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Evaporation time, verifying calculations
In Black_hole_evaporation#Black_hole_evaporation, the following 2 values are given for :
The evaporation time of a black hole is proportional to the cube of its mass:
The time that the black hole takes to dissipate is:
Where is the mass of the black hole.
Are these equations talking about the same quantity? If so, shouldn't their values be the same? Instead, the first line is it is 8.407x10^-17 and in another it is 1.33x10^-17. They seem to differ by a factor of 2*pi. I suspect that in the first line the listed Reduced_Planck_constant was used, and the second line the Planck_constant was used instead by mistake. But I don't understand the physics well enough to be sure. If you do understand, would you please recheck these calculations? Mynameisnoted (talk) 05:03, 18 October 2011 (UTC)
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.
Decoupling of physics and mathematics
This problem arises over a whole series of articles stretching from Hawking radiation to Rindler coordinates and possibly beyond. I encountered it when I tried to use Wikipedia to grok (understand) Hawking radiation.
The problem is that: (1) all articles reference a new physical process or mathematical transformation that is not natively explained by the article. (2) following the hyperlink to the article that was supposed to explain the unexplained produces only a partial explanation and repeats the problem (1) for the rest of the explanation. (3) the number of questions and unknowns increases during the following of this chain instead of decreasing.
To illustrate: I want to know what is the process by which Hawking radiation comes about, but the explanatory paragraph references the Unruh effect without much explanation (really, without any explanation). Then I go to the Unruh effect article and it references Minkowski spacetime and Rindler coordinates. By the time I get to the Rindler coordinates article, I am not reading about Hawking radiation anymore, I am studying hard-core mathematical topology.
The core problem then is that the amount of (human) energy required to parse the Hawking radiation is at least an order of magnitude larger than what the article size and apparent complexity would lead you to believe. Because you first have to parse topology itself and then work your way up to what you actually need.
What should be done is that that energy expenditure for understanding Hawking radiation should be decreased, and namely this should be done by not requiring the reader to understand the whole scientific field just so he/she can understand a small part of the field. The concrete solution appears to be decoupling of various topics. The explanations should be converging and if a hapless reader needs to follow a hyperlink to a different article, he/she should do so with a clear picture in his/her head about the questions that need to be answered to complete the understanding.
I am willing to do the legwork for this, however I can not do this in a vacuum. I am thinking about, first, explaining all the equations right there where they appear ("explain" means that all variables and constants are identified) and, second, by adding "in-a-nutshell" explanations of lower-level phenomena (for example: Unruh effect) inline with the main explanation.
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.
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.
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 184.108.40.206 (talk) 01:34, 24 May 2014 (UTC)