# I What is the mechanism behind Hawking radiation?

#### Grinkle

Gold Member
I thought Hawking radiation was a virtual particle pair emerging from nothing, one particle falling into the event horizon and the other particle tunneling out of the event horizon.

https://www.physicsforums.com/insights/vacuum-fluctuation-myth/

and now I think a virtual particle pair is always nothing, a pair never emerges from nothing in any observable manner.

I am left wondering where the particles come from that constitute Hawking radiation.

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#### vanhees71

Gold Member
A black hole is far from being nothing. That's why there's also nothing just popping out of nothing (aka. the vacuum).

#### phinds

Gold Member
I thought Hawking radiation was a virtual particle pair emerging from nothing, one particle falling into the event horizon and the other particle tunneling out of the event horizon.

https://www.physicsforums.com/insights/vacuum-fluctuation-myth/

and now I think a virtual particle pair is always nothing, a pair never emerges from nothing in any observable manner.

I am left wondering where the particles come from that constitute Hawking radiation.
As Hawking himself has said, the "virtual particle" description is NOT actually what's happening. It was just the best he could do to translate into English something that really can only be explained with math.

#### Grinkle

Gold Member
At the end of the first paragraph of my article I gave a link that answers this.
Thanks for the reminder. From the post -

"The dry facts are that two real particles (e.g., two photons, or an electron and a positron) are created from the energy in the very strong gravitational field near the horizon of the black hole - from two gravitons or from an external gravitational field, not from the vacuum."

Very digestible!

#### SerbianQuantum

Thanks for the reminder. From the post -

"The dry facts are that two real particles (e.g., two photons, or an electron and a positron) are created from the energy in the very strong gravitational field near the horizon of the black hole - from two gravitons or from an external gravitational field, not from the vacuum."

Very digestible!
The dry facts? Hardly so since gravitons are mentioned. They are still hypothetical particles since they haven't been experimentally proven to exist.

#### A. Neumaier

The dry facts? Hardly so since gravitons are mentioned. They are still hypothetical particles since they haven't been experimentally proven to exist.
That's why I gave two (in quantum gravity possibly equivalent) alternatives, and had added a postscript explaining more details. Quantum field theory in an external classical gravitational field (such as the one created by a classical black hole) has none of the problems of full quantum gravity, and is all needed! I now also edited the original sentence to make this even more clear!

#### SerbianQuantum

Yes but you need to have in mind:

"The dry facts are that two real particles (e.g., two photons, or an electron and a positron) are created from the energy in the very strong gravitational field near the horizon of the black hole - from two gravitons or from an external gravitational field ..."

This is an educated guess.

"...not from the vacuum."

This is a factual statement.

where italic is a factual statement and bold is for educated guess, just to clear it up.

Thank you for clearing up what your statements actually are, in great context.

#### A. Neumaier

This is an educated guess.
''from a strong external field'' is not a guess. It is a prediction of traditional quantum field theory, and is experimentally verified in the case of strong external electromagnetic field. Strong external fields with energies significantly above the pair creation energy threshold necessarily create the corresponding particle pairs.

#### vanhees71

Gold Member
That's very interesting! In which experiment is the Schwinger pair-production mechanism verified? I'd say that could lead to a Nobel prize!

#### A. Neumaier

That's very interesting! In which experiment is the Schwinger pair-production mechanism verified? I'd say that could lead to a Nobel prize!
I though it was verified; need to check. In any case I had read some time ago quite a number of papers on this, though I must admit that I had only looked at the theoretical side of the problem.

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#### vanhees71

Gold Member
This would be a sensation! As far as I know, so far there's no experimental proof, although there are many groups trying to prove it using very strong laser fields. Of course, the Schwinger effect is an inevitable consequence of standard QFT. If it can be proven, it's another hint that QED is the right game (also in the strong-field case, which extends the usual empirical tests to this realm), if it's unanimously disproven it's the first hint that QED (and then perhaps any local QFT) is not the full truth!

#### SerbianQuantum

''from a strong external field'' is not a guess. It is a prediction of traditional quantum field theory, and is experimentally verified in the case of strong external electromagnetic field. Strong external fields with energies significantly above the pair creation energy threshold necessarily create the corresponding particle pairs.
You forgot the "or...". The entire sentence is an educated guess since you wrote "two gravitons or...".

#### Demystifier

2018 Award
This would be a sensation! As far as I know, so far there's no experimental proof, although there are many groups trying to prove it using very strong laser fields.
Why would that be a sensation? A collision of the laser beams can also be thought of as a collision of photons, and I see nothing sensational about creation of electron-positron pairs from collision of sufficiently energetic photons.

#### Haelfix

Note that the collision of photons that then output an electron positron pair is a decidedly perturbative problem in QED, whereas the Schwinger effect requires a strong field source and is a decidedly nonperturbative effect (it requires summing a whole class of Feynman diagrams). The result might look the same, but the fundamental mechanism is different.

There would even be an ambiguity with lasers, as they really simulate a timevarying inhomogenous field at the focal point, and so one might complain about the results. In any event as far as I know, no such experiment has the necessary laser intensity to even probe such a thing, so it remains a moot point.

#### mfb

Mentor
Pair production from photon collisions is not new, but here the photons need a high energy (1 MeV invariant mass for a pair). Schwinger pair production would work at lower energies. The lasers are not there yet (the time variation should not be an issue if the laser frequency is reasonable), maybe in a few years.

Photon-photon scattering is another effect waiting for experimental confirmation. The LHC ion collisions might make it possible.

Edit: Oh, one day ago!
I'll split the discussion if it continues.

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Staff Emeritus

#### mfb

Mentor
This has nothing to do with the Schwinger pair production - which itself is off-topic here.

#### strangerep

This would be a sensation! As far as I know, so far there's no experimental proof, although there are many groups trying to prove it using very strong laser fields. Of course, the Schwinger effect is an inevitable consequence of standard QFT. If it can be proven, it's another hint that QED is the right game (also in the strong-field case, which extends the usual empirical tests to this realm), if it's unanimously disproven it's the first hint that QED (and then perhaps any local QFT) is not the full truth!
??? Afaik, pair production in superstrong EM fields has been experimentally known for decades in heavy ion collision experiments, where immense EM fields are created temporarily as the ions meet.

One of the earliest papers is this one by the late Walter Greiner and colleagues. Greiner subsequently did a lot of research on heavy ion collision physics, and also authored several related books, e.g., this rather old book. IIRC, the subject is also mentioned in some of his later books. (Try googling for: greiner strong field heavy ion )

Note that one needs to distinguish between:

- Pair production from immense EM fields created in heavy ion collisions;

- Delbruck scattering of electrons off the EM field of a nucleus;

- Light-by-light scattering, which is related to Delbruck scattering, but more difficult to achieve experimentally, iiuc.

mfb said:
[...] Schwinger pair production - which itself is off-topic here.
Possibly, although it's not clear (at least to me) whether Hawking radiation (and its cousins) are primarily related to the strength of the curvature, or that many radiation-producing horizons seem to be Killing horizons. I.e., which is the more fundamental feature enabling the radiation effect? Strong curvature or Killing horizon? For Unruh radiation it's the latter, right?

In both cases (Hawking/Unruh radiation, and Schwinger pair production), each effect arises (theoretically) via unitarily inequivalent representations (i.e., inequivalent vacua) of the basic quantum fields, iiuc.

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#### haushofer

How I like to explain it: what we call particles and antiparticles depend on how we divide the quantum field in positive and negative frequencies. However, this procedure depends on the observer. Just like a force in newtonian gravity is only a tensor under Galilei-transformations, the frequency splitting changes if one starts to accelerate. Hence the notion of the vacuum. According to the equivalence principle, the same should apply outside a black hole.

#### Haelfix

Possibly, although it's not clear (at least to me) whether Hawking radiation (and its cousins) are primarily related to the strength of the curvature, or that many radiation-producing horizons seem to be Killing horizons. I.e., which is the more fundamental feature enabling the radiation effect? Strong curvature or Killing horizon?
I would say that it is the time dependance of the metric that allows for particle production to occur. Strictly speaking, this has nothing to do with blackholes, or even with the magnitude of the curvature.

For the moment, ignore the case of a blackhole, and simply ask whether a star with a radius of say 8 GM radiates particles (assume a scalar field evolving within the background geometry). The answer is that in general it does not. The physical portion of the metric is time independant, and no particle production will take place. However if you were to allow it to lose some of its mass (say by a supernovae) and its radius shrunk to say 6 GM over a time frame of order GM, then you will in general detect particles with wavelengths of the same order (eg ~GM) via the usual field theory calculation.. Once the star has settled down, particle production of course stops. These particles (unlike Unruh radiation) will register and do work on a detector located at asymptotic infinity.

So whats different with a blackhole? Naively, the Schwarschild solution seems time independant, when viewed in Schwarschild coordinates. However, this is an artifact of a bad coordinate choice. When you pick better coordinates and focus on a region that straddles the horizon, you will observe the presence of stretching factors as can be seen by slicing the spacetime with spacelike surfaces that are regular across the horizon and taking appropriate time steps. The interesting point is that it is precisely b/c there exists no timelike killing vector in the geometry that forbids us from ever having a time independant evolution (this gets to your point about the presence of a Killing horizon).

The full Hawking calculation will then take into account the entanglement between vacuum modes outside the horizon and modes inside the horizon, and the particle production will be allowed to become 'real' as it escapes to infinity (again unlike the case of Unruh radiation).

#### vanhees71

Gold Member
That's not what's usually meant when one speaks about the Schwinger effect. The original Schwinger effect is about the spontaneous creation of electron-positron pairs due to the presence of a strong homogeneous electrostatic field. Nowadays one is considering this process rather for very strong laser light. What's reported in the above cited paper (I've unfortunately no access to) is the process $\gamma \gamma \rightarrow \text{e}^+ \text{e}^-$, i.e., the inverse process to pair annihilation to two photons.
This has nothing to do with the Schwinger pair production - which itself is off-topic here.
It's of course not off-topic here, but the perfect analogue of Hawking radation, which is due to strong gravitational fields around the horizon of a black hole. Here we consider pair creation due to an electromagnetic field. The difference is that we understand QED much better than quantum gravity, although here you have a classical gravitational field coupling to quantized matter fields, although even this is pretty complicated and not fully free of controversy. Another QED analogue to Hawking radiation is Unruh radiation, i.e., the formulation of QED in non-inertial reference frames which mimics of course local aspects of a gravitational field due to the equivalence principle.

#### vanhees71

Gold Member
??? Afaik, pair production in superstrong EM fields has been experimentally known for decades in heavy ion collision experiments, where immense EM fields are created temporarily as the ions meet.

One of the earliest papers is this one by the late Walter Greiner and colleagues. Greiner subsequently did a lot of research on heavy ion collision physics, and also authored several related books, e.g., this rather old book. IIRC, the subject is also mentioned in some of his later books. (Try googling for: greiner strong field heavy ion )
I'm well aware of this work. I got my PhD at GSI. Unfortunately the Schwinger mechanism in heavy-ion experiments could never be confirmed finally, and today it's commonly accepted that the effect has not been observed. The reason is that the Schwinger pair production needs time, and the strong fields in heavy-ion collisions last only for a very short time.

Nevertheless, of course the theory book on QED for strong fields is very valuable:

http://inspirehep.net/record/222557?ln=en

#### strangerep

[...]
So whats different with a blackhole? Naively, the Schwarschild solution seems time independant, when viewed in Schwarschild coordinates. However, this is an artifact of a bad coordinate choice. When you pick better coordinates [...]
Which coordinates?
and focus on a region that straddles the horizon, you will observe the presence of stretching factors as can be seen by slicing the spacetime with spacelike surfaces that are regular across the horizon and taking appropriate time steps.
Can you suggest a link or reference that elaborates this in more detail, pls?

In ordinary (most?) coordinate systems used with Schwarzschild geometry, $\partial_t$ is a Killing vector. The Killing equation is a tensor equation, so the most one could do with different coordinates is transform $\partial_t$ into something else. But it will still be a Killing vector. What am I missing?

The full Hawking calculation will then take into account the entanglement between vacuum modes outside the horizon and modes inside the horizon, and the particle production will be allowed to become 'real' as it escapes to infinity (again unlike the case of Unruh radiation).
What's the criterion for deciding whether particle production is 'real'. Becoming on-shell at infinity?

"What is the mechanism behind Hawking radiation?"

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