Question about black holes orbiting each other elliptically.

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Aelfyre
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Question about black holes orbiting each other elliptically.

Postby Aelfyre » Fri Jun 22, 2012 5:04 pm UTC

ok, so just random thought went streaming by and bruised my temple.

Assume you had two black holes of equivalent mass that were orbiting each other in a very elliptical orbit so that they started quite far away and came zooming towards each other only missing by a very small margin then whipping around each other and back out to their original distance. And lets say that they got close enough that they event horizons intersected but neither singularity crossed the event horizon of the other black hole so they did not absorb ach other.

basically at their closest approach they looked something like this.
Image

(please don't hate on me for my mad paint skills.. :D)

the question mark in the middle is a particle that was just chilling in space at the time and became engulf by both event horizons simultaneously. What would happen to it when they went whipping away again, it would presumably need to exit the event horizon of one or both of the black holes thus breaking the universe? I dunno but I thought I would throw it out there and see what you all thought.
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Re: Question about black holes orbiting each other elliptica

Postby letterX » Fri Jun 22, 2012 5:35 pm UTC

Remember that the Event Horizon is defined as the region from which you can't escape a black hole's gravitational influence. Nothing says it has to be a sphere. You're probably thinking of black holes in terms of their Schwartzchild radius, which is the spherical radius for the event horizon of an uncharged, non-rotating black hole in an otherwise empty universe. However, if there's other gravitational sources around, or the black hole is spinning, etc., then the event horizon doesn't have to be spherical. You've identified one of the cases where the event horizon clearly isn't spherical. Couldn't tell you what shape it actually is, though, as I don't know enough about the mathematics...

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benneh
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Re: Question about black holes orbiting each other elliptica

Postby benneh » Fri Jun 22, 2012 7:03 pm UTC

That's an interesting question, and I have a relevant point to add:
If you assume that both black holes are identical and the whole situation is symmetric, then its clear that any particle just sitting around at the centre of mass of the system isn't going to go anywhere - the black holes will exert equal and opposite forces on the particle at all times. This means that, even at the point of closest approach, this particle will be sitting directly between the two black holes and inside neither's event horizon. Presumably, this means that the event horizons never touch, that they instead just get squashed as the black holes near each other.

Although, that reasoning doesn't mention the actual distance of closest approach. What happens if said distance is less than the Schwarzschild radius? Presumably, it's simply not possible for such an orbit to occur?

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Re: Question about black holes orbiting each other elliptica

Postby LaserGuy » Fri Jun 22, 2012 7:37 pm UTC

I think in reality what would probably happen would be that any slight, even thermal, perturbation would kick the particle slightly closer to one black hole rather than the other when they came close, at which point the particle would be invariably trapped within the radius of one black hole or another.

If it could remain in perfect equilibrium, I'd speculate that the forces on the particle as the black holes were moving apart would be so strong that it would eventually overcome its nuclear binding energy and rip it apart, and each black hole would absorb a portion of the outgoing photons.

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Re: Question about black holes orbiting each other elliptica

Postby pyronius » Fri Jun 22, 2012 7:49 pm UTC

seems to me that in similar fashion to what letterx said, that area is no longer a part of the event horizon. the event horizon has been warped such that within a certain area between the two (the area with the question mark) the gravity is effectively canceled such that you might escape. if something the size of a planet where there though it might be ripped apart if perfectly centered. if not it would be drawn toward the closer of the two.

edited: weak is not the correct way to describe the gravity between the two.
Last edited by pyronius on Sun Jun 24, 2012 3:39 am UTC, edited 1 time in total.

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Re: Question about black holes orbiting each other elliptica

Postby Goemon » Sat Jun 23, 2012 12:39 am UTC

Actually I suspect it's the other way around. There's a zone just outside the event horizon where it isn't possible to orbit, namely a region where the velocity of a circular orbit is greater than c. Anything that falls into this zone might still get out again if it has thrusters or collides with something else, but if nothing else happens, it'll spiral inward and cross the event horizon. It can't just fall out again.

So if two black holes were to pass close enough for the event horizons to "touch", they'd already be in the zone where they wouldn't normally escape anyway.

In addition, I believe each event horizon would bulge outward under the influence of the other, so they'd merge into a big blob that just ends up as a bigger black hole.
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Re: Question about black holes orbiting each other elliptica

Postby benneh » Sat Jun 23, 2012 6:53 am UTC

Goemon wrote:In addition, I believe each event horizon would bulge outward under the influence of the other, so they'd merge into a big blob that just ends up as a bigger black hole.

PIcture a black hole, with a particle some distance to the left of it. This particle may or may not be able to escape the black hole, depending on how close it is to it. Now add another black hole far to the left of the particle. This black hole exerts a leftward force on the particle, so surely that can only make it easier for the particle to escape the first black hole. Wouldn't that mean the event horizon of the first black hole is pushed inwards by the presence of the second black hole?

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Re: Question about black holes orbiting each other elliptica

Postby idobox » Sat Jun 23, 2012 9:39 am UTC

And if you add a black hole to the right, it makes it more difficult for the particle to escape.
So the event horizon should be stretched away from the centre of gravity.

But we have to remember that in this kind of scenario, newtonian physics are totally unusable. There are simulations of black holes interacting and colliding, and some really weird stuff can happen, like two black holes orbiting each other, but revolving in opposite directions. Apparently, a bridge is also supposed to form between the event horizon of the two black holes, according to wikipedia
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Re: Question about black holes orbiting each other elliptica

Postby eSOANEM » Sat Jun 23, 2012 10:04 am UTC

benneh wrote:That's an interesting question, and I have a relevant point to add:
If you assume that both black holes are identical and the whole situation is symmetric, then its clear that any particle just sitting around at the centre of mass of the system isn't going to go anywhere - the black holes will exert equal and opposite forces on the particle at all times. This means that, even at the point of closest approach, this particle will be sitting directly between the two black holes and inside neither's event horizon. Presumably, this means that the event horizons never touch, that they instead just get squashed as the black holes near each other.

Although, that reasoning doesn't mention the actual distance of closest approach. What happens if said distance is less than the Schwarzschild radius? Presumably, it's simply not possible for such an orbit to occur?


No, the reasoning doesn't hold. In the situation you suggest the particle can only enter both horizons and not one on its own. From this you reason that because it will have no net force on it, it must remain at the centre of mass and so it cannot enter the horizons ergo the horizons cannot touch.

This doesn't hold however. Once the particle is inside the horizon of one black or t'other or both, all information about it is lost and we cannot know which black hole it ends up in so everything will be fine. In fact, I suspect that half its mass, charge and any other interesting quantities would end up in each of the black holes.

Also, here's a simulation of two rotating black holes merging from a distant circular orbit. You can see here that the horizons bulge tidally (or in a way similar to how you'd expect for tidal forces) towards each other (albeit towards the past position of the other black hole due to light-speed propagation, this is why in the first part of the video they seem to bulge towards each other, but in the second part seem to bulge towards a point nearer 1/6 of the way round the orbit from them). Once they get too close, the horizons just merge and you end up with the horizon smoothing out to that you'd expect for the appropriate Kerr black hole.
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Re: Question about black holes orbiting each other elliptica

Postby gmalivuk » Sat Jun 23, 2012 4:43 pm UTC

Goemon wrote:Actually I suspect it's the other way around. There's a zone just outside the event horizon where it isn't possible to orbit, namely a region where the velocity of a circular orbit is greater than c. Anything that falls into this zone might still get out again if it has thrusters or collides with something else, but if nothing else happens, it'll spiral inward and cross the event horizon. It can't just fall out again.

So if two black holes were to pass close enough for the event horizons to "touch", they'd already be in the zone where they wouldn't normally escape anyway.
The limit of possible orbits is at 1.5 times the event horizon's radius, for a static black hole. If the event horizons didn't change shape, two equally massive black holes would touch when the singularities were still out at 2.0rs from each other.
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Re: Question about black holes orbiting each other elliptica

Postby starslayer » Sun Jun 24, 2012 2:23 am UTC

The limit of stable circular orbits for massive objects is 3Rs. 1.5Rs is the photon sphere, where photons/massless particles can be on unstable circular orbits. If the event horizons touch, the black holes are going to merge on that pass.

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Re: Question about black holes orbiting each other elliptica

Postby gmalivuk » Sun Jun 24, 2012 2:09 pm UTC

I know that touching horizons mean the black holes will merge, but Goemon's explanation of that was faulty. At any distance greater than 1.5R, it's possible for a freefalling massive particle to get back beyond 3R if it has enough energy.
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Re: Question about black holes orbiting each other elliptica

Postby legend » Mon Jun 25, 2012 9:52 am UTC

Remember the second law of black hole dynamics http://en.wikipedia.org/wiki/Black_hole_thermodynamics#The_Second_Law; You can't simply merge two black holes and than take them apart again. All the photon sphere and orbits stuff works only for massless test particles. When you have two BH orbiting each other the things get much more complicated and the newtonian intuition doesn't get you very far.


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