Question: Two Black Holes Passing Each Other

[Roboramma]

A thought just occurred to me, and I'm wondering if I can get a clear explanation as to why it wouldn't work:

Two black holes, say of equal mass, pass near each other. Let's say so close that their event horizons just "touch".

It seems to me that at that point of "contact" the space-time curvature of one black hole should exactly cancel that of the other, and anything trapped at the event horizon should be free to escape from both...

Of course, the same idea should apply to less extreme circumstances: both for black holes not quite so close to each other: the curvature caused by one canceling to some degree the curvature of the other and thus the event horizon would shrink and some matter, or at least light should be able to escape where in a closed system with only the single black hole it would have been impossible.

Taken further it's obvious that this should work if one of the objects in question is not a black hole but simply a massive body who's gravitational affects are strong enough to "uncurve" some area previously inside the event horizon of the black hole so it's only just outside of it.

I'm assuming that this doesn't work, mainly because from what I've read there's simply no way to get something that's fallen into a black hole back out again. I'm curious as to why however.

This question actually has some similarity to one I asked previously regarding throwing massive amounts of, say, negatively charged particles into a black hole until, theoretically, the negative charge would be so strong as to overcome the gravitational attraction. I have to admit that I still don't entirely understand but the explanation was something along the lines of "gravity is different from electromagnetism and can't be viewed as a conventional force, the force of charge can never change the geometry of space time, and within that geometry there are simply no paths that lead out of the black hole". (that's my poorly remembered interpretation of I'm sure a much better explanation).
Now, if I'm understanding that right, however, gravitation shouldn't be limited in the same way when it comes to counteracting it's own effects. So, what am I missing?

And yes, I'm sure that I probably won't follow the answers very well as I can't follow general relatively very well in general, but, well, I'm hoping something will click anyway.

 

[nota]

join these guy's board if you want a PhD quality answer

http://www.bautforum.com/index.php

 

[Metullus]

Would not the two black holes begin to orbit one another, eventually spiraling inward until they collide and become one?

 

[sol invictus]

A thought just occurred to me, and I'm wondering if I can get a clear explanation as to why it wouldn't work:

Two black holes, say of equal mass, pass near each other. Let's say so close that their event horizons just "touch".

It seems to me that at that point of "contact" the space-time curvature of one black hole should exactly cancel that of the other, and anything trapped at the event horizon should be free to escape from both...

At most, the gravitational force along the axis that connects the centers of the holes will cancel. But it doesn't cancel in the two directions transverse to that axis the moment you move that way a little, and it's in those directions you'd need to go to escape.

If the black holes were stationary, something could remain indefinitely in unstable equilibrium at that central point. But of course the two holes will be falling towards each other, disallowing even that possibility.

In any case, the horizon is by definition the region from which nothing can escape, so it's a bit meaningless to ask if anything can escape from a horizon... if there was a point from which something could escape, then it wouldn't be behind a horizon.

This question actually has some similarity to one I asked previously regarding throwing massive amounts of, say, negatively charged particles into a black hole until, theoretically, the negative charge would be so strong as to overcome the gravitational attraction. I have to admit that I still don't entirely understand but the explanation was something along the lines of "gravity is different from electromagnetism and can't be viewed as a conventional force, the force of charge can never change the geometry of space time, and within that geometry there are simply no paths that lead out of the black hole". (that's my poorly remembered interpretation of I'm sure a much better explanation).

Actually you can charge up a hole to just that point (at least in theory). Such a black hole is termed "extremal" (specifically in that case, "extremal Riessner-Nordstrom"). Two such holes, at relative rest, exert precisely zero force on each other. However it is not possible to charge a hole past that point, essentially because it would require energy to force additional charge onto such a hole, and that energy goes into increasing the mass of the hole by just enough to prevent you from ever exceeding extremality.

Incidentally there's a similar story with angular momentum.

 

[Roboramma]

Actually you can charge up a hole to just that point (at least in theory). Such a black hole is termed "extremal" (specifically in that case, "extremal Riessner-Nordstrom"). Two such holes, at relative rest, exert precisely zero force on each other. However it is not possible to charge a hole past that point, essentially because it would require energy to force additional charge onto such a hole, and that energy goes into increasing the mass of the hole by just enough to prevent you from ever exceeding extremality.

Incidentally there's a similar story with angular momentum.

Thanks, that makes sense to me now! I had forgotten to account for the energy necessary to get the charge in. Of course, I knew that you needed that energy, but I didn't account for it's also having a gravitational effect. I think the last time I asked this question someone pointed out that gravity is non-linear, but I didn't really make the connection as to what that meant.

As to the rest of your post I need to think about it more and see if I can understand... have to run off to work now!

 

[ben m]

A thought just occurred to me, and I'm wondering if I can get a clear explanation as to why it wouldn't work:

Two black holes, say of equal mass, pass near each other. Let's say so close that their event horizons just "touch".

It seems to me that at that point of "contact" the space-time curvature of one black hole should exactly cancel that of the other, and anything trapped at the event horizon should be free to escape from both...

If you want to picture it in a classical-gravity way: picture the Moon and the Earth being so close together that their gravitational pulls "cancel" near-ish to the Earth's surface. (If you tried to accomplish this you'd find yourself on a very distorted Earth, but never mind that for now.) Picture going to a point on the Earth's surface and finding that g = 0.01 m/s^2 and that the Moon is a hundred feet above you. You could take a gentle leap into the air and land on the Moon; you could leap off the Moon and fall back to Earth; if you could get to the halfway point you could float there. Sound good? Is that the sort of cancellation you're picturing for a pair of black holes?

OK, so starting from this point it's easy to get to the Moon. Does that mean that it's easy to get to Mars, or Jupiter? No. It's easy to get the first 50 feet off the ground (the Earth and Moon g-forces cancel.) But to get to Mars you need to get out from between the Earth and Moon---sideways. Fly 100 miles "sideways" and you'll find gravity pulling you backwards (the Earth's and Moon's masses are, on average, behind you). Fly another 10000 miles and you'll see the Earth-Moon system all together in your rearview mirror, pulling you downwards.

All that force pulling you backwards means: there is still an nonzero escape velocity from a "touching" Earth-Moon system, even if you start from a point with zero gravitational force. Likewise, there's still an escape velocity from a "touching" black hole pair, and if your starting point was inside either of the escape horizons then that velocity is greater than c.

 

[Roboramma]

Hey Ben, thanks for that, I like that picture.

I was thinking about it as the black holes both having spherical event horizons, and when they "touch" something moving tangent to that point would be able to escape because, while it would still be affected by both black holes, it seemed that if it could just escape a tiny bit it would (if it were light, anyway), be able to "get out".

But when I think more about it now it would still follow the curvature of the event horizon and not escape. I think it makes sense now. The other issue is that perhaps if the two event horizons did come into contact like that, the two black holes should be viewed as a single black hole at that point. Because, it seems that stuff could go from one to the other...

Which makes me wonder again, what about if there were a massive (non-black hole) object near to a black hole? Could it pull stuff out? In the same way that your analogy suggests jumping from the earth to the moon?

The obvious objection to that seems to be that in order for it to do so any object would itself have to be so close to the black hole as to have already found itself inside the event horizon. Is that true?

 

[Roboramma]

Hey Sol, I just reread your post, and yeah, I guess I see where I went wrong, thanks for that explanation. What do you think about the question posed in my response to ben? Particularly, what if the second body is not a black hole but rather simply a massive body? Could it exert a force on something at the horizon of the black hole such that it would come out? Obviously not, but what stops it doing so?

Actually that leads me to a similar question: what if we second force were electromagnetic instead? Drop an electron into a black hole then bring a massive amount of protons near by... could they pull out the electron? As I said, obviously not, but why not?

In any case, the horizon is by definition the region from which nothing can escape, so it's a bit meaningless to ask if anything can escape from a horizon... if there was a point from which something could escape, then it wouldn't be behind a horizon.

Yeah, I know. I guess I was suggesting that something that had passed the horizon would find that the horizon had shrunk and thus it was no longer inside of it. And yeah, as I said, I know that's impossible, I just want to understand why. But in regards to my first question, I think I do understand it now.

 

[sol invictus]

Yeah, I know. I guess I was suggesting that something that had passed the horizon would find that the horizon had shrunk and thus it was no longer inside of it. And yeah, as I said, I know that's impossible, I just want to understand why.

Because horizons aren't defined locally. There's no experiment that would tell you whether or not you're behind a horizon and fated to hit a black hole singularity. Horizons are defined taking into account the future as well as the present. So if a situation like the one you're asking about arose, it would simply mean that the object wasn't ever behind a horizon after all.

Here's a very clear example of that: imagine a perfectly spherically symmetric thin shell of matter. The shell starts with a very large radius, and then begins to collapse. If it continues to fall freely, at some point its radius will be equal to its Schwarzschild radius, and after that time it's a hole.

But what's interesting is that something inside the region where the hole will form in the future can be behind an event horizon before the hole actually forms - that is, the event horizon appears at the center of the shell before it arrives at its Schwarzschild radius. It then grows and meets the shell just as it crosses.

So the horizon appears in advance - but if the shell were suddenly arrested in its motion and yanked back out towards infinity (maybe each piece had a rocket attached, and the rockets fired before the hole formed), it would never appear at all.

 

[ben m]

Which makes me wonder again, what about if there were a massive (non-black hole) object near to a black hole? Could it pull stuff out? In the same way that your analogy suggests jumping from the earth to the moon?

The obvious objection to that seems to be that in order for it to do so any object would itself have to be so close to the black hole as to have already found itself inside the event horizon. Is that true?

You've pretty much answered your own question. Yes, a large object very close to a black hole (let's say "right at the event horizon") can pull things towards itself. However, remember that the large object itself is itself moving towards the black hole (at the event horizon, there's no other possible trajectory) so falling towards this object does not allow you to escape the hole---the most you can do is change your trajectory on the way in.

 

[Ziggurat]

Which makes me wonder again, what about if there were a massive (non-black hole) object near to a black hole? Could it pull stuff out? In the same way that your analogy suggests jumping from the earth to the moon?

One thing that hasn't been explicitly stated yet which may help clarify this stuff is that in the presence of other large bodies, the event horizon of a black hole does not need to be symmetric. Other bodies will affect the location of the event horizon. In this sense, it's possible for a nearby large object to "rescue" something from the event horizon, but it does so not by pulling an object through the event horizon, but by moving where the event horizon was to begin with. Once you're past the event horizon, there's never any going back (that's what defines the event horizon, so the statement that you can't escape is really a tautology), but the horizon itself is not some perfectly rigid sphere.

 

[rjh01]

I would also like to remind everyone that going anywhere near a black hole will tear you apart via tidal forces.

The other thing is that two black holes that are rotating around each other in very close orbit will emit gravity waves and so lose mass. These waves, with the right equipment would be able to be detected anywhere in the universe.

 

[Ziggurat]

I would also like to remind everyone that going anywhere near a black hole will tear you apart via tidal forces.

Not necessarily. It depends quite a bit on the size of the black hole. A large black hole will have weaker tidal forces than a small black hole at the same relative radius (ie, your radius divided by the event horizon radius).

 

[nota]

I would also like to remind everyone that going anywhere near a black hole will tear you apart via tidal forces.

The other thing is that two black holes that are rotating around each other in very close orbit will emit gravity waves and so lose mass. These waves, with the right equipment would be able to be detected anywhere in the universe.

yes maybe but no such or any other waves detected yet

and if a back hole has an acceleration due to gravity of = or < C
the holes each should speed up not slow down even if they emit the G-waves
as they get closer
and if the speeds get near a high % of C
the mass goes up adding more forces
a lot depends on if they really are a point or not and have a real size
then there is the time stretching effect to jump in and make the whole mess
even weirder by taking all the time that ever will exist for the total event to play out

 

[rjh01]

yes maybe but no such or any other waves detected yet

and if a back hole has an acceleration due to gravity of = or < C
the holes each should speed up not slow down even if they emit the G-waves
as they get closer
and if the speeds get near a high % of C
the mass goes up adding more forces
a lot depends on if they really are a point or not and have a real size
then there is the time stretching effect to jump in and make the whole mess
even weirder by taking all the time that ever will exist for the total event to play out

I do agree the maths and the physics involved would be very messy. But no the mass cannot go up as they get nearer each other. That would violate the conservation of energy.

If you want to listen to people, who know what they are talking about, discussing what happens when black holes collide then watch this

 

[Andrew Wiggin]

I would think that if two black holes passed each other, you'd have to calculate the possibility of the center of mass of the system its self being a black hole. I can certainly see a case where two masses, say neutron stars of just below the mass needed for a black hole, in orbit around a mutual center of mass, would be inside a shared event horizon centered on the shared center of mass.

 

[Roboramma]

I do agree the maths and the physics involved would be very messy. But no the mass cannot go up as they get nearer each other. That would violate the conservation of energy.

It seems to me that the additional relativistic mass that comes from the kinetic energy increasing as they approach should be cancelled by the loss of gravitational potential energy, and so the total energy (and thus gravitation) should remain the same...

Right?

 

[sol invictus]

I would think that if two black holes passed each other, you'd have to calculate the possibility of the center of mass of the system its self being a black hole. I can certainly see a case where two masses, say neutron stars of just below the mass needed for a black hole, in orbit around a mutual center of mass, would be inside a shared event horizon centered on the shared center of mass.

Yes, that can happen at least in principle.

It seems to me that the additional relativistic mass that comes from the kinetic energy increasing as they approach should be cancelled by the loss of gravitational potential energy, and so the total energy (and thus gravitation) should remain the same...

Right?

Yes - the total energy will remain the same, but some of it will be radiated as gravity waves as the two holes merge. That radiation is one of the most interesting aspects of this, because it should be detectable in the (very) near future using gravity wave detectors.

 

[HansMustermann]

Actually, it just occured to me that since the Schwarzschild radius is linearly proportional with mass, a system as described in the OP will always be itself a black hole. The Schwarzschild radius of the system with mass 2M will be twice the radius of the individual black holes, i.e., equal to a diameter. If the event horizons touch, then there you go, they both fit inside the larger black hole.

 

[sol invictus]

Actually, it just occured to me that since the Schwarzschild radius is linearly proportional with mass, a system as described in the OP will always be itself a black hole. The Schwarzschild radius of the system with mass 2M will be twice the radius of the individual black holes, i.e., equal to a diameter. If the event horizons touch, then there you go, they both fit inside the larger black hole.

You've come to an impossible conclusion, so you might want to examine your assumptions! Since the two holes start off separated and end up as one, there is obviously a moment when the two disconnected horizons first touch (as described in the OP).

But you're correct that it doesn't happen when the centers of the two (let's say they've of equal mass) are separated by the diameter a single one would have by itself. Instead - at least in the absence of angular momentum - I think the horizons become elongated along the axis connecting them (i.e. they become egg shaped) and first touch along that long axis.

It's only very recently that numerical general relativity has progressed to the point that such questions can be answered in detail. The problem is too hard to solve analytically.