Hawking radiation is produced at the black hole horizon, and other pop-science myths

[Genady]

The other myth is, for example, that the Hawking radiation is result of virtual pair production when one of the virtual particles becomes real.

I've found this article that tries to straighten some misconceptions:

Sabine Hossenfelder: Backreaction: Hawking radiation is not produced at the black hole horizon.

Quote

All this supports the conclusion that Hawking particles are not created in the near vicinity of the horizon, but instead come from a region surrounding the black hole with a few times the black hole’s radius.

 

Edited February 22 by Genady

[swansont]

I’m not so sure I’d call these things myths; no matter what physics you’re talking about, there’s a good chance that you’re discussing an approximation and that a deeper dive will show that. When you discuss a topic with someone without that background, the deeper dive isn’t possible. Simple explanations are simple, and actual physics is not.

Are we perpetuating a myth when we say that kinetic energy is 1/2 mv^2?

 

[Genady]

No, I don't call approximations, myths. They are different things. Is it an approximation to say that all life forms were created at once from scratch?

[MigL]

I wouldn't exactly call it a pop-sci myth.
The Event Horizon is a condition of the space-time surrounding the collapsed mass-energy.
At the Event Horizon, a mathematical condition is exceeded, but there is no actual physical structure.

One can say that the space-time surrounding the collapsed object is the source of Hawking radiation, and you would be correct.
You could say that the condition of the space-time is the source, or you could say the EH is the source, and you would still be correct.

I've also read of many 'mechanisms' for Hawking radiation production, ranging from the virtual particle pair capture and emission ( as real ) which you described, to particles ( radiation ) tunneling through the EH, as if the EH was a real structure, and many other 'interpretational' mathematical models which give the same results.
( this is a Quantum Mechanical effect, after all )

What is certain is that BHs have entropy, and therefore must have a temperature.
That temperature requires them to emit radiation characteristic of a black body at that temperature.

Here are two differing 'interpretational' mechanisms for radiation production from a google search

Hawking Particle Creation.pdf (brainmaster.com)

0409024.pdf (arxiv.org)

Both are fairly understandable ( math light ) and don''t give me 'headaches' when reading them 🙂

 .

Edited February 24 by MigL

[Genady]

Yes, for an audience that thinks that Event Horizon is an actual physical structure, there is no difference between an approximation and a myth.

[swansont]

Part of the issue here is the general lack of math you have in pop-sci descriptions. (IIRC Hawking noted the adage that your audience drops in half for each equation in a book; he only had E=mc^2) which forces one into imprecise language.

 

Take “Hawking particles are not created in the near vicinity of the horizon, but instead come from a region surrounding the black hole with a few times the black hole’s radius”

What does “near the vicinity” actually mean? It’s not quantified. A 10 solar mass BH has a Schwarzschild radius of under 30 km. Are Hawking particles created 50 or 100 km away in the vicinity, or not? 100 km is quite a small distance in astronomical/cosmological terms, and these numbers would be small even for a 10x or 100x bigger BH. We get reassured that some rock passing within 50,000 km or so of earth will exhibit a near-miss. That’s almost 10x the radius, and it’s considered nearby.

 

[J.C.MacSwell]

3 hours ago, Genady said:

No, I don't call approximations, myths. They are different things. Is it an approximation to say that all life forms were created at once from scratch?

It depends on the time scale you're comparing it to...it's well known that it took the better part of a week...😀

[Genady]

5 hours ago, swansont said:

Part of the issue here is the general lack of math you have in pop-sci descriptions. (IIRC Hawking noted the adage that your audience drops in half for each equation in a book; he only had E=mc^2) which forces one into imprecise language.

 

Take “Hawking particles are not created in the near vicinity of the horizon, but instead come from a region surrounding the black hole with a few times the black hole’s radius”

What does “near the vicinity” actually mean? It’s not quantified. A 10 solar mass BH has a Schwarzschild radius of under 30 km. Are Hawking particles created 50 or 100 km away in the vicinity, or not? 100 km is quite a small distance in astronomical/cosmological terms, and these numbers would be small even for a 10x or 100x bigger BH. We get reassured that some rock passing within 50,000 km or so of earth will exhibit a near-miss. That’s almost 10x the radius, and it’s considered nearby.

 

I agree, the vagueness of such statements is an issue. Next time somebody says, "Hawking radiation is generated just outside the event horizon", I will ask first, how far is "just".

[KJW]

One thing that is not generally recognised is when you see an image representing a black hole, the outer edge of the black disc is not the event horizon. In fact, it is the photon sphere at [math]r = \dfrac{3r_s}{2}[/math], where [math]r_s[/math] is the Schwarzschild radius (the radius of the event horizon). Note that the photon sphere is the minimum radius for light to escape transversely away from a black hole.

 

 

Edited February 24 by KJW

[Genady]

36 minutes ago, KJW said:

One thing that is not generally recognised is when you see an image representing a black hole, the outer edge of the black disc is not the event horizon. In fact, it is the photon sphere at r=3rs2 , where rs is the Schwarzschild radius (the radius of the event horizon). Note that the photon sphere is the minimum radius for light to escape transversely away from a black hole.

 

 

A light that is produced by hot infalling matter between the photon sphere and the event horizon can still escape radially, right?

[J.C.MacSwell]

6 minutes ago, Genady said:

A light that is produced by hot infalling matter between the photon sphere and the event horizon can still escape radially, right?

Yes. Depending on angle it can escape. Radially right down to the EH, where it would almost escape but approach infinite wavelength trying to get out if I understand it correctly.

Edited February 25 by J.C.MacSwell

[KJW]

18 minutes ago, Genady said:

A light that is produced by hot infalling matter between the photon sphere and the event horizon can still escape radially, right?

Yes. As a light-emitter goes from the event horizon to further away, the outwardly-directed solid angle of the beam of light that escapes the black hole increases from zero at the event horizon to a hemisphere at the photon sphere and continues to increase further out.

 

 

Edited February 25 by KJW