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## Common errors in calculating radiated Hawking power.

Perhaps every discussion of the power radiated by a black hole that I have seen makes the following error: The total radiating area of the (Schwartzschild) black hole is taken to be the area of the event horizon, 4 pi Rs^2. But this is not the effective radiating area as seen from a distance. As stated on p 679 of Misner, Thorne and Wheeler, the capture cross section of a black hole is 27 pi M^2 (gravitational units), larger than pi Rs^2 because of the gravitational bending in of light rays. This makes the effective absorbing, and hence radiating, area larger than the area of the horizon by a factor of 6.75. This is pretty piddling compared to the tiny and huge numbers coming out of the power and lifetime calculations, but deserves to be considered if factors like pi are not also dropped.

There is also a physical optics effect that I have never seen mentioned, and that in fact will probably heavily modify what I have said above in a way that I am not prepared to estimate. This is the fact that the black hole source of the Hawking radiation is very small compared to the dominant wavelength of thermal radiation at the Hawking temperature. When the radiation must squeeze out of such a small hole it is probably not correct to use the geometric area in the way it is usually done, even as corrected above. And finally of course, as HAS been pointed out by others, a black hole is black for all forms of radiation, not just electromagnetic.

Sprite82 (talk) 22:30, 11 April 2013 (UTC)

The 1977 Page analysis, which I just added, appears to get take into account all those elements you mentioned. I couldn't find a later analysis factoring in that neutrinos have mass; maybe Misner et al has it but I don't have access to that text. Rolf H Nelson (talk) 03:48, 22 December 2015 (UTC)

## Deletion of BICEP2 experiment info?

The following edit was deleted as an "inaccuracy." I quoted a credible source, but don't know enough about the topic to say if it should stay or go. Anyway, this is what it was...

The BICEP2 experiment detected the early universe's horizon's Hawking radiation, in the form of gravitational waves.[1]
1. ^ Camille Carlisle. "First Direct Evidence of Big Bang Inflation". SkyandTelescope.com. Retrieved 2014 March 18. Check date values in: `|access-date=` (help)

This is the relevent reference from the S&T article, which I did not include in full due to copyright concerns:

This is the first detection of Hawking radiation. Hawking radiation is usually associated with the slow evaporation of black holes, as photons emitted from the event horizon. But the observable universe also has a horizon. Hawking radiation should be coming from this horizon, and also from every horizon in the universe — in other words, from every point in the universe, says cosmologist Max Tegmark (MIT). Today the cosmic horizons are huge and their Hawking radiation is utterly insignificant. But in the universe’s first fraction of a second, the horizons were tiny and sharply curved. The gravitational waves announced today are these horizons’ Hawking radiation.

Eoghanacht talk 16:48, 31 March 2014 (UTC)

## Why Hawking?

Why isn't it named Starobinsky-Zel'dovich? Or: did the argument Hawking provided transcend in any important way what the Soviets said? (The cited website is down now.) — Preceding unsigned comment added by 189.6.253.80 (talk) 01:34, 24 May 2014 (UTC)

## far from the black hole

What exactly is meant by "far from the black hole" in this section of the article?

"... nothing, not even electromagnetic radiation, can escape from the black hole. It is yet unknown how gravity can be incorporated into quantum mechanics. Nevertheless, far from the black hole the gravitational effects can be weak enough for calculations to be reliably performed in the framework of quantum field theory in curved spacetime."

Can Hawking radiation be derived using calculations that only "look at" locations far outside the event horizon, and so can be calculated even for objects that are not yet black holes?

If so, I suggest that section be rephrased to something like

"Nevertheless, far outside a black hole's event horizon, the gravitational effects can be weak enough ..."

Or does Hawking radiation, like spaghettification inside a supermassive black hole, require assumptions about stuff that happens at the event horizon? I.e., assumptions that may be perfectly reasonable and perhaps can be indirectly confirmed, but no one can directly confirm those assumptions and return to tell about it? Then I suggest that section be rephrased to something like

"Nevertheless, far from a black hole's central singularity, the gravitational effects at the event horizon can be weak enough ..."

--DavidCary (talk) 16:23, 21 April 2015 (UTC)

## Hawking Radiation not visible to an observer falling into a black hole

I'm not an expert on this at all myself. But in other accounts of this, they say that the particle count depends on your rest frame. If you are in an accelerating frame falling into a black hole, then you won't see any particles at the event horizon. But if you could be suspended just above the event horizon you'd see the Hawking radiation because you count particles differently.

Calling it "an accelerating frame" is confusing, but yes, you're correct that your particle detector clicks if you're suspended above the black hole while your free-falling neighbor's detector does not. If you have a specific source we can add it in. Rolf H Nelson (talk) 02:27, 27 January 2016 (UTC)

Also - there's a question, what type of radiation is produced? The particle / anti-particle explanation would seem to suggest all the radiation would be protons, anti protons, electrons, anti-electrons and such like - and probably equal numbers of each as there is no particular reason for one or other of the pair to fall into the black hole. But Hawking radiation is said to be mainly photons, and when a black hole evaporates it's almost entirely gamma rays at that point. So that suggests something wrong with this simple picture.

Photons are their own anti-particles, so there's no contradiction. If we believe this is a common source of confusion, we should definitely clarify it in the article. Rolf H Nelson (talk) 02:27, 27 January 2016 (UTC)

So, I think it would be good if someone expert on this was to write something about this. Either a clear explanation if it is well understood but not widely known, or if nobody knows, to explain what is known and what is uncertain about it. It's possible that the technical section of this paper makes it clear for theorists who are expert already as that is too technical for me to read, but it's not clear from the intro anyway.

Here are a couple of academic web pages on these points:

Thanks Robert Walker (talk) 17:35, 26 January 2016 (UTC)

FWIW Mr. Walker, I agree with everything you're saying. I came here to understand exactly that question: what type of radiation is Hawking Radiation? If that info is implied in the article, it's certainly not clear to me as a layman. Thanks! 148.87.19.210 (talk) 20:40, 14 June 2016 (UTC)
What would people think of mostly removing the pop-science "virtual pair production" content? According to John Baez [1], it's not really how the physicists who work with it seem to frame it. I'm not a physicists, but to me it doesn't seem to me very insightful for analyzing the hypothetical phenomenons of Hawking and Unruh radiation at a deeper level, and it probably confuses people about how virtual particles normally behave. The main scholarly articles don't seem to lean heavily on the virtual pair production analogy; the closest I found was Kiefer 1998, which says only as an aside "It turns out that the vacuum expectation value of the energy-momentum tensor of the quantum field is negative near the horizon, corresponding to a flux of negative energy into the hole (this is the basis for the pictorial interpretation of the Hawking effect, where one partner of a pair of virtual particles can fall into the hole, thus enabling the other partner to become real and escape to infinity, where it can be observed as Hawking radiation)". Rolf H Nelson (talk) 00:27, 19 June 2016 (UTC)

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