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BrotherLaz
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I've looked around and all information on Hawking radiation is either so popular as to be illogical or filled with scary math and still illogical.

If I understand correctly, Hawking radiation is when imaginary particle pairs form in the vacuum and the antiparticle falls in, causing the black hole to lose mass while the particle escapes and turns real because 'the black hole gave its energy to it'. Repeat until black hole disappears. Questions:

- How does the mere presence of a gravity field cause imaginary particles to become real? Is this just because they can't get to each other to annihilate?
- How does swallowing a particle with positive mass cause the black hole to lose mass?
- Why won't the real particle (which is attracted to the antiparticle) just follow the other into the black hole?
- In a contained system, when the black hole has shrunk to the mass of one particle and it emits one particle with kinetic energy and vanishes, is this reversible? Can you take an arbitrary particle and turn it into a black hole using kinetic energy?
- A bit OT: if you take an uniformly orbiting object with a plunger assembly (that goes fowards and backwards), you are creating constant back and forth acceleration that seems to go on forever if there are no losses from friction. The Unruh effect should heat the plunger. Does this mean you are getting perpetual free heating?

Sorry for the stupid questions...

doogly
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### Re: Explain Hawking radiation plz?...

Second question first: to the extent that you have free acceleration, you can have free heating. You can't have free acceleration. Physics is saved!

Hawking radiation: you are right, the heuristic explanation of Hawking radiation is riddled with conceptual flaws. If you want it to make sense, you have to stop worrying and learn to love the math. The actual calculation has nothing to do with virtual/real particles whatsoever. In fact a principal lesson of QFT in curved space is that the particle concept is not very useful at all. It's best to just keep your focus on the fields all the time. It is sort of like in special relativity, when distance and time get all funky, but proper length is the concept that remains well behaved.
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Xanthir
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### Re: Explain Hawking radiation plz?...

BrotherLaz wrote:- How does the mere presence of a gravity field cause imaginary particles to become real? Is this just because they can't get to each other to annihilate?

Yes. If they can no longer annihilate, then they must be real.
- How does swallowing a particle with positive mass cause the black hole to lose mass?

It can't. Virtual particle pairs are *not* particle-antiparticle (if they were, the entire universe would explode spectacularly in constant matter-antimatter collisions). They're positive-energy/negative-energy. The universe doesn't like negative energy, so the particle that escapes becomes the positive-energy one, and the black hole eats the negative-energy one, losing energy in the process.
- Why won't the real particle (which is attracted to the antiparticle) just follow the other into the black hole?

Because when that happens, there's no radiation. Obviously some of the time that occurs, but when it doesn't, you have hawking radiation.
- In a contained system, when the black hole has shrunk to the mass of one particle and it emits one particle with kinetic energy and vanishes, is this reversible? Can you take an arbitrary particle and turn it into a black hole using kinetic energy?

If you can compress it enough, sure. That's all a blackhole is - a concentration of mass-energy that is compact enough that the potential energy gradient has an event horizon.
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hideki101
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### Re: Explain Hawking radiation plz?...

--"Imaginary" particles aren't imaginary, per see, but rather the fact that you can never observe them due to them being created and annihilating in a smaller time interval than anyone can ever measure. The following picture shows what happens:
Spoiler:
I15-49-Hawking.jpg (54.83 KiB) Viewed 2926 times
Because the total creation/annihilation process results in zero energy, and the particle given off results in a positive energy gain to the rest of the universe, the particle that entered the black hole imparts a negative energy to the total energy of the black hole. Then through the energy-mass conversion, this results in a net loss in mass as well. Also, if the other particle follows the other in, there's no net gain of energy to the universe, and thus, nothing happens.

interesting fact, the magnitude of the Hawking radiation from a black hole is supposed to be inversely related to the mass (and thus the radius) of the black hole. So the smaller the black hole is, the more radiation it emits. There's actually a point at which a black hole wouldn't shrink from Hawking radiation because the radiation would be below the ~3K of the Cosmic Background radiation. On the other side of the scale, a tiny black hole would probably look like a glowing ball, very soon before it evaporates entirely.
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doogly
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### Re: Explain Hawking radiation plz?...

OK, but I want to reiterate my warning that this pair creation picture is really just a hand wavy heuristic, and is probably misleading.
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Ingolifs
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### Re: Explain Hawking radiation plz?...

There's actually a point at which a black hole wouldn't shrink from Hawking radiation because the radiation would be below the ~3K of the Cosmic Background radiation.

So do you mean that radiation going in from the CMB is enough to offset the radiation lost through hawking evaporation?

Won't the CMB radiation decrease in energy as the universe gets older and larger anyway?
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Nande_Ebisu?
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### Re: Explain Hawking radiation plz?...

But even then, I assume it won't ever actually go away, so as long as its below a certain epsilon, which is the CMB, it won't disappear, and I assume the amount of hawking radiation decays faster than the magnitude of CMB, so after a certain point the black hole would be sustained almost exclusively based on CMB. (although I'm pulling most of this out of my ass, since almost everything I know about Hawking radiation has come out of this thread alone...)
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andyisagod
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### Re: Explain Hawking radiation plz?...

doogly wrote:OK, but I want to reiterate my warning that this pair creation picture is really just a hand wavy heuristic, and is probably misleading.

Xanthir wrote:Virtual particle pairs are *not* particle-antiparticle (if they were, the entire universe would explode spectacularly in constant matter-antimatter collisions). They're positive-energy/negative-energy. The universe doesn't like negative energy, so the particle that escapes becomes the positive-energy one, and the black hole eats the negative-energy one, losing energy in the process.

By what process does the universe not like negative energy particles but black holes do? I was under the impression that the reasoning given for this kind of explanation is that you have a virtual particle premoted to a real particle, this would cause problems for energy conservation since the energy has to come from somewhere and the effect is caused by the black holes horizon it must come from the gravitational field of the black hole and it was by removing energy from the gravitational field that shrinks the blackhole but this is still not a very satisfactory answer.

Wouldn't this lead to a prediction of hawking radiation being comprised of particles (I guess including exotic ones which could possibly even be stable ie dark matter) rather than thermal radiation.

In the virtual pair idea where does the temperature of the radiation appear?

I'm also not sure if I agree with virtual particles being negative and positive energy pairs, If you allowed such pair production the net energy difference would be zero it would be an entirely allowed process as in their would be no need for them to be virtual. You could produce as many such pairs as you want with no need for them to anhilate. Also in the other methods of premoting virtual pairs to real particles both particles have positive energy and remove energy from a field.

PM 2Ring
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### Re: Explain Hawking radiation plz?...

doogly wrote:OK, but I want to reiterate my warning that this pair creation picture is really just a hand wavy heuristic, and is probably misleading.

This.

Xanthir wrote:Virtual particle pairs are *not* particle-antiparticle (if they were, the entire universe would explode spectacularly in constant matter-antimatter collisions). They're positive-energy/negative-energy. The universe doesn't like negative energy, so the particle that escapes becomes the positive-energy one, and the black hole eats the negative-energy one, losing energy in the process.

Sorry, these virtual particle pairs can indeed be particle-antiparticle (or pairs of photons, which are their own antiparticle). Universal explosion is prevented by the time-energy constraint, and basic energy conservation.

andyisagod wrote:I was under the impression that the reasoning given for this kind of explanation is that you have a virtual particle premoted to a real particle, this would cause problems for energy conservation since the energy has to come from somewhere and the effect is caused by the black holes horizon it must come from the gravitational field of the black hole and it was by removing energy from the gravitational field that shrinks the blackhole but this is still not a very satisfactory answer.

The thing you're missing is the Uncertainty Principle. The exact energy of the black hole is uncertain & thus the exact position of the event horizon is uncertain. Hawking radiation arises in this fuzzy zone. Two particle's worth of energy is borrowed from the BH's gravitational field, one particle's worth of energy returns to the BH & one escapes.

andyisagod wrote:Wouldn't this lead to a prediction of hawking radiation being comprised of particles (I guess including exotic ones which could possibly even be stable ie dark matter) rather than thermal radiation.
Sure. But as Doogly mentioned above, this whole virtual particle picture is a bit misleading.

John Baez wrote:In 1975 Hawking published a shocking result: if one takes quantum theory into account, it seems that black holes are not quite black! Instead, they should glow slightly with "Hawking radiation", consisting of photons, neutrinos, and to a lesser extent all sorts of massive particles.
[...]
The most drastic consequence is that a black hole, left alone and unfed, should radiate away its mass, slowly at first but then faster and faster as it shrinks, finally dying in a blaze of glory like a hydrogen bomb.
[...]
How does this work? Well, you'll find Hawking radiation explained this way in a lot of "pop-science" treatments:

Virtual particle pairs are constantly being created near the horizon of the black hole, as they are everywhere. Normally, they are created as a particle-antiparticle pair and they quickly annihilate each other. But near the horizon of a black hole, it's possible for one to fall in before the annihilation can happen, in which case the other one escapes as Hawking radiation.

In fact this argument also does not correspond in any clear way to the actual computation. Or at least I've never seen how the standard computation can be transmuted into one involving virtual particles sneaking over the horizon, and in the last talk I was at on this it was emphasized that nobody has ever worked out a "local" description of Hawking radiation in terms of stuff like this happening at the horizon. I'd gladly be corrected by any experts out there... Note: I wouldn't be surprised if this heuristic picture turned out to be accurate, but I don't see how you get that picture from the usual computation.

Tass
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### Re: Explain Hawking radiation plz?...

andyisagod wrote:Wouldn't this lead to a prediction of hawking radiation being comprised of particles (I guess including exotic ones which could possibly even be stable ie dark matter) rather than thermal radiation.

Sure, but thermal radiation includes these. At the low energies we are used to you get mostly regular old massless photons and low energy ones at that. As kbT/c2 approaches the electron mass you would start to get electrons and positrons as well as of course plenty of X- and gammarays. At TeV's as in the LHC you gets all sorts of particles.

andyisagod
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### Re: Explain Hawking radiation plz?...

Tass wrote:
andyisagod wrote:Wouldn't this lead to a prediction of hawking radiation being comprised of particles (I guess including exotic ones which could possibly even be stable ie dark matter) rather than thermal radiation.

Sure, but thermal radiation includes these. At the low energies we are used to you get mostly regular old massless photons and low energy ones at that. As kbT/c2 approaches the electron mass you would start to get electrons and positrons as well as of course plenty of X- and gammarays. At TeV's as in the LHC you gets all sorts of particles.

Except in this case the particle content would be independent of the temperature of the black hole, I think the spectrum of any reasonably large blackhole would have a low enough temperature to not include a particle content.

Tass
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### Re: Explain Hawking radiation plz?...

andyisagod wrote:
Tass wrote:
andyisagod wrote:Wouldn't this lead to a prediction of hawking radiation being comprised of particles (I guess including exotic ones which could possibly even be stable ie dark matter) rather than thermal radiation.

Sure, but thermal radiation includes these. At the low energies we are used to you get mostly regular old massless photons and low energy ones at that. As kbT/c2 approaches the electron mass you would start to get electrons and positrons as well as of course plenty of X- and gammarays. At TeV's as in the LHC you gets all sorts of particles.

Except in this case the particle content would be independent of the temperature of the black hole, I think the spectrum of any reasonably large blackhole would have a low enough temperature to not include a particle content.

The higher the mass of the particle the less likely it would be to produced. A black hole of any reasonable size would only make massless particles, just like ordinary matter with a temperature.

andyisagod
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### Re: Explain Hawking radiation plz?...

Tass wrote:
andyisagod wrote:
Tass wrote:
andyisagod wrote:Wouldn't this lead to a prediction of hawking radiation being comprised of particles (I guess including exotic ones which could possibly even be stable ie dark matter) rather than thermal radiation.

Sure, but thermal radiation includes these. At the low energies we are used to you get mostly regular old massless photons and low energy ones at that. As kbT/c2 approaches the electron mass you would start to get electrons and positrons as well as of course plenty of X- and gammarays. At TeV's as in the LHC you gets all sorts of particles.

Except in this case the particle content would be independent of the temperature of the black hole, I think the spectrum of any reasonably large blackhole would have a low enough temperature to not include a particle content.

The higher the mass of the particle the less likely it would be to produced. A black hole of any reasonable size would only make massless particles, just like ordinary matter with a temperature.

So this implies that the actual process involving virtual pairs at the horizon of a black hole involves only virtual photon pairs and that massive virtual particle pairs are nessecarily both captured by the black hole (or they can both avoid the black hole and annihilate). Is the temperature then dependent on the mass of the black hole because of the redshift of the photons near the horrizon?

Ignoring that for a minute if you did have particles like electrons/positrons being emitted would this work to neutralise any charged black hole? the electric field from a charged black hole would (I assume) emmit more particles with the same charge as the black hole since these are repled and more likely to escape leading to a decrease in the charge of the black hole over time.

Tass
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### Re: Explain Hawking radiation plz?...

andyisagod wrote:So this implies that the actual process involving virtual pairs at the horizon of a black hole involves only virtual photon pairs and that massive virtual particle pairs are nessecarily both captured by the black hole (or they can both avoid the black hole and annihilate).

They are just very unlikely to be made and separated.

andyisagod wrote:Is the temperature then dependent on the mass of the black hole because of the redshift of the photons near the horrizon?

Yes. The smaller mass, the hotter.

andyisagod wrote:Ignoring that for a minute if you did have particles like electrons/positrons being emitted would this work to neutralise any charged black hole? the electric field from a charged black hole would (I assume) emmit more particles with the same charge as the black hole since these are repled and more likely to escape leading to a decrease in the charge of the black hole over time.

Yes, charged black holes should discharge rather quickly this way. They will of course also tend to preferentially eat normal matter with the right charge.

PM 2Ring
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### Re: Explain Hawking radiation plz?...

Yes, charged black holes should discharge rather quickly this way.

For very slow values of quickly. Stellar mass black holes have temperatures of a few nanokelvins, so they aren't actually doing much radiating. And being much colder than the CMBR, they are currently absorbing far more thermal energy than they are emitting.

thoughtfully
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### Re: Explain Hawking radiation plz?...

andyisagod wrote:Is the temperature then dependent on the mass of the black hole because of the redshift of the photons near the horrizon?

Gravitational redshift is the change in wavelength due to climbing out of a gravitational well. It isn't a property of radiation near the horizon. It isn't a special property of photons. Redshift is due to time dilation. The photons acquire a longer wavelength due to their "internal clocks" running slow.

Incidentally, the redshift decreases (as observed from a fixed distance from the singularity) as the black hole evaporates. Yes, a photon of fixed wavelength at the horizon will appear to an outside observer to be more energetic as the redshift decreases, but this does not account for the increase in observed luminosity, nor does it determine what the luminosity at the horizon might be.

Getting an intuitive idea for why hawking radiation increases as the mass decreases is tricky. One can imagine increasing tidal forces at the horizon separating virtual pairs with increasing forcefulness; temperature increasing as entropy decreases (the entropy of a black hole is proportional to its surface area), which isn't a universal relationship, but is a Universal relationship (haha! The Universe had lower entropy and higher temperature in the past).

An important point about Hawking Radiation that might trip you up later is that a freely falling observer doesn't observe any. This is due to the Equivalence Principle, which states that acceleration and gravitation are (locally) equivalent. An observer in free fall doesn't feel any acceleration, or notice any effects of gravitation (except tidal forces, which can be small at the horizon of a large enough black hole). It works both ways. An accelerating observer observes Unruh Radiation, although it takes a lot of acceleration to get a noticeable effect.

You should search the fora for more info. This topic gets beaten to bits on a regular basis.

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JWalker
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### Re: Explain Hawking radiation plz?...

thoughtfully wrote:
andyisagod wrote:Is the temperature then dependent on the mass of the black hole because of the redshift of the photons near the horrizon?

Gravitational redshift is the change in wavelength due to climbing out of a gravitational well. It isn't a property of radiation near the horizon. It isn't a special property of photons. Redshift is due to time dilation. The photons acquire a longer wavelength due to their "internal clocks" running slow.

Great post overall, but I just wanted to clarify that gravitational redshift isn't due to the internal clock of a photon running slow, as photons as a rule experience no passage of time (even near black holes). Their internal clocks always run at a rate of zero. Probably a better way to think about gravitational redshift is through conservation of energy.

The typical thought experiment is this: a photon is created at the surface of the Earth, and travels straight up for a distance D (according to an external observer) without becoming redshifted. when it reaches this altitude, it undergoes pair production and produces a positron and an electron. These particles can now be captured, and returned to the starting location of the photon. Since these particles have mass, we can extract the gravitational potential energy of the particles as we bring them back to the starting location. Once we arrive at the starting location, the electron and positron can be allowed to annihilate, producing the original photon again. This process can be repeated an infinite number of times, and we can therefore extract an infinite amount of energy by doing this. Thus we conclude that the energy of the photon must decrease as it moves away from the surface, and therefore must become redshifted, or we have a violation of conservation of energy.

Note that the reactions [imath]e^+e^-\to\gamma[/imath] and [imath]\gamma\to e^+e^-[/imath] are prohibited, but this doesn't change the validity of the argument, we could do the same thing with reactions that are allowed but the thought experiment would be less clear.