Black Hole Decay

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BlackSails
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Black Hole Decay

Postby BlackSails » Tue Feb 09, 2010 6:33 am UTC

So Hawking radiation predicts that black holes emit energy and decay by photon emission. Photons carry energy and spin.

What happens to all the other things that are conserved, such as angular momentum, charge and all the other quantum numbers? If we assume that the photons are emitted in such a way that their spin angular momentum more often than not lines up with the black holes angular momentum (that is, it emits circularly polarized photons) we can take care of the angular momentum, but we still have the other things to get rid of.

Is this unknown, or is there some mechanism?

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Re: Black Hole Decay

Postby Tass » Tue Feb 09, 2010 7:04 am UTC

BlackSails wrote:So Hawking radiation predicts that black holes emit energy and decay by photon emission. Photons carry energy and spin.

What happens to all the other things that are conserved, such as angular momentum, charge and all the other quantum numbers? If we assume that the photons are emitted in such a way that their spin angular momentum more often than not lines up with the black holes angular momentum (that is, it emits circularly polarized photons) we can take care of the angular momentum, but we still have the other things to get rid of.

Is this unknown, or is there some mechanism?


Those quantities coupled to far-reaching fields should be conserved. Those being energy (mass), charge and angular momentum. If I understand correctly that should be it. Things like baryon number are not conserved.

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Re: Black Hole Decay

Postby thoughtfully » Tue Feb 09, 2010 9:58 am UTC

Hmm, but B-L might be. Hard to say without having a fleshed-out theory of Quantum Gravity.
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Re: Black Hole Decay

Postby massivefoot » Tue Feb 09, 2010 12:57 pm UTC

BlackSails wrote:So Hawking radiation predicts that black holes emit energy and decay by photon emission.

The calculation works for any free field, so naively they decay by everything-emission.

Being slightly more sophisticated, we have to remember than in reality out universe isn't made up of free fields. The emission of the weakly coupled ones should be well-approximated by Hawking radiation, but emission of strongly coupled fields may not be. Also, the approximation is likely to be good for large black holes, but may become an inaccurate picture for small black holes.

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Re: Black Hole Decay

Postby Diadem » Tue Feb 09, 2010 2:07 pm UTC

A classical black hole (that is, a black hole described by General Relativity and not Quantum Gravity) is completely determined by 5 degrees of freedom. Mass, Angular Momentum and Charge*. The key word here is 'completely'. In physics it's common to describe things like solids or gasses by just a few parameters. But those are approximations. A real gas may be pretty accurately described by temperature, pressure, volume and composition, but it still has 10^26 or so degrees of freedom. Because every single molecule in the gas has a position (x,y,z) and a velocity (x,y,z). So to give an exact description of a gas, you'd have to take all those into account.

Not so for black holes. Black holes have no microstructure. They have mass, angular momentum and charge, and that's all there is. All other information about the matter that makes up the black hole is destroyed. This is sometimes called a paradox, because well, this means information is destroyed, and we know of no physical process that can do that.

So Hawking radiation conserves those 5 quantities, but nothing else. Since anything else is already destroyed by the black hole.

If you add quantum gravity this might no longer be true. It is hypothized that in a complete theory of quantum gravity the microproperties of the matter that makes up the black hole might somehow be conserved. But who knows? We don't understand quantum gravity. So it's impossible to say.

* Yes, that's 5 quantities. Angular momentum has 3 directions.
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Re: Black Hole Decay

Postby BlackSails » Wed Feb 10, 2010 12:15 am UTC

It seems unlikely at best, that charge is the only conserved quantum number, out of all the others. If it gobbles up a kaon, its strangeness changes, no?

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Re: Black Hole Decay

Postby massivefoot » Wed Feb 10, 2010 10:30 am UTC

BlackSails wrote:If it gobbles up a kaon, its strangeness changes, no?

Well this is kind of the point, it appears that it doesn't.

If we had a black hole made by collapsing some matter of net strangeness zero, and then we threw a kaon in, there wouldn't be any change in the spacetime geometry outside the event horizon (except from the slight change due to the different mass and electric charge the black hole now possesses.) And in the Hawking radiation calculation, it the geometry of this region that's responsible for particle creation.

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Re: Black Hole Decay

Postby Diadem » Thu Feb 11, 2010 12:24 am UTC

Exactly.

But of course that's the classical picture of a black hole. We don't know how a quantum black hole would behave.
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Re: Black Hole Decay

Postby Goemon » Thu Feb 11, 2010 12:42 am UTC

I have here a coffee mug full of "strange" beverage. And here I have three black holes. I place them all behind my back, presto change-o. And, voila! An empty coffee mug, and here are the three black holes. Now: can you tell me which of the black holes I poured the "strange" coffee into? Feel free to use any equipment, make any measurements, perform any experiment whatsoever. No? You have no way to tell? There's no experiment or test possible that can determine which black hole swallowed the "strange" coffee?

Then what feature of our universe (external to the event horizons) could possibly cause any one of these otherwise identical black holes to emit more strange particles than the others? Beyond random chance, of course...
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Re: Black Hole Decay

Postby BlackSails » Thu Feb 11, 2010 1:22 am UTC

Sure, I wait around and see which one emits particles that carry strangeness.

Your example is like saying: "I have two sealed boxes with gas inside. One gas is blue and one is green. Which one is the green one?"

From the outside yeah, its impossible to tell, but that doesnt change the fact that each gas has a color.

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Re: Black Hole Decay

Postby Diadem » Thu Feb 11, 2010 1:26 pm UTC

But black holes don't have colour. They don't have strangeness either. Black holes do not have hair.

Such information about particles is destroyed upon crossing the event horizon.
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Re: Black Hole Decay

Postby thoughtfully » Thu Feb 11, 2010 2:40 pm UTC

That's a classical black hole you're referring to. And it violates a fundamental, noncontroversial principle of Quantum Mechanics and takes troubling liberties with Thermodynamics (where's the entropy?). It is very much a matter of dispute whether BHs in a complete theory of Quantum Gravity actually have no hair.
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Re: Black Hole Decay

Postby doogly » Thu Feb 11, 2010 4:18 pm UTC

Strangeness is also not a conserved quantum number, we have the weak force. There is no reason to expect black hole radiation to conserve any almost-conserved quantum numbers.
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Re: Black Hole Decay

Postby BlackSails » Thu Feb 11, 2010 5:05 pm UTC

doogly wrote:Strangeness is also not a conserved quantum number, we have the weak force. There is no reason to expect black hole radiation to conserve any almost-conserved quantum numbers.


Yeah, I remembered that after I used it as my example.

A realization I just had: Since the interior of a black hole is spacelike seperated from the outside, all the mass and charge of the black hole must reside at the event horizion, otherwise how could it interact with things passing by?

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Re: Black Hole Decay

Postby Diadem » Thu Feb 11, 2010 5:09 pm UTC

thoughtfully wrote:That's a classical black hole you're referring to.

Yes. Read the thread. I said that, twice, so far, in this thread.
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Re: Black Hole Decay

Postby Tass » Thu Feb 11, 2010 7:25 pm UTC

BlackSails wrote:
doogly wrote:Strangeness is also not a conserved quantum number, we have the weak force. There is no reason to expect black hole radiation to conserve any almost-conserved quantum numbers.


Yeah, I remembered that after I used it as my example.

A realization I just had: Since the interior of a black hole is spacelike seperated from the outside, all the mass and charge of the black hole must reside at the event horizion, otherwise how could it interact with things passing by?


Yes you can look at it that way. Everything just fades to blackness hovering ever closer to the event horizon where time is stopped. -From the point of view of the outside that is.

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Re: Black Hole Decay

Postby Yakk » Thu Feb 11, 2010 8:10 pm UTC

Tass wrote:
BlackSails wrote:
doogly wrote:Strangeness is also not a conserved quantum number, we have the weak force. There is no reason to expect black hole radiation to conserve any almost-conserved quantum numbers.


Yeah, I remembered that after I used it as my example.

A realization I just had: Since the interior of a black hole is spacelike seperated from the outside, all the mass and charge of the black hole must reside at the event horizion, otherwise how could it interact with things passing by?


Yes you can look at it that way. Everything just fades to blackness hovering ever closer to the event horizon where time is stopped. -From the point of view of the outside that is.

And then the black hole evaporates out from under the thing that has faded to near black right near the event horizon...

Which seems inconsistent, to my naive brain. To someone outside, the thing falling in evaporates before it hits the event horizon in a finite amount of time (I suppose the brightness of the black hole grows nearly without bound, and makes it too hard to see the increasingly dark thing falling in?).

To the thing falling in, it spaghettis in a finite amount of time.

But the thing falling in gets illuminated from the bottom by a large fraction of the entire mass of the black hole, and never crosses the event horizon!

Space time is clearly more twisted than my brain can grasp.
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Re: Black Hole Decay

Postby Tass » Thu Feb 11, 2010 9:02 pm UTC

Yeah. In the end we need a working quantum gravity theory to understand it.

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Re: Black Hole Decay

Postby Xanthir » Thu Feb 11, 2010 9:51 pm UTC

Yakk wrote:
Tass wrote:
BlackSails wrote:
doogly wrote:Strangeness is also not a conserved quantum number, we have the weak force. There is no reason to expect black hole radiation to conserve any almost-conserved quantum numbers.


Yeah, I remembered that after I used it as my example.

A realization I just had: Since the interior of a black hole is spacelike seperated from the outside, all the mass and charge of the black hole must reside at the event horizion, otherwise how could it interact with things passing by?


Yes you can look at it that way. Everything just fades to blackness hovering ever closer to the event horizon where time is stopped. -From the point of view of the outside that is.

And then the black hole evaporates out from under the thing that has faded to near black right near the event horizon...

Which seems inconsistent, to my naive brain. To someone outside, the thing falling in evaporates before it hits the event horizon in a finite amount of time (I suppose the brightness of the black hole grows nearly without bound, and makes it too hard to see the increasingly dark thing falling in?).

To the thing falling in, it spaghettis in a finite amount of time.

But the thing falling in gets illuminated from the bottom by a large fraction of the entire mass of the black hole, and never crosses the event horizon!

Space time is clearly more twisted than my brain can grasp.

There's no contradiction, you've just set up an inconsistent situation. If you assume that black holes *don't* evaporate, then the outside observer sees the victim infinitely approach the event horizon, while the victim passes through the horizon in finite personal time. If you assume that black holes *do* evaporate, then the outside observer sees the victim approach the black hole for a large-but-finite period of time before it evaporates away underneath the victim, and the victim sees the black hole suddenly explode as they near the horizon.

In your thoughts, the victim was personally approaching a non-evaporating black hole,while the observer was watching the victim approach an evaporating black hole. Thus the inconsistency.
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Re: Black Hole Decay

Postby massivefoot » Thu Feb 11, 2010 11:58 pm UTC

BlackSails wrote:Your example is like saying: "I have two sealed boxes with gas inside. One gas is blue and one is green. Which one is the green one?"

From the outside yeah, its impossible to tell, but that doesnt change the fact that each gas has a color.

Perhaps I haven't made something entirely clear here - in the Hawking radiation calculation, only the geometry outside the event horizon influences particle emission. But the calculation just looks at emission in a fixed background, so it certainly isn't exact, since gravity isn't taken to be (even a classical) a dynamical field.

BlackSails wrote:all the mass and charge of the black hole must reside at the event horizion

I'm afraid that this isn't true either. If we ignore charge for now, we can look at the Schwartzchild solution. This is a solution to the vacuum Einstein equations with the origin deleted. The fact that it's a vacuum solution seems to suggest that we should regard it as massless, which is a bit unsatisfactory. But there's obviously something dodgy going on at the origin, so we can avoid this point by resorting to the divergence theorem (suitably generalised to curved spacetime) and write the mass as some flux integral over a large sphere. This does give the number [imath]M[/imath] that appears in the metric as the mass. So (in this classical model) if you want to assign the mass to a location, it has to be in a "delta function" at the origin.

BlackSails wrote:otherwise how could it interact with things passing by?

It interacts by the gravitational field (which is massless). This then raises the question "how does a field remove mass from the black hole?" Again, this isn't something dealt with in the semi-classical calculation, since the spacetime background is fixed in that case.

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Re: Black Hole Decay

Postby Oort » Sat Feb 13, 2010 6:45 am UTC

Is it possible to measure the charge of a black hole? I would think that if light can't escape, neither can the effects of charge, if electromagnetism travels by photons.

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Re: Black Hole Decay

Postby Yakk » Sat Feb 13, 2010 12:43 pm UTC

Xanthir wrote:There's no contradiction, you've just set up an inconsistent situation. If you assume that black holes *don't* evaporate, then the outside observer sees the victim infinitely approach the event horizon, while the victim passes through the horizon in finite personal time. If you assume that black holes *do* evaporate, then the outside observer sees the victim approach the black hole for a large-but-finite period of time before it evaporates away underneath the victim, and the victim sees the black hole suddenly explode as they near the horizon.

In your thoughts, the victim was personally approaching a non-evaporating black hole,while the observer was watching the victim approach an evaporating black hole. Thus the inconsistency.

Ah, so the models that show you reach the center of a black hole don't take into account black hole evaporation?
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Re: Black Hole Decay

Postby thoughtfully » Sat Feb 13, 2010 1:47 pm UTC

There is no Hawking Radiation (hence, no evaporation) for an observer in free-fall. Those tidal forces are a bitch, though!
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Re: Black Hole Decay

Postby Xanthir » Sun Feb 14, 2010 3:06 am UTC

thoughtfully wrote:There is no Hawking Radiation (hence, no evaporation) for an observer in free-fall.

That doesn't seem to make sense. No evaporation seems like it would lead to a contradiction, as Yakk discovered.

Those tidal forces are a bitch, though!

No, for a sufficiently large black hole (like Sag A*) the tidal forces are insignificant, at least near the event horizon. You'll pass right through without a problem. Closer to the singularity the tidal forces would theoretically be stronger. It's only relatively small black holes (like one newly created from a star) that have deadly tides near their event horizon.
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Re: Black Hole Decay

Postby thoughtfully » Sun Feb 14, 2010 10:31 am UTC

Xanthir wrote:
thoughtfully wrote:There is no Hawking Radiation (hence, no evaporation) for an observer in free-fall.

That doesn't seem to make sense. No evaporation seems like it would lead to a contradiction, as Yakk discovered.

Think of Hawking Radiation as Unruh Radiation via the Equivalence Principle. Acceleration == gravitational field. Free fall is no acceleration. No acceleration, no radiation. Susskind's book The Black Hole War has an extended discussion of this apparent contradiction.
Those tidal forces are a bitch, though!

No, for a sufficiently large black hole (like Sag A*) the tidal forces are insignificant, at least near the event horizon. You'll pass right through without a problem. Closer to the singularity the tidal forces would theoretically be stronger. It's only relatively small black holes (like one newly created from a star) that have deadly tides near their event horizon.

I didn't mention the event horizon. It isn't observed by a victim in free fall, anyway. It gets you in the end, as we agree.
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