Cartoon picture of Hawking Radiation-is it accurate?

[fliptomato]

Cartoon picture of Hawking Radiation--is it accurate?

Hello everyone,

The 'cartoon' picture of Hawking Radiation that I keep hearing is that you have a black hole and and particle-anti-particle pair production near the event horizon. One of the particles escapes, while the other is eaten by the black hole. The escaping particle is Hawking Radiation.

However, Hawking Radiation is supposed to account for the evaporation of black holes; i.e. black holes losing energy and shrinking by emitting radiation. In the cartoon picture above, I don't understand how this happens.

While there's certainly 'radiation' in terms of the emitted particle, the black hole has absorbed the particle's (anti-)partner, and hence it's energy has increased, right? (Even if it absorbed an anti-matter particle, those still have positive energy.)

Also, what about the vacuum? In principle the particle-anti-particle pair was created out of the vacuum energy. I'm still a little unclear about this idea. Presumably the Standard Model vertex for pair creation comes rom the mass term $$m^2\psi\bar{\psi}$$, for some field $$\psi$$. Usually (i.e. neglecting vacuum energy) this vertex is not allowed, since it violates conservation of energy. However, one can extract vacuum energy and pair produce, apparently. What happens to the energy that was taken from the vacuum? Is there a vacuum energy "hole"?

Would it be incorrect for me to think about vacuum energy as coupling to a graviton field near a black hole? (I guess this is fundamentally a different thing, so it probably is incorrect--but does this come into play?)

Thanks,
Flip

 

[George Jones]

See if Steve Carlip's description of Hawking radiation makes more sense.

Regards,
George

 

[LURCH]

Hello everyone,

The 'cartoon' picture of Hawking Radiation that I keep hearing is that you have a black hole and and particle-anti-particle pair production near the event horizon. One of the particles escapes, while the other is eaten by the black hole. The escaping particle is Hawking Radiation.

However, Hawking Radiation is supposed to account for the evaporation of black holes; i.e. black holes losing energy and shrinking by emitting radiation. In the cartoon picture above, I don't understand how this happens.

While there's certainly 'radiation' in terms of the emitted particle, the black hole has absorbed the particle's (anti-)partner, and hence it's energy has increased, right?

For me, the key to understanding this (well, to the extent that I do understand it) was the realization that the mass form which the Virtual Partical Pair is formed starts out as energy, and that energy is the stress placed on the vacuum by the black hole. So both Virtual Particals in the VPP are made from mass that came from the black hole, and only one falls in. The other is mass that used to be inside and is now escaping outside the event horizon.

I'm sure it's an imperfect understanding, but it does get the general idea.

 

[El Hombre Invisible]

That would make sense. The energy to create the pair has to come from somewhere. The HUP will give you enough energy for a very short period of time, but for permanent pairs it can only come from the gravitational energy of the black hole. This isn't my thread, but thanks! I never understood how the hole lost energy by this process.

 

[dgiznya]

lost energy

Another way to think about it is that the particle that escapes carries away energy, so to obey conservation of energy, the particle that remains inside the event horizon has a negative energy if you will, this decreases the overall mass of the black hole causing it to get smaller and over time the hole will continue to get smaller and smaller.

dgiznya

 

[El Hombre Invisible]

Another way to think about it is that the particle that escapes carries away energy, so to obey conservation of energy, the particle that remains inside the event horizon has a negative energy if you will, this decreases the overall mass of the black hole causing it to get smaller and over time the hole will continue to get smaller and smaller.

dgiznya

Yes, I think that's the way Hawking describes it, but that just begs the question of how a real particle can have negative energy, irrespective of conservation of energy. I imagine it ends up saying much the same thing - that the particle has negative total energy because the gravitational potential energy Epot is greater than the particle's total energy Etot. This can happen, and makes some sort of sense. Usually, a particle moving towards a gravitationally large body like a black hole will increase in Etot as it decreases its Epot. However, one of a produced pair is created with an instantaneous potential energy which could well be greater than the actual energy it was created with.

 

[dgiznya]

Look at George Jones' reply above,
He is right, the link he has gives a very nice description of the whole negative energy argument.

 

[Norman]

This is what Baez says about it:
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html

He appears to say that the cartoon cannot rigorously be connected to the actual calculation that is done. It is a little technical in its description but a worthwhile read non-the-less.

Cheers,
Ryan

 

[El Hombre Invisible]

Okay, I don't want to hijack this thread, but I have a slew of questions now. I'll stick with one for now: is the produced pair created as a positive-negative pair (as George's link infers)? If so, then the total energy of the pair is zero, energy is conserved and the HUP is irrelevant. This is kind of paradoxical, since it is HUP that requires these virtual pairs to exist in the first place.