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Consider two black holes traveling near the speed of light towards each other. No rotation, charge or other complexities and they are of equal mass. They move at near the speed of light towards each other. They pass each other very very close but not close enough to have any debate about merging. About one year later one of them is seen one light year down the road somewhere and that is my definition of not merging. I don't care if in a trillion years they come back together.

Because nothing can escape a black hole, setting aside things like Hawking Radiation, if their event horizons touch they can't re-separate (correct?). If the escape velocity is the speed of light at the event horizon but the center of masses of them pass far from the event horizon would the fact the event horizons barely touch cause them to essentially come to a halt just after they were traveling close to the speed of light. Obviously I could imagine some deformed blob forming and stretching out briefly but still connected and ?ringing down? ?in seconds? to a single rapidly spinning black hole. Not a "hard" stop but one where you still are amazed that something moving so fast got sucked up in a short distance with nothing close to a collision. Just a brush.

But if they are 1 Planck length further apart at closest approach will it still follow that parabolic path and show up one light year down the road in just over one year? After all they are both exceeding escape velocity perhaps significantly so.

Their centers' of mass are well outside of what is needed to "escape" yet their surfaces, for lack of a better word, are not. What happens and is the difference of a small distance closer, enough to make a dramatic change in the direction and momentum of movement in a short period of time?

Qmechanic
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Dan Wood
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  • Please do not nit pick with something like: Well the event horizons as defined by an external view is different than that experience by the black holes.
    Ok. Either a LIGO like event occurs or it does not. Then use your description of my intent. I'm not an expert. If a LIGO event does not occur I assume that the objects pass by each other as conventionally described. Perhaps bleeding some speed off due to gravitational radiation but that's just a guess. If my usage of "merge" is sloppy I hope it can be cleaned up and still have a valid question. Thanks.     – Dan Wood Jun 27 '22 at 05:50
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    Does this answer your question? Black holes: Is merger inevitable when horizons touch? – Stéphane Rollandin Jun 27 '22 at 06:31
  • If any trajectory brings a massive object within $2r_s$ of a black hole then it will inevitably enter the black hole. If it is in a circular orbit it is $3r_s$. These are for non-spinning black holes, but other limits exist for spinning black holes. These limits are unconnected with escape speeds. – ProfRob Jun 27 '22 at 07:02
  • @ProfRob That should be $\frac{3}{2} r_s$ (the light ring radius) not $2r_s$ (which is the IBCO radius). – TimRias Jun 27 '22 at 14:19
  • @TimRias The "IBCO" for a massive body is $3r_s/2$. But I agree, if the two objects are not in a bound orbit at all, then $3r_s/2$ is the limit. $2r_s$ is the closest the body can approach and still be in a stable bound (highly elliptical) orbit I think. – ProfRob Jun 27 '22 at 14:37
  • @ProfRob Agreed. Note IBCO = "Innermost Bound Circular Orbit" For Schwarzschild this is $2r_s$, any circular orbit inside $2r_s$ is unbound in the sense that it has sufficient energy to reach infinity. – TimRias Jun 27 '22 at 15:07
  • @TimRias got it. I was not familar with the acronym. So the IBCO is where the maximum in the effective potential equals zero. If the maximum is $3r_s/2<r<2r_s$ then it will also be $>0$. – ProfRob Jun 27 '22 at 15:32
  • “Their centers' of mass are well outside of what is needed to ‘escape’” - This is not true. The spacelike radius of a black hole is zero. The radial “distance” (interval) between the horizon and the origin is measured seconds, not in meters - it is zero meters. – safesphere Jun 27 '22 at 15:53
  • In the Newtonian “linear” gravity, two objects coming from infinity and missing each other will fly away to infinity. In GR, gravity is “non-linear”. So is it possible for two stars approaching each other from infinity to form a binary star system? Your question was misinterpreted and closed as a duplicate, but you can always phrase it better to ask again. – safesphere Jun 27 '22 at 16:09

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Consider two black holes traveling near the speed of light towards each other. No rotation, charge or other complexities and they are of equal mass. They move at near the speed of light towards each other. They pass each other very very close but not close enough to have any debate about merging. About one year later one of them is seen one light year down the road somewhere and that is my definition of not merging. I don't care if in a trillion years they come back together.

When these black holes are passing, both enter a very large gravity field which causes both of them to change direction a lot, which causes a large amount of gravity-wave emissions, which causes a large decrease of mass of the system.

The black holes and the radiation can escape each other, because we have so assumed.

I can't tell what the masses and speeds and the safety gap must be for the assumption to be true, because I don't have a super-computer and a suitable simulation program.

stuffu
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