you understood, your picture is not correct in the details), your binary system will either be "merged" or "in-falling".

If merged, then the portion of event horizon on your slice will encompass both singularities and this "Lagrange point" in the center. In this case, if you found yourself at the special point between them, you might still be able to choose which of the two singularities you hit, but you will hit one of them eventually. You cannot escape that result. (Or, in a super-special case, they will both hit you simultaneously when they fall together.)

In the in-falling case, the portion of the event horizon on your slice will be disconnected, appearing like two distinct regions. If you're at the midpoint in that case, you might still escape - if you start soon enough to avoid the merger - by traveling perpendicular to the line connecting the holes for a while. There's no contradiction though because you were never in a black hole in this case. Gravity will attract the black holes toward each other in this case, so you better clear before they get close enough to you for the horizons to merge, trapping you in the case above.

  • $\begingroup$ Not really, based on velocities, the black holes could also be on hyperbolic or parabolic "slingshot" orbit. That would be they'd never merge. $\endgroup$ – Tomáš Zato - Reinstate Monica Oct 2 '18 at 12:48
  • $\begingroup$ OK, so that's another case. I inferred (wrongly, apparently) that you intended them to be moving in line. The basic answer remains. You are either in the event horizon or you are not. Once you are in, you cannot get out. Nothing about the relative motion of the black holes changes that. You've got three answers now that overlap significantly. If you are not getting an answer to your underlying question, I suggest an edit. $\endgroup$ – Brick Oct 2 '18 at 13:00
  • $\begingroup$ I don't see how could I phrase more clearly what the last sentence of my question asks about. Could you maybe suggest a clarification in comments under my question? I really thought making an animation of black holes that don't merge would make it clear I'm talking about black holes that pass each other without merging. $\endgroup$ – Tomáš Zato - Reinstate Monica Oct 2 '18 at 13:15
  • $\begingroup$ Well, for one thing, your actual question was: "How does event horizon survive distortion caused by another black hole, such as when two black holes are merging?" But now you are saying they are not merging. That's one issue of clarity. The other problem seems to be that you are, on one hand, acknowledging that your simulation is Newtonian and has mathematical issues, but, on the other hand, relying on some of those issues to draw your conclusion. The "distortion" that you suggest via your simulation does not occur - at least not like that - with event horizons of black holes in GR. $\endgroup$ – Brick Oct 2 '18 at 13:18

The configuration in the question is a compound system for which the overall event horizon should be simulated numerically. Intuitively, as per Newtonian similarity, a first Lagrangian point should be on the line joining the two black holes in between them. If an object is in that point, it should maintain its position relative to them.

However it is not correct to say that the object can escape the black hole, as it should be outside the event horizon of the compound. I expect the event horizon of the system to be formed by two not connected surfaces, each of them surrounding one of the black holes and closer to the respective black hole in the spacetime region between them. In such a way that in the region in between there is a sort of corridor viable for time-like paths.

  • $\begingroup$ From far-away observer's point of view, anything that fell "into" any of the black holes is frozen at the event horizon, redshifted to the point of invisibility. The situation I have demonstrated "moves" the event horizon closer to the black hole, temporarily affecting that redshift as well as passage of time in general. $\endgroup$ – Tomáš Zato - Reinstate Monica Oct 2 '18 at 12:53
  • $\begingroup$ The far-away observer's point of view seems to be the least suitable for observing or analyzing what's happening. How can you use it to deduce anything at all? $\endgroup$ – D. Halsey Oct 3 '18 at 0:06

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