Hawking radiation

[swansont]

In another thread I saw a comment about Hawking radiation, which I found confusing, and it's repeated in other online sources: that Hawking radiation is electromagnetic. I'm not a cosmologist, so I'm missing something here.

The common explanation for Hawking radiation (e.g. https://www.universetoday.com/40856/hawking-radiation/) is

"this process is also called black hole evaporation. In brief, this theoretical process works like this: particle-antiparticle pairs are constantly being produced and rapidly disappear (through annihilation); these pairs are virtual pairs, and their existence (if something virtual can be said to exist!) is a certain consequence of the Uncertainty Principle. Normally, we don’t ever see either the particle or antiparticle of these pairs, and only know of their existence through effects like the Casimir effect. However, if one such virtual pair pops into existence near the event horizon of a black hole, one may cross it while the other escapes; and the black hole thus loses mass. A long way away from the event horizon, this looks just like black body radiation."

So the process creates particles, but the radiation is deemed electromagnetic. That does not jibe. What is being glossed over here, in the transition from particles, to electromagnetic radiation? Is it as simple as the particles interacting and creating EM radiation, and that radiation has a blackbody spectrum? (not unlike the CMBR having a blackbody spectrum)? And that this is just a terminology shortcut, when really it's the signature being electromagnetic, even though the radiation itself is comprised of massive particles?

 

 

[MigL]

It is my understanding that ( at least in the explanation for HR you mention ) virtual particles can be any particles.
Ranging from photons, to electrons and protons, and even more 'massive' short-lived particles.
The 'mass' of these particles is dependent on the energy of the event which led to their production.
This would be the characteristic energy of the black body radiation.

[swansont]

48 minutes ago, MigL said:

It is my understanding that ( at least in the explanation for HR you mention ) virtual particles can be any particles.
Ranging from photons, to electrons and protons, and even more 'massive' short-lived particles.
The 'mass' of these particles is dependent on the energy of the event which led to their production.
This would be the characteristic energy of the black body radiation.

But if they are non-photons, they are not electromagnetic. And there are descriptions that say Hawking radiation is electromagnetic. That's why I am suspecting that the EM signature is that of a blackbody, but the original radiation is not necessarily EM.

[MigL]

I have not seen descriptions that HR is assumed to be purely EM.
Then again, you can describe temperature in terms of energy, and mass in terms of energy, so maybe sometimes talking about one thing, we understand it about something else.

[Airbrush]

3 hours ago, swansont said:

...if one such virtual pair pops into existence near the event horizon of a black hole, one may cross it while the other escapes; and the black hole thus loses mass. 

My questions about Hawking Radiation:  (1) When 2 virtual particles appear, how far apart are they?  It is hard to imagine how one of the pair enters the black hole, but the other one doesn't.  (2) How many of these virtual pairs can pop into existence in a cubic centimeter during one second?

Edited April 6, 2020 by Airbrush

[StringJunky]

18 minutes ago, Airbrush said:

My questions about Hawking Radiation:  (1) When 2 virtual particles appear, how far apart are they?  It is hard to imagine how one of the pair enters the black hole, but the other one doesn't.  (2) How many of these virtual pairs can pop into existence in a cubic centimeter during one second?

This is swansont's thread. You are hijacking.

Edited April 6, 2020 by StringJunky

[koti]

3 hours ago, swansont said:

So the process creates particles, but the radiation is deemed electromagnetic. That does not jibe. What is being glossed over here, in the transition from particles, to electromagnetic radiation? Is it as simple as the particles interacting and creating EM radiation, and that radiation has a blackbody spectrum? (not unlike the CMBR having a blackbody spectrum)? And that this is just a terminology shortcut, when really it's the signature being electromagnetic, even though the radiation itself is comprised of massive particles?

 

 

Heres a relevant excerpt from Hawkings Brief History of Time:

"...However, when I did the calculation, I found, to my surprise and annoyance, that even non-rotating black holes should apparently create and emit particles at a steady rate. At first I thought that this emission indicated that one of the approximations I had used was not valid. I was afraid that if Bekenstein found out about it, he would use it as a further argument to support his ideas about the entropy of black holes, which I still did not like. However, the more I thought about it, the more it seemed that the approximations really ought to hold. But what finally convinced me that the emission was real was that the spectrum of the emitted particles was exactly that which would be emitted by a hot body, and that the black hole was emitting particles at exactly the correct rate to prevent violations of the second law. Since then the calculations have been repeated in a number of different forms by other people. They all confirm that a black hole ought to emit particles and radiation as if it were a hot body with a temperature that depends only on the black hole’s mass: the higher the mass, the lower the temperature."

 

[swansont]

36 minutes ago, koti said:

Heres a relevant excerpt from Hawkings Brief History of Time:

"...However, when I did the calculation, I found, to my surprise and annoyance, that even non-rotating black holes should apparently create and emit particles at a steady rate. At first I thought that this emission indicated that one of the approximations I had used was not valid. I was afraid that if Bekenstein found out about it, he would use it as a further argument to support his ideas about the entropy of black holes, which I still did not like. However, the more I thought about it, the more it seemed that the approximations really ought to hold. But what finally convinced me that the emission was real was that the spectrum of the emitted particles was exactly that which would be emitted by a hot body, and that the black hole was emitting particles at exactly the correct rate to prevent violations of the second law. Since then the calculations have been repeated in a number of different forms by other people. They all confirm that a black hole ought to emit particles and radiation as if it were a hot body with a temperature that depends only on the black hole’s mass: the higher the mass, the lower the temperature."

 

Interesting; Planck' s law depends on the frequency of the EM radiation, so something has to be different if the particles are not photons, but you still have a temperature for thermal particles. You could, for example consider a "perfect absorber" of atoms and subject it to an ideal gas at some temperature — it absorbs all the energy of the atoms, and you could model a perfect emitter as well (you have trouble with not having fundamental bosons as the particles, since there are conservation laws to worry about, but Hawking radiation avoids this)

[koti]

3 minutes ago, swansont said:

Interesting; Planck' s law depends on the frequency of the EM radiation, so something has to be different if the particles are not photons, but you still have a temperature for thermal particles. You could, for example consider a "perfect absorber" of atoms and subject it to an ideal gas at some temperature — it absorbs all the energy of the atoms, and you could model a perfect emitter as well (you have trouble with not having fundamental bosons as the particles, since there are conservation laws to worry about, but Hawking radiation avoids this)

I'm not sure if I understand this correctly but the virtual particles are emitted not from the inside of the BH but from the space very close to the edge of the event horizon which contains fields with values which are not zero so the uncertainty principle is not violated. PM me if you want the whole thing.

[MigL]

So is the issue the fact that the radiation is particulate in nature and not EMR, or is the issue the fact that it is non thermal ?

The two virtual particle interpretation, where one falls through the EH and the other escapes and becomes real at the expense of the BH's mass-energy, is just one of many. Another involves quantum fluctuations just inside the EH, where one particle tunnels out; but that still involves particles.
This interpretation is straight out of wiki at    https://en.wikipedia.org/wiki/Hawking_radiation#Trans-Planckian_problem

"Hawking radiation is required by the Unruh effect and the equivalence principle applied to black hole horizons. Close to the event horizon of a black hole, a local observer must accelerate to keep from falling in. An accelerating observer sees a thermal bath of particles that pop out of the local acceleration horizon, turn around, and free-fall back in. The condition of local thermal equilibrium implies that the consistent extension of this local thermal bath has a finite temperature at infinity, which implies that some of these particles emitted by the horizon are not reabsorbed and become outgoing Hawking radiation."

The difference between HR and black body radiation is summarized as ...

"An important difference between the black hole radiation as computed by Hawking and thermal radiation emitted from a black body is that the latter is statistical in nature, and only its average satisfies what is known as Planck's law of black-body radiation, while the former fits the data better. Thus thermal radiation contains information about the body that emitted it, while Hawking radiation seems to contain no such information, and depends only on the mass, angular momentum, and charge of the black hole (the no-hair theorem). This leads to the black hole information paradox.

However, according to the conjectured gauge-gravity duality (also known as the AdS/CFT correspondence), black holes in certain cases (and perhaps in general) are equivalent to solutions of quantum field theory at a non-zero temperature. This means that no information loss is expected in black holes (since the theory permits no such loss) and the radiation emitted by a black hole is probably the usual thermal radiation. If this is correct, then Hawking's original calculation should be corrected, though it is not known how."

Also from Wiki at      https://en.wikipedia.org/wiki/Hawking_radiation#Emission_process

Hawking's original calculation and it correction ( mentioned above ) is known as the trans-Planckian problem because of the infinite frequency of the radiation that results at the EH as seen by a distant observer. More information on the trans-Planckian problem at the 1st link I provided.

Edited April 6, 2020 by MigL

[swansont]

3 hours ago, koti said:

I'm not sure if I understand this correctly but the virtual particles are emitted not from the inside of the BH but from the space very close to the edge of the event horizon which contains fields with values which are not zero so the uncertainty principle is not violated. PM me if you want the whole thing.

I wasn’t talking about virtual particles. I was talking about a thermal distribution of massive particles. The only bit in that post that’s about Hawking radiation is the last comment.

47 minutes ago, MigL said:

So is the issue the fact that the radiation is particulate in nature and not EMR, or is the issue the fact that it is non thermal ?

The first one. That it’s explained as particles in describing the mechanism, but claimed to be EMR - in the same article.

[MigL]

There are some caveats, like the fact that the analysis is from 1976, using 2 neutrino flavors. and zero rest mass, but here are the expected radiation types, also from        https://en.wikipedia.org/wiki/Hawking_radiation#Emission_process

"For a mass much larger than 10¹⁷ grams, Page deduces that electron emission can be ignored, and that black holes of mass M in grams evaporate via massless electron and muon neutrinos, photons, and gravitons in a time τ of

τ = 8.66 × 10 − 27 [ M g ] 3 s . {\displaystyle \tau =8.66\times 10^{-27}\;\left[{\frac {M}{\mathrm {g} }}\right]^{3}\;\mathrm {s} \,.}

For a mass much smaller than 10¹⁷ g, but much larger than 5×10¹⁴ g, the emission of ultrarelativistic electrons and positrons will accelerate the evaporation, giving a lifetime of

τ = 4.8 × 10 − 27 [ M g ] 3 s . {\displaystyle \tau =4.8\times 10^{-27}\;\left[{\frac {M}{\mathrm {g} }}\right]^{3}\;\mathrm {s} \,.}  "

IOW the smaller the BH, the more energy it is able to invest in particle production.

 

Ooops.
That didn't copy/paste too well.

Edited April 6, 2020 by MigL