Dualing Black Holes

[KingMerv00]

Imagine there are two identical black holes and that their event horizons touch at a single point we will call "X".

If I shine a beam of light through point X tangental to both black holes, it should act normally since the gravitational forces are cancelled out.

Did a beam of light just escape the event horizon of a black hole? Isn't that impossible?

[KingMerv00]

Actually, the event horizons could overlap now that I think about it.

As long as the beam of light is an equal distance from both singularities, everything would be cool...right?

[Badly Shaved Monkey]

Quote:

Originally posted by KingMerv00
Actually, the event horizons could overlap now that I think about it.

As long as the beam of light is an equal distance from both singularities, everything would be cool...right?

Hey, let's laugh at the vet answering a physics question!

1. The will fall towards each other very quickly, so you don't have long.

2. They would have to be perfectly balanced for size, not rotating, the beam would have to bisect the midline perfectly. Too many perfects needed, but whatever you do, at the tiny scales at which that perfection would need to be maintained, quantum fuzziness is going to come in and make the beam choose one over the other at random.

[Gwyn ap Nudd]

A wierd fact about the Scwarzschild radius (the distance from the center of gravity to the event horizon) is that it is linear to the mass of the black hole.

This means that if you have two black holes touching at their event horizons, the Swarzschild radius of their combined mass is the sum of their individual Swarzschild radii. Since all of that combined mass is within that larger radius, you do not have two smaller black holes touching, but a single huge black hole.

If instead of touching at their event horizons, the two black holes were merely close, there might be some weird effects in the space between them, but I am not ready to perform the math to determine what those effects might be.

[rppa]

The mathematical cop-out: Let's say the event horizon is R0, so everything at distance r < R0 is inside the event horizon and falls in, while everything at r >= R0 is outside the event horizon. Then the point of intersection is just outside both event horizons.

The physics cop-out: No idea. The real world doesn't tend to manifest such mathematical abstractions as boundaries so sharp that what happens between two points (r<R0, r=R0) is so different even when the two points are an atomic nucleus apart. In the real universe, things are a little fuzzier. So I suspect that when two actual black holes come together, what really happens is that there's a boundary region which fluctuates a little, and that light traveling through that region sometimes is trapped and sometimes isn't.

But I'm no expert on this stuff by any means.

Edited to add: Administrator, please eliminate this duplicate post.

Has anyone else ever found that the "Delete" feature doesn't work when trying to delete your own messages?

[rppa]

The mathematical cop-out: Let's say the event horizon is R0, so everything at distance r &lt; R0 is inside the event horizon and falls in, while everything at r >= R0 is outside the event horizon. Then the point of intersection is just outside both event horizons.

The physics cop-out: No idea. The real world doesn't tend to manifest such mathematical abstractions as boundaries so sharp that what happens between two points (r&lt;R0, r=R0) is so different even when the two points are an atomic nucleus apart. In the real universe, things are a little fuzzier. So I suspect that when two actual black holes come together, what really happens is that there's a boundary region which fluctuates a little, and that light traveling through that region sometimes is trapped and sometimes isn't.

But I'm no expert on this stuff by any means.

[Badly Shaved Monkey]

BTW, did you mean"dueling" not "dualing"? (Brits, feel free to add additional "l"s to taste.)

[MESchlum]

Look up the LISA project (Laser Interferometer Space Antenna) at NASA Goddard. They are working on detecting gravity waves, and hope to understand inspirraling black holes.

Fun stuff, models are very far from complete. They know what happens early (black holes spiral closer) what happens late (the aggregated black holes pulse), but in between?

[KingMerv00]

Quote:

Originally posted by Badly Shaved Monkey
BTW, did you mean"dueling" not "dualing"? (Brits, feel free to add additional "l"s to taste.)

uh....hmmm...I spelled it wrong on purpose. (Yea that's it)

I wunted to advertize how bad my speeling wuz.




Anyway, I feel cheated somehow. Two black holes become one if they touch? Why?

[TillEulenspiegel]

Just to make this a little less fuzzy. Many use the terms “Black Hole” and “singularity” interchangeably, they are not . The BH is a spherical domain dominated by the attraction of the singularity at it's center .,where nothing can escape. Not even light.

The singularity is the “engine” that drives the black hole. That object is described as an anomaly in space time with infinite density and zero mass ( as one approaches the center of the singularity).

The outcome of the joining of two BHs effectively makes the event horizon equal to the combined volume of both. Think of two soap bubbles joining. The singularities , however, remain seperate.

Depending upon the size of the singularity they will do an elliptical dance around each other until combining of both to a singular body. Small BHs will combine violently and quickly while supermassive BHs >10*10^9 have an huge event horizon that would be probably unnoticeable when passed and the singularities rotation around each other would take a longer amount of time for these objects to coalesce .Its not quite the smooth transition in either case like a film of mitosis run in reverse. It is a violent warping of spacetime with incredible amounts of energy being released and consumed.

As to You original question, if you could have a single instant of time where the forces are balanced the outcome would be a question of QM probability. Not a very satisfying outcome. In real space time the perfect balance of 2 BH could never occur and the constantly shifting dynamic forces of 2 supermassive bodies and and describing their effect on a single or a few photons, is nothing short of impossible to quantify.

Heres a weird little footnote: All the particales that fall past the event horizon speed toward the singularity and approach c. While the mass added to the Bh's total mass held within the event horizon, they theroitically will never reach the singularity because the faster they go the more time slows down in addition to the Lorenz contractions.

[RussDill]

Quote:

Originally posted by TillEulenspiegel
Depending upon the size of the singularity they will do an elliptical dance around each other until combining of both to a singular body. Small BHs will combine violently and quickly while supermassive BHs >10*10^9 have an huge event horizon that would be probably unnoticeable when passed and the singularities rotation around each other would take a longer amount of time for these objects to coalesce .Its not quite the smooth transition in either case like a film of mitosis run in reverse. It is a violent warping of spacetime with incredible amounts of energy being released and consumed.

Given that the rotation is behind the event horizon, would you even be able to see that with gravity waves? That would be information escaping the black hole. Also, due to the effects of general relativity, at what rate would they even orbit from the viewpoint of an observer outside the gravitational field of the singualities?

[TillEulenspiegel]

RussDill :
"Given that the rotation is behind the event horizon, would you even be able to see that with gravity waves? That would be information escaping the black hole. Also, due to the effects of general relativity, at what rate would they even orbit from the viewpoint of an observer outside the gravitational field of the singulalities?"

No you could not quantify any property from Grav waves, In fact a collapsing spherical body collapsing in upon it self generates no Grav waves but in any event GTR breaks down inside an event horizon
We can measure certain aspects of the singularity that do not require any knowledge from inside of the BH. We can measure spin, mass, and size .Prehaps perturbations in the disks behavior in the example of a collision of two BHs, we could tell something about their position relative each other.

All this is done by behavior of the accretion disk around the BH. Like an invisible boat ( or a cloaked Klingon starship) there are effects around those entities that can describe certain properties. A wake from a invisible boat could describe many aspects of the boat I.E. Size , weight, speed , direction. We could even tell the hull type.

So no there is no information passing from the BH itself. Altho......

Hawking at GR-17 presented a last minute paper where he describes a schema where information can be leaked. I have not looked at anything but the abstract but I'm sure that it fomented discussion , to say the least. I will wait for the experts judgments.

[RussDill]

Quote:

Originally posted by TillEulenspiegel
Hawking at GR-17 presented a last minute paper where he describes a schema where information can be leaked. I have not looked at anything but the abstract but I'm sure that it fomented discussion , to say the least. I will wait for the experts judgments.

From my understanding, the pattern of hawking radiation leaks information. Information storage is also an issue. How is so much information stored in such an environment, heard one theory related to string theory about all the matter in the black hole consisting of a single string.

Course, both are theories, with very little opportunity for backing.

[Soapy Sam]

Insofar as light is energy and energy is / has mass equivalent- does this qualify as a three body problem?

(This is a serious, though probably stupid question.)

[69dodge]

Quote:

Originally posted by Soapy Sam
Insofar as light is energy and energy is / has mass equivalent- does this qualify as a three body problem?

Yes, I guess. But light isn't very heavy, so it hardly matters.

Anyway, I think the idea of a three body problem is mainly useful only in Newtonian gravity. There's a clear difference there between the simple elliptical or hyperbolic orbits of two bodies and the complicated orbits of three or more bodies.

In general relativity, everything is complicated.

Ok, that's a bit of an exaggeration. Some things are more complicated than others. But just saying, "we have two bodies here" doesn't characterize the situation as completely in GR as it does in Newtonian gravity. In Newtonian gravity, all spheres are basically the same, as long as they have the same mass. In GR, a very dense sphere is a black hole while a less dense sphere of the same mass isn't one; that's a big difference.

Quote:

Originally posted by Gwyn ap Nudd
A wierd fact about the Scwarzschild radius (the distance from the center of gravity to the event horizon) is that it is linear to the mass of the black hole.

This means that if you have two black holes touching at their event horizons, the Swarzschild radius of their combined mass is the sum of their individual Swarzschild radii. Since all of that combined mass is within that larger radius, you do not have two smaller black holes touching, but a single huge black hole.

The Schwarzschild solution is spherically symmetric, so I don't see how it could apply to the pair, even if it applies to each separately.

Quote:

Originally posted by KingMerv00
Imagine there are two identical black holes and that their event horizons touch at a single point we will call "X".

If I shine a beam of light through point X tangental to both black holes, it should act normally since the gravitational forces are cancelled out.

Did a beam of light just escape the event horizon of a black hole? Isn't that impossible?

I have no idea what the exact solution looks like. I would guess that a black hole's event horizon will change shape if there's a massive object nearby (like another black hole, for example).

But in any case, if the situation is symmetric between the two black holes, the light will go straight; it has no more reason to bend toward one than toward the other. Also, if the light enters an event horizon, it won't leave. Now, how can those both be true?

Well, what happens if you're inside a single black hole's event horizon and you shine your flashlight straight up? The light goes straight; it doesn't bend left or right. It also doesn't escape. It slows to a standstill and then falls back in. So to speak.

("So to speak" means "I don't know what I'm talking about, but it sure sounds good, doesn't it?". No, seriously, I think it's basically right.)

Quote:

Originally posted by TillEulenspiegel
The singularity is the “engine” that drives the black hole. That object is described as an anomaly in space time with infinite density and zero mass

Zero mass? Shouldn't that be zero size, instead?

Quote:

Originally posted by TillEulenspiegel
in any event GTR breaks down inside an event horizon

It does? That doesn't sound right. It might be said to break down at the singularity, but as you've stated, that's not the same thing. The event horizon isn't singular; you just can't get out once you go in. Nothing discontinuous happens as you fall through it.

[Ziggurat]

Quote:

Originally posted by 69dodge
I would guess that a black hole's event horizon will change shape if there's a massive object nearby (like another black hole, for example).

Yes indeed. Calculating it isn't trivial either.

Quote:

Well, what happens if you're inside a single black hole's event horizon and you shine your flashlight straight up? The light goes straight; it doesn't bend left or right. It also doesn't escape. It slows to a standstill and then falls back in. So to speak.

("So to speak" means "I don't know what I'm talking about, but it sure sounds good, doesn't it?". No, seriously, I think it's basically right.)

No, this is incorrect. Once you pass the event horizon, the singularity is no longer spatially separated from you, it is TEMPORALY separated from you. The singularity is your future. You can move as fast as you want, in ANY direction, no falling backwards involved, but you will always reach the singularity because it is, litterally, your future in EVERY direction. Similarly, the event horizon is no longer spatially separated from you, rather it is your past.

This is a kind of hard reality to wrap your head around, but the math is actually fairly straightforward. The metric for flat space-time (ignoring factors of c) is:

ds^2 = -dt^2 + dx^2 + dy^2 + dz^2

The Schwarzschild metric for a black hole is:

ds2 = - ( 1 - rs / r ) dt^2 + (1/( 1 - rs / r )) dr^2 + r2 dO^2

"dO" is an interval of solid angle, rs is the Shwarzschild radius. For r >> rs, this approaches the flat space-time metric, just in spherical coordinates. Notice that the dt term carries the negative sign, and that the other terms are positive: that's what distinguishes the time-like direction from space-like directions. Now look what happens when r < rs: the dt term becomes positive, and the r term becomes negative! r is now your time direction. Time moves inexhorably forward: once you're inside the event horizon, it's not about acceleration or speed. You can go as fast as you want in any direction, but it won't matter, because you can't stop time, and the forward march of time pushes you inevitably towards the singularity. And because "r" is now your time direction, it's not even possible to point your flashlight "towards" the event horizon, any more than you can point a flashlight backwards in time.

[Ziggurat]

Quote:

Originally posted by RussDill
Given that the rotation is behind the event horizon, would you even be able to see that with gravity waves?

Rotation doesn't produce gravity waves, which require some sort of oscillation: a uniform rotating body doesn't oscillate. But rotation of a massive body DOES produce something called frame dragging. The details are messy, but suffice to say it's an effect that is measurable from a distance, and could be observed (at least in principle) for black holes from outside the event horizon. In fact, there's an experiment going on right now called Gravity Probe B to measure frame dragging around earth. Basically, if you put a perfect gyroscope in orbit around a massive object, classically you'd expect the axis of rotation for the gyroscope to remain fixed. But in GR, the axis of rotation can change if the object you're orbiting around is rotating, as the earth is.

http://einstein.stanford.edu/

[Matabiri]

Quote:

Originally posted by TillEulenspiegel
Heres a weird little footnote: All the particales that fall past the event horizon speed toward the singularity and approach c. While the mass added to the Bh's total mass held within the event horizon, they theroitically will never reach the singularity because the faster they go the more time slows down in addition to the Lorenz contractions.

From the point of view of the particle, it will reach the singularity. From the point of view of an observer, it will never even reach the event horizon - it will increasingly red-shift until it fades out.

[RussDill]

Quote:

Originally posted by Ziggurat
Rotation doesn't produce gravity waves, which require some sort of oscillation: a uniform rotating body doesn't oscillate. But rotation of a massive body DOES produce something called frame dragging. The details are messy, but suffice to say it's an effect that is measurable from a distance, and could be observed (at least in principle) for black holes from outside the event horizon. In fact, there's an experiment going on right now called Gravity Probe B to measure frame dragging around earth. Basically, if you put a perfect gyroscope in orbit around a massive object, classically you'd expect the axis of rotation for the gyroscope to remain fixed. But in GR, the axis of rotation can change if the object you're orbiting around is rotating, as the earth is.

http://einstein.stanford.edu/

Sorry, not rotation, but two massize bodies orbiting eachother.

[69dodge]

Quote:

69dodge: Well, what happens if you're inside a single black hole's event horizon and you shine your flashlight straight up? The light goes straight; it doesn't bend left or right. It also doesn't escape. It slows to a standstill and then falls back in. So to speak.

Ziggurat: No, this is incorrect.

Yeah, I agree. I didn't really phrase it right. Saying "the light slows down and then falls back" sounds like the light did travel up a bit, which nothing inside the event horizon ever does.

Quote:

Ziggurat: [...] it's not even possible to point your flashlight "towards" the event horizon, any more than you can point a flashlight backwards in time.

There's no direction you can point a flashlight that will result in its light getting out. But that's not what I meant. I'm pretty sure up and down look different even if you're inside the event horizon. If you look down, you see nothing. If you look up, you can see stuff outside the event horizon. There's just no way to get to that stuff; not even the light from the flashlight you're pointing at it can get to it.

Instead of "the light slows down and then falls back," I should have said "it starts off moving backward." Is that phrasing better, do you think?

Whichever direction you point the flashlight, its light will eventually reach the singularity. But it will reach it quicker if you point it down than if you point it up. No?

[Ziggurat]

Quote:

Originally posted by 69dodge
Yeah, I agree. I didn't really phrase it right. Saying "the light slows down and then falls back" sounds like the light did travel up a bit, which nothing inside the event horizon ever does.There's no direction you can point a flashlight that will result in its light getting out. But that's not what I meant. I'm pretty sure up and down look different even if you're inside the event horizon.

Once you're inside, there IS no up and down. There are three kinds of sideways, with the event horizon in the past and the singularity in the future.

Quote:

If you look down, you see nothing. If you look up, you can see stuff outside the event horizon.

No. Look in any direction, and you see the event horizon, because the event horizon covers your entire past. There is no looking down. That's precisely my point. From your position in space-time, you can project a cone forward in time to all your possible futures, and a cone backwards in time that covers everything that could have reached you. In the coordinate system I wrote down, that cone now points sideways: your past is larger r, your future is smaller r. The event horizon covers your entire past, and the sigularity covers your entire future. This is VERY strange, and it takes some time to wrap your mind around, but it's all there in the math. This isn't just hand-waving or qualitative arguments, it's quite rigorous.

Quote:

Instead of "the light slows down and then falls back," I should have said "it starts off moving backward." Is that phrasing better, do you think?

Not really.

[Mason]

My guess...

Would the point in question function similarly to a trojan point? My guess is that it would, but I couldn't guess how strong the gravity at that point would be. I doubt it could trap light, but there would no doubt be debris of some sort there, and possibly a great (and safe!) view of the event horizons of both BHs.

Or maybe not.

[69dodge]

Quote:

Originally posted by Ziggurat
Once you're inside, there IS no up and down. There are three kinds of sideways, with the event horizon in the past and the singularity in the future.
[...]
No. Look in any direction, and you see the event horizon, because the event horizon covers your entire past. There is no looking down.

Suppose three people---call them A, B, and C---jump straight down towards a black hole, one after the other, in that order. If B looks down, he sees A. If he looks up, he sees C. After they've all passed through the event horizon, won't B still see A if he looks in one direction, and still see C if looks in the opposite direction? I think so. That's all I meant by "up" and "down".

(So, now I think I was wrong when I said you wouldn't see anything if you looked down. Light from "below" can't get past the event horizon, but it can get past you, because you're falling in even faster than it is.)

[Suezoled]

Quote:

Originally posted by Ziggurat
Yes indeed. Calculating it isn't trivial either.


(snipped)

This is a kind of hard reality to wrap your head around, but the math is actually fairly straightforward. The metric for flat space-time (ignoring factors of c) is:

ds^2 = -dt^2 + dx^2 + dy^2 + dz^2

The Schwarzschild metric for a black hole is:

ds2 = - ( 1 - rs / r ) dt^2 + (1/( 1 - rs / r )) dr^2 + r2 dO^2

"dO" is an interval of solid angle, rs is the Shwarzschild radius. For r >> rs, this approaches the flat space-time metric, just in spherical coordinates. Notice that the dt term carries the negative sign, and that the other terms are positive: that's what distinguishes the time-like direction from space-like directions. Now look what happens when r < rs: the dt term becomes positive, and the r term becomes negative! r is now your time direction. Time moves inexhorably forward: once you're inside the event horizon, it's not about acceleration or speed. You can go as fast as you want in any direction, but it won't matter, because you can't stop time, and the forward march of time pushes you inevitably towards the singularity. And because "r" is now your time direction, it's not even possible to point your flashlight "towards" the event horizon, any more than you can point a flashlight backwards in time.

Whoa...I actually understood that....isn't that one of the signs of the impending Ragnorak?

[Ziggurat]

Quote:

Originally posted by 69dodge
Suppose three people---call them A, B, and C---jump straight down towards a black hole, one after the other, in that order. If B looks down, he sees A. If he looks up, he sees C. After they've all passed through the event horizon, won't B still see A if he looks in one direction, and still see C if looks in the opposite direction? I think so. That's all I meant by "up" and "down".

Sort of. B will be able to watch A and C, that is true. But once you're inside, the two directions that B looks in are parameterized by t in the metric I gave you: it's not so much down and up as who jumped in first and who jumped in last: you're looking along what used to be your time direction.

Quote:

(So, now I think I was wrong when I said you wouldn't see anything if you looked down. Light from "below" can't get past the event horizon, but it can get past you, because you're falling in even faster than it is.)

That's much closer to it, yes. But I'd say light from "before", not "below".

[TillEulenspiegel]

69 dodge:

Originally posted by TillEulenspiegel
The singularity is the “engine” that drives the black hole. That object is described as an anomaly in space time with infinite density and zero mass

“Zero mass? Shouldn't that be zero size, instead?”

Doh! ...language . The condition could be described a few ways I.E. 0 size= 0 volume = 0 radius = 0 mass. The correct term is probably zero volume, but they all mean the same thing in this case.


quote:

Originally posted by TillEulenspiegel
in any event GTR breaks down inside an event horizon

“It does? That doesn't sound right. It might be said to break down at the singularity, but as you've stated, that's not the same thing. The event horizon isn't singular; you just can't get out once you go in. Nothing discontinuous happens as you fall through it. “


Not AT the EH but inside of it. GTR breaks down at extreme energies and highly curved spacetime.

So in the case of a many stellar mass BH the curvature is not great at the EH but further in, The breakdown would be closer to the singularity. In a smaller BH, however the curvature is much steeper and the failure of GTR would occur much sooner.

[Ziggurat]

Quote:

Originally posted by TillEulenspiegel
Not AT the EH but inside of it. GTR breaks down at extreme energies and highly curved spacetime.

So in the case of a many stellar mass BH the curvature is not great at the EH but further in, The breakdown would be closer to the singularity. In a smaller BH, however the curvature is much steeper and the failure of GTR would occur much sooner.

We don't actually know when GR breaks down. All we know is that GR and quantum mechanics don't mesh beyond a certain point. But we do not know how much each theory needs to be tweaked to fit reality. Doing a direct experiment on a black hole is, of course, rather out of the question.