# Virtual Particles and Hawking radiation

• rhenretta
In summary,Hawking radiation is caused by virtual particles coming into existence near the event horizon of a black hole. The virtual particles come in matter / anti matter pairs, and in some way result in the eventual evaporation of the black hole. I had been under the impression this was accomplished because the antimatter particle would have a stronger attraction to the black hole, and would annihilate, while the matter particle would be ejected. This would result in a net loss of mass in the black hole. The problem is, I can't remember why the antimatter particle would be the one attracted, and if it is random chance with equal opportunity which falls in, the black hole would gain mass as often as it would lose mass andf

#### rhenretta

I was having a conversation with a physicist on Facebook (author of a book I rather enjoyed - "Users guide to the universe"), and he let the conversation end without my question ever being fully answered. Perhaps someone here can help explain this to me.

I'll paste the entire conversation, but the executive summary is:

Hawking radiation is caused by virtual particles coming into existence near the event horizon of a black hole. The virtual particles come in matter / anti matter pairs, and in some way result in the eventual evaporation of the black hole. I had been under the impression this was accomplished because the antimatter particle would have a stronger attraction to the black hole, and would annihilate, while the matter particle would be ejected. This would result in a net loss of mass in the black hole.

The problem is, I can't remember why the antimatter particle would be the one attracted, and if it is random chance with equal opportunity which falls in, the black hole would gain mass as often as it would lose mass and would never actually evaporate.

My question is, by what mechanism does Hawking Radiation cause the mass of the black hole to decrease over time

#
Richard Henretta
You confuse me, sir...

Quote
[But as luck would have it, the electron falls beneath the event horizon of the black hole and is gone forever. The positron, (like every malfunction on the holodeck ever), goes from being virtual to real, and flies off into the cosmos.]

I thought the particle gets emitted, and the anti-particle falls into the black hole annihilating, thus resulting in the eventual evaporation of the black hole? If the electron falls and the positron is emitted wouldn't the mass of the black hole increase over time?

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A User's Guide to the Universe
Either one can fall in. The universe doesn't distinguish between the two, so it's random luck which one gets eaten. In practice (in my example), the positron will hit an electron eventually and annihilate, producing photons. More commonly, the "pair" will be two photons (since photons are their own anti-particles), one of which will fall in, and one of which will escape.

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Richard Henretta
Black hole evaporation can't happen then if it is random luck.

If the antiparticle falls in, and the particle escapes: the mass of the black hole will decrease

If the particle falls in, and the antiparticle escapes: the mass of the black hole will increase

In any case with photons, no change to mass occurs (which I still don't understand since photons have energy and energy equates into mass)

If we are talking random chance, then the top two cases will happen approximately the same number of times, resulting in no change to the mass.

I remember reading somewhere an explanation on why the antimatter particle had more attraction than the matter particle, but for the life of me I can't remember what it was. In fact, based on my rudimentary understand of physics, I see no reason why that would be the case anyway. So, do black holes not evaporate over time?

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A User's Guide to the Universe
No no. The masses of both are positive. Forget about the particle that falls in. The particle that escapes carries energy away, and since ultimately energy borrowed from the vacuum must be paid back, that energy comes from the mass-energy of the black hole, causing it to evaporate.

#
Richard Henretta
But then by what mechanism is it paid back? If the energy of both particles is positive, and one particle falls into the black hole, how does that decrease the mass of the black hole?

Also, if anyone is wondering the context of this conversation, it stemmed from this article:
http://io9.com/5731463/are-virtual-particles-for-real

Both particles and antiparticles have positive mass, so it doesn't matter which one escapes the event horizon--the black hole loses mass in either case.

That is how Dr Goldberg explained it too, but if a particle of positive mass falls into the black hole, the mass of the black hole will increase, so what mechanism causes the black hole to actually lose mass? If the antimatter particle was the one to fall in, then the mass would decrease because it would annihilate with the matter in the black hole, and convert it to photons.

Matter can be turned into energy and vice versa. So it doesn't make sense to talk solely about the mass inside the black hole, you have to talk about the total energy content.

In order to produce the particle/anti-particle pair in the first place, it costs some amount of energy. So in the instant after the pair production, the mass of the system has increased, and the energy has decreased accordingly. So far, everything still balances. However, if one of the particles is on the other side of the event horizon, it can escape the black hole, meaning that what's left inside the black hole now has less mass/energy than before, so energy has left the black hole.

So to answer your question in the way that you phrased it in your original conversation: the way that the energy is 'paid back' is that you spent it up front to create the particles in the first place. So you were already in 'debt' after that happened, and if one of the particles escapes, you can never balance it again, leading to a net loss.

In order to produce the particle/anti-particle pair in the first place, it costs some amount of energy. So in the instant after the pair production, the mass of the system has increased, and the energy has decreased accordingly.

I'm lost here, the energy to create the pair doesn't come from the black hole, but from the vacuum energy, hence the virtual particles. If we are talking only uncertainty principle, it is possible for the particles inside the black hole to appear outside the event horizon, but I would think the chance of this happening would be a lot less than hawking radiation theory calls for. However, that being said, it would explain a mechanism by which black holes evaporate. This is far different from virtual particles however, which pop in and out of existence, and only get around the conservation laws because they annihilate before they can be measured. If Hawking radiation is due to virtual particles, as far as I can tell this would violate conservation.

An unfortunate feature of the virtual particle view is that people who have just read popularizations but don't know any field theory ascribe all sorts of properties to virtual particles that they just don't have. They then get mentally tied up in knots trying to reconcile this view with reality.

It is possible to discuss Hawking radiation without any reference to virtual particles whatsoever. I don't have the original Hawking paper in front of me, but I am pretty sure that he didn't use them either. There's a very nice paper by Davies (Rep. Prog. Phys. 41, 1313(1979)) that works this out more-or-less classically. It explains the relationship between Hawking and Unruh radiation, which is very hard to do with the virtual particle picture.

That sounds like the perfect paper to read to answer my question... I don't suppose there is any resource out there to read these papers without having to pay \$88

You should Google Davies' web page.

hah! got it, thanks :)

Afaik Hawking constructed the "particles" and "antiparicles" according to standard QFT using positive and negative frequencies. Then he observed that this can't be done uniquely for the complete spacetime but that one needs something like a matching condition at the horizon. So the choice of vacuum states differs in the presence of a horizon (see also Unruh effect).

Afaik discussing a simple step function as potential in relativistic QM (not QFT) mimics this affect and produces a current of outgoing "real" particles. This has nothing to do with virtual particles.

I have to find Hawking paper which should be available on the internet for free.

An unfortunate feature of the virtual particle view is that people who have just read popularizations but don't know any field theory ascribe all sorts of properties to virtual particles that they just don't have. They then get mentally tied up in knots trying to reconcile this view with reality.

It is possible to discuss Hawking radiation without any reference to virtual particles whatsoever. I don't have the original Hawking paper in front of me, but I am pretty sure that he didn't use them either.

In
http://projecteuclid.org/DPubS/Repo...ew=body&id=pdf_1&handle=euclid.cmp/1103899181
he mentions it precisely once, in the middle of p. 202:
''Just outside the event horizon there will be virtual pairs of particles, one with negative
energy and one with positive energy. The negative particle is in a region which
is classically forbidden but it can tunnel through the event horizon to the region
inside the black hole where the Killing vector which represents time translations
is spacelike. In this region the particle can exist as a real particle with a timelike
momentum vector''

But he says at the bottom of the page:
''It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally.''

What happens is that the high energy of the gravitational field of the black hole creates real particle-antiparticle pairs -- that before that event it could be viewed in terms of Feynman diagrams as virtual is completely irrelevant to his argument. One of the particles is swallowed by the black hole, the other is radiated away. As a result, the black hole loses radiation, hence total energy, and its effective mass decreases because of mass-energy equivalence.

An unfortunate feature of the virtual particle view is that people who have just read popularizations but don't know any field theory ascribe all sorts of properties to virtual particles that they just don't have. They then get mentally tied up in knots trying to reconcile this view with reality.

It is possible to discuss Hawking radiation without any reference to virtual particles whatsoever. I don't have the original Hawking paper in front of me, but I am pretty sure that he didn't use them either. There's a very nice paper by Davies (Rep. Prog. Phys. 41, 1313(1979)) that works this out more-or-less classically. It explains the relationship between Hawking and Unruh radiation, which is very hard to do with the virtual particle picture.

I've been actually looking for explanation which does not use virtual particles as basis, because one very experienced quantum physicist told me that he saw truly immense number of expert works regarding Hawking's radiation, but neither shows the use of virtual particles. Virtual particles are only present in popular literature, and actually to be perfectly honest, popular literature has many holes.
Experts are actually using Bogoliubov transformation as basis for Hawking's radiation, Unruh effect and etc...
The question is what is the main explanation for Hawking's radiation without using virtual particles and with using Bogoliubov transformation as basis?

This is why I'm in search what exactly is explanation of Hawking's radiation without using virtual particles?
I still haven't seen it, but I now it's there somewhere, I just hope I will find it.
Of course, even that explanation has its holes as well, from what I've heard.

I would try to avoid any 'explanation' and just refer to the math. It says that there is a "mismatch" or non-uniqueness of vacuum states at horizons.

I've been actually looking for explanation which does not use virtual particles as basis, because one very experienced quantum physicist told me that he saw truly immense number of expert works regarding Hawking's radiation, but neither shows the use of virtual particles. Virtual particles are only present in popular literature, and actually to be perfectly honest, popular literature has many holes.
Experts are actually using Bogoliubov transformation as basis for Hawking's radiation, Unruh effect and etc...
The question is what is the main explanation for Hawking's radiation without using virtual particles and with using Bogoliubov transformation as basis?

This is why I'm in search what exactly is explanation of Hawking's radiation without using virtual particles?
I still haven't seen it, but I now it's there somewhere, I just hope I will find it.
Of course, even that explanation has its holes as well, from what I've heard.
Hi No-where-man,

As you know, I have already suggested
http://xxx.lanl.gov/abs/gr-qc/0308048
to you at another forum.

If it is still too difficult for you, try Secs. 9.5 and 9.6 of
http://xxx.lanl.gov/abs/quant-ph/0609163