A Question Regarding Hawking Radiation and the Evaporation of Black Holes.

[Yreval]

Firstly, I'd like to apologize if I've posted this in the wrong section, as I wasn't sure if it belonged in Relativity, Quantum Theory, Modern/Theoretical Physics, or here in Astronomy and Cosmology; my question really relates to all these topics in one way or another.

 

Anyway, on to the meat of my query:

 

As I understand, "Hawking Radiation" is a result of the meeting between Heisenberg's Uncertainty Principle and the incredible gravity at and around the event horizon of a black hole; as a particle-antiparticle pair "pops" into existence, one of these particles is sucked into the hole and the other, in turn, is cannoned off into space, (thus the radiation) rather than their usual collision and evaporation. What I don't understand about this proposed phenomenon is how it is responsible for the evaporation of the Black Holes, seeing as the radiation isn't being emitted from the Black Hole itself, but rather from the quantum fluctuations of spacetime around it. It seems to me that it would cause only the accretion of more mass—being that the Black Hole is swallowing particles that "pop" into existence around it—rather than the evaporation of it.

 

Can someone explain to me what it is about this process that results in the evaporation of the black hole?

[JTankers]

You are correct, particles entering a black hole would cause growth. Common sense.

 

30 years ago Dr. Hawking appears to have made a mistake and for 30 years other physicists have tried to explain how his conjecture might be plausible. Conjectures that anti-matter contains negative energy (wrong) and conjecture that in order to conserve energy, energy must some how tunnel out of the black hole (again wrong).

 

Recent speculation predicting the existence of dark energy tends to suggest that quantum effects may cause black hole growth, Reverse Hawking Radiation. Observational evidence of rapid growth for all but the most massive black holes tends to give some credibility to this conjecture.

[Klaynos]

It's because the energy for the particle outiside has to come from somewhere...

 

And that somewhere is the black hole...

 

You can think of the mechanisim for this being due to conservation of energy the one that falls into the black hole must have had negative energy... Or that they get their energy from the gravitational field therefore taking energy from that.... I think nice word descriptions of how it really works fails a bit and you need to apply quantum field theory in a curved space-time to really see what's going on...

 

30 years ago Dr. Hawking appears to have made a mistake and for 30 years other physicists have tried to explain how his conjecture might be plausible. Conjectures that anti-matter contains negative energy (wrong) and conjecture that in order to conserve energy, energy must some how tunnel out of the black hole (again wrong).

 

Why don't you write and publish a correction paper then?

Edited August 11, 2008 by Klaynos
multiple post merged

[Arch2008]

Bearing in mind that none of this is supported by observational evidence, this is the theory:

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

Supposedly, the infalling particle is made of “negative energy” and causes the singularity to lose mass. Simply put, the particle with negative mass falls in so that the real particle can get away.

[Yreval]

Thanks for the answers, guys. I appreciate not only hearing the explanations of how the theory works, but also getting to know that my confusion was understandable.

[ajb]

I have never really liked the explanation of Hawking radiation as negative energy virtual particles falling into the black-hole. The calculations of Hawking radiation don't really describe this.

 

It is really to do with there being no unique vacuum on a curved space-time and the fact that this leads to different observers not agreeing on the vacuum. Some will see what someone called the vacuum as being filled.

 

The closest to particle and anti-particle "splitting" is when you decompose the classical fields into positive and negative frequencies. These correspond to particles and antiparticles.

 

How you do this splitting defines the vacuum. If you do this splitting another way then you will have different vacuum. In flat space-time the Poincare symmetry allows you to select the "best" vacuum. And we all agree on it. This is not the case on curved space-times where although we have local Poincare invariance, we have no way to singling out a preferred vacuum.

 

Another way of putting it is that we have many (infinite) representations of the CCR or CAR (canonical commutation /anticommuataion relations). These are related by a Bogoliubov transformation.

 

Anyway, when you calculate Hawking radiation you can either consider the positive frequency solutions and an observer far away from the black hole and far in the future. Or you can consider the positive frequency solutions and an observer far in the past before the black hole formed. You will get the same result.

 

I will stress this point again, black hole temperature and evaporation etc are really due to the fact there is no preferred vacuum on a curved space-time. It is the lack of this vacuum that makes it difficult to associate particles states to the fields.

 

So, this splitting into positive and negative frequencies is the closest thing to anti-particles falling in. Maybe there is a way to relate the calculation to the particle anti-particle pairs using a Bogoliubov transformation? I have not come across any such explanation. But then I am no expert on this!

 

Does anyone know when this heuristic explanation first came about and who made it?

[Arch2008]

According to NASA, there are two ways to look at this:

 

“You are correct that there are multiple ways to visualize the generation of Hawking radiation. The first is indeed the separation of virtual matter/antimatter pairs by the intense gravitational force exerted by the black hole and the other is the quantum tunneling of a particle, such as a photon out of the black hole event horizon.”

http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/011125b.html

 

However I suppose that the real “culprit” for particle creation is Hawking.

Here is Hawking’s paper:

http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.cmp/1103899181

[ajb]

A fairly recent discovery is that Hawking radiation is precisely what is needed to cancel a gravitational anomaly. This was discovered by Robinson and Wilczek in 2005 [1].

 

This is an extremely interesting way to view it. Hawking radiation is required to keep general covariance in semiclassical gravity.

 

 

[1]S. P. Robinson and F. Wilczek, Phys. Rev. Lett. 95, 011303 (2005)

[Arch2008]

I suppose that what we really need is for the LHC to make a mini black hole so that we can get some actual observational evidence. It's too bad that Congress didn't fund that super collider in Texas. To paraphrase Tom Hanks in "The Bonfire of the Vanities":

"All I need is a measely, f-ing billion dollars."