Evaporation of Black Holes

[bumab]

Hawking proposed black holes evaporated over time, and I'm pretty sure that's been observed recently when small black holes were apparently created in the lab (and disapeared pretty quick).

 

I was under the impression this was due to virtual particle pairs popping in and out of existance along the event horizon. Sometimes, one falls in and the other escapes before they can anhiliate each other. this leads to an apparent radiation from the black hole.

 

All fine and dandy. How does this reduce the mass of the black hole? If the anti-particle falls in, it will, because presumably, the anti-particle will subtract from the black holes mass. If the regular particle falls in, however, it should add. Wouldn't those two effects cancel out, leading to no overall change? Is there a tendancy for one to fall in more often? That doesn't make sense, however, since they should be equivalent.

[nkt]

The thing that counts is the Schwartzchild Radius, as your first port of call.

 

If you make a tiny black hole, the required density is just far too high for the black hole to be a black hole, and so radiation rapidly escapes, and the hole evaporates.

 

The large black holes require a very much lower density, since the mass inside the Schwartzchild radius is high enough to maintain the black hole. If it gets big enough, the density doesn't have to be very high at all to maintain the black hole.

 

Now, as for the "virtual particles" evaporation idea, well, I just don't see it as a viable mechanism in the lifetime of the universe. A pair pops into existance, one gets swallowed, and the other escapes, taking a small amount (tiny!) of mass away from the hole. Except it doesn't, since the matter was never in the black hole to start with! In fact, the mass of the black hole has gone up, by one particle.

 

Now, assume that the particle was something big, like a neutron or proton. How many times a second would this process have to take place to evaporate a star? Not really a useful mechanism, imo. Perhaps with billions of events per second, and a few hundreds universe lifetimes...

 

If the anti-particle got eaten, it would greatly increase the energy inside the black hole, whereas the normal matter particle would add very little of anything.

 

Also, the graviy of the black hole tends to pull other matter towards it, and so the hole gains mass and continues growing. Once it has eaten everything local to it, the rate may slow, but gravity will keep slowly pulling at anything else nearby, and eat that. The hole just would never evaporate.

 

It's a bit like saying the water is all going to escape from your ice field due to evaporation, while it snows and hails and sleets every few days.

[bumab]

Time was never a problem in his proposal, it was always known it would take almost forever.

 

Isn't the density basically infinite at the singularity, thus producing infinite density within the Swartzchild radius?

[nkt]

Time was never a problem in his proposal, it was always known it would take almost forever.

 

Isn't the density basically infinite at the singularity, thus producing infinite density within the Swartzchild radius?

Yes, but forever is a long time. ;)

 

And we both agree that the mechanism works in the opposite way, so either we are missing something, or it is wrong. Given who came up with it, we are probably missing something.

 

http://www.absoluteastronomy.com/encyclopedia/S/Sc/Schwarzschild_radius.htm is a good description. It isn't infinite density, it is the event horizon. You can determine the (average) density inside the event horizon from it.

[Erasmus00]

I'm not an astrophysicist, condensed matter is more my field, but I do remember from a GR class that black holes do radiate as if they have a temperature inversely proportional to the area of their event horizon. (and their entropy is proportional to the area of the event horizon) this means that smaller blackholes radiate more then larger ones.

The mechanism works like you had described, one member of a particle antiparticle pair escapes from the black hole. The particle and antiparticle pairs are virtual particles, but when one escapes it makes the transition to real particle. Instead of analyzing it in terms of particle number think in terms of energy. If a particle of energy E escapes from the region of the black hole, the energy of the black hole must go down. This energy decrease is in the form of a mass decrease.

-Will

[bumab]

Ahh... so it doesn't matter which drops in. Makes sense- but why does the virtual particle become real after escaping, while the one that drops in stays virtual?

[Erasmus00]

Ahh... so it doesn't matter which drops in. Makes sense- but why does the virtual particle become real after escaping, while the one that drops in stays virtual?

 

My knowledge of quantum electrodynamics is a bit rusty, and black holes are strange creatures. But, the essential difference between virtual and real particles is that the second can be measured, the first cannot. By escaping from the black hole, the escaped particle is no longer a transient. However, the one in the black hole still cannot be measured, as its inside the black hole.

-Will

[bumab]

Clever. By that definition, however, a black hole is a big ol' virtual particle itself.

[Erasmus00]

Clever. By that definition, however, a black hole is a big ol' virtual particle itself.

 

:;): The other possible explanation is that the energy density inside and outside the black hole are different enough that the one outside the hole can become real, the one inside however, never gets that chance. Always lots of ways to explain the same situation.

-Will

[bumab]

The other possible explanation is that the energy density inside and outside the black hole are different enough that the one outside the hole can become real, the one inside however, never gets that chance.

 

That's what I was thinking, but then one would imagine the energy density inside a black hole would be huge.

 

Always lots of ways to explain the same situation.

 

No kidding! ;)