Evaporating Black Holes

[Sharapovaphan]

Does the event horizon survive an evaporated black hole? I couldn't decide if the question should be can, could, or does. Since the answer must be definitive, does, is the proper connotation. For 30 years, Stephen Hawking thought that the uncertainty principle allowed particles to, for short bursts, accelerate beyond light speed, thereby giving them the ability to escape the gravity of a black hole. Well, Sorry Gene Roddenberry, but the mythical tachyon particle just doesn't exist.

 

The theory now is that the information for any particle passing through the event horizon is converted to light and then reassembled outside the black hole, in or around the event horizon, in holographic form... or is it?

 

Here's where I get into trouble concerning this subject. I think what is really happening is that, it is actually take longer for some particles (not all) to progress past the event horizon and into the black hole than it would take for the black hole to evaporate. Hense the information never really progressed past the event horizon, and is therefore is not lost.

 

Pummel me... I probably deserve it.

[ajb]

Does the event horizon survive an evaporated black hole? I couldn't decide if the question should be can, could, or does. Since the answer must be definitive, does, is the proper connotation.

 

This is currently an open question.

 

For 30 years, Stephen Hawking thought that the uncertainty principle allowed particles to, for short bursts, accelerate beyond light speed, thereby giving them the ability to escape the gravity of a black hole. Well, Sorry Gene Roddenberry, but the mythical tachyon particle just doesn't exist.

 

I am not sure how useful the interpretation of Hawking radiation in terms of pair production really is.

 

I do not know how this relates well to the actual calculation.

 

The theory now is that the information for any particle passing through the event horizon is converted to light and then reassembled outside the black hole, in or around the event horizon, in holographic form... or is it?

 

Classically, the only information that a black hole can posses is mass, electric charge and angular momentum.

 

Semi-classically (include some quantum) it appears that the information (entropy) about a black hole is all contained in the surface area of the horizon.

 

It is not immediately clear what the degree of freedom on the horizon are. String theory does provide candidates.

 

 

To resolve all this one would really need a quantum theory of gravity. Semi-classical calculations and string theory give us a window on quantum gravity. Still plenty of work left to be done.

[Spyman]

Hmm, maybe I don't understand the question or at least I interpret it differently than ajb.

 

Does the event horizon survive an evaporated black hole?

The Event Horizon is a feature of the Black Hole and the radius depends on the mass, so when the Black Hole evaporates the Event Horizon will shrink towards the center to finally vanish together with the Black Hole.

 

Here's where I get into trouble concerning this subject. I think what is really happening is that, it is actually take longer for some particles (not all) to progress past the event horizon and into the black hole than it would take for the black hole to evaporate. Hense the information never really progressed past the event horizon, and is therefore is not lost.

If the Black Hole is so starved compared to its mass that it will evaporate before some particles outside of the Event Horizon would not have time to enter then those particles will obviously not be swallowed by the Black Hole and therefor not loose their information either.

 

 

The Event Horizon is not a physicall object, it's a mathematical limit and as such it's thinner than the edge of a razor blade, any particles progressing through will normally pass quite fast.

 

Infalling particles will observe a different and smaller radius for the Event Horizon than a distant observer and as such they will pass the larger radius observed by the distant observer in finite time according to their own clock.

 

 

Event horizon

 

The defining feature of a black hole is the appearance of an event horizon—a boundary in spacetime through which matter and light can only pass inward towards the mass of the black hole. Nothing, including light, can escape from inside the event horizon. The event horizon is referred to as such because if an event occurs within the boundary, light from that event cannot reach an outside observer, making it impossible to determine if such an event occurred.

 

As predicted by general relativity, the presence of a large mass deforms spacetime in such a way that the paths particles take bend towards the mass. At the event horizon of a black hole, this deformation becomes so strong that there are no paths that lead away from the black hole.

 

To a distant observer, clocks near a black hole appear to tick more slowly than those further away from the black hole. Due to this effect, known as gravitational time dilation, an object falling into a black hole appears to slow down as it approaches the event horizon, taking an infinite time to reach it. At the same time, all processes on this object slow down causing emitted light to appear redder and dimmer, an effect known as gravitational redshift. Eventually, at a point just before it reaches the event horizon, the falling object becomes so dim that it can no longer be seen.

 

On the other hand, an observer falling into a black hole does not notice any of these effects as he crosses the event horizon. According to his own clock, he crosses the event horizon after a finite time, although he is unable to determine exactly when he crosses it, as it is impossible to determine the location of the event horizon from local observations.

 

http://en.wikipedia.org/wiki/Black_hole

[ajb]

The Event Horizon is a feature of the Black Hole and the radius depends on the mass, so when the Black Hole evaporates the Event Horizon will shrink towards the center to finally vanish together with the Black Hole.

 

To my knowledge this is still an open question. The final state of the black hole is not understood. It could totally evaporate, but what then happens to the information contained on the horizon? Remember that Hawking radiation if thermal. Maybe the information is lost, though I am not sure if this sits well with the laws of black hole thermodynamics. Maybe they will need further modification.

 

It is also possible that there is some remnant left over that stores all this information.

 

 

Either way, a black hole near the end of it's evaporation is going to be a highly quantum object. It will require a quantum theory of gravity to completely answer this question.

[Spyman]

It could totally evaporate, but what then happens to the information contained on the horizon?

Do you think that the information gets more densely packed on the surface when it shrinks or that it will continue to keep its size when the mass starts to decrease?

[ajb]

Do you think that the information gets more densely packed on the surface when it shrinks or that it will continue to keep its size when the mass starts to decrease?

 

The information is quantised in units of Planck area.

[Spyman]

Semi-classically (include some quantum) it appears that the information (entropy) about a black hole is all contained in the surface area of the horizon.

Why is the information inside a Black Hole thought to be attached to the Event Horizon?

 

 

1) The Event Horizon is not a physical object, it is a mathematical calculated boundary in spacetime.

 

2) If we neglect the problem with information inside a Black Hole and only look at General Relativity or Newton Gravity the Event Horizon must shrink and disappear if the mass/energy inside evaporates and vanish.

 

3) The entropy of a Black Hole are proportional to the surface area of the Event Horizon but both the area and the radius depends primarily on its mass/energy inside.

 

4) Any information a Black Hole manages to contain is already related to the mass/energy that is swallowed together with it.

 

5) For an infalling observer that has passed the Event Horizon from any distant observers view, there will be lots of particles in the close neighborhood that seems to be well below the Event Horizon from the distant observers standpoint. All these particles must bring with them a lot of information, they can't leave all information at the Event Horizon and then continue on inward without it.

 

6) When a Black Hole swallows more mass/energy the size of the Event Horizon grows forcing it to move outwards from the center, which means that any information contained within must be relocated together with it.

 

 

I can understand that from our point of view, as the distant outside observers, anything on the other side of the Event Horizon are beyond our reach, but the inside of a Black Hole is still also inside the Universe. If objects inside a Black Hole are able to be outside of our observable view, so should information also be able to be outside our observable view.

 

IMHO, I think it would be a simpler solution to let any information continue to be attached to whatever mass/energy that gets swallowed and thereby locate the information to anywhere the mass/energy reside inside the Black Hole. It wouldn't make much difference like solve the information paradox and explain how the information could leak out when a Black Hole evaporates but it would let the Event Horizon change and disappear without loss of information.

[ajb]

Why is the information inside a Black Hole thought to be attached to the Event Horizon?

 

It is an amazing result.

 

The temperature of a black hole goes like [math]1/Mass[/math] and then the entropy goes like surface area. Then it is natural to suppose all the information about the black hole is somehow encoded in the event horizon.

 

I don't really understand it past this.

 

I do know that since 1995 or so Vafa and Strominger have developed the statistical mechanics of this using string theory and branes.

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I did not realise this, but Parikh and Wilczek used the WKB approximation to get a direct calculation of Hawking radiation.

 

Maulik K. Parikh, Frank Wilczek. Hawking Radiation as Tunneling. Phys.Rev.Lett. 85 (2000) 5042-5045 also available as arXiv:hep-th/9907001v3

[vordhosbn]

What will happen if the gravitational singularity inside a black hole, which rotates very fast, is stretched to a disk with diameter, greater than the event horizon? Is it even possible?

[ajb]

What will happen if the gravitational singularity inside a black hole, which rotates very fast, is stretched to a disk with diameter, greater than the event horizon? Is it even possible?

 

Look up Kerr metric.

[Sharapovaphan]

"I am not sure how useful the interpretation of Hawking radiation in terms of pair production really is.

 

I do not know how this relates well to the actual calculation."

 

 

Whether it's the force behind a giant going super nova, or the force behind Hawking's belief that faster than light speed is happening because when in and around a black hole the pair separates before annihilation with one succumbing to the singularity and the other accelerating from that separation, beyond light speed and escaping. If Hawking had been/is correct, wouldn't that indicate time travel? Is the universe resorting to time travel in order to preserve the information?

 

I know how broad this interpretation really is and the number of problems surrounding it, but speak to it if you will (humor me). Also, if it's happening there, in a black hole (the singularity at the center), was the first order of business taken up by the known universe time travel???

[dalemiller]

What will happen if the gravitational singularity inside a black hole, which rotates very fast, is stretched to a disk with diameter, greater than the event horizon? Is it even possible?

 

Why should we suppose that the singularity rotates very fast?

[Sisyphus]

Why should we suppose that the singularity rotates very fast?

 

Conservation of angular momentum?

[Sharapovaphan]

What will happen if the gravitational singularity inside a black hole, which rotates very fast, is stretched to a disk with diameter, greater than the event horizon? Is it even possible?

 

Define fast. Isn't the real problem that singularities exist in the first place? General Relativity predicts singularities but does it govern them? So how do we define fast?

[dalemiller]

Conservation of angular momentum?

 

Oh. I thought that angular momentum had to dissipate before stuff could come down into the event horizon. Barred galaxies make it look as though that is what often happens.

[Sharapovaphan]

To my knowledge this is still an open question. The final state of the black hole is not understood. It could totally evaporate, but what then happens to the information contained on the horizon? Remember that Hawking radiation if thermal. Maybe the information is lost, though I am not sure if this sits well with the laws of black hole thermodynamics. Maybe they will need further modification.

 

It is also possible that there is some remnant left over that stores all this information.

 

 

Either way, a black hole near the end of it's evaporation is going to be a highly quantum object. It will require a quantum theory of gravity to completely answer this question.

 

Since anything could be in a black hole, and if the laws of physics allowed for it, anything could come out of it. It would then be impossible to predict what would come out of a black hole if it could. It's own little Breakdown of Predictability in a Gravitational Collapse kinda' thing. However, prediction would not be necessary if the event horizon retained the information serving as the keeper of the manifest, so to speak. Of course nothing can escape a black hole in the known universe, so as Hawking Radiation runs it's course, the all important manifest is seemingly in jeopardy. If it goes, the information goes with it, and a bunch of pretty smart theoretical physicists are left scratching their heads. We are now either at the mercy of infinite complimentary black holes in an infinite number of universes canceling each other out, or holograms containing the information as the black hole and the event horizon shrink from existence. Intuitively, however, it seems to me that even if the information is saved in a hologram, and it survives the loss of it's shrinking keeper, there could be a universe where it doesn't survive, thereby canceling it out. Ultimately, doesn't this make Hawking more plausible?

 

Alas... there also could be a universe where the contents of a black hole can escape... and so on, and so on, and so on. We need a quantum gravity theory that we can sink our teeth into almost as bad as dear Stephen needs more time and energy. Speaking of time...