Is there a temperature that black holes cease to emit non-zero mass particles.
I think you can still pretty much get away with using Planck's law, just interpreting hf as the mass-energy of the particle. I'm sure the statistical counting of polarization states is wrong, and the stuff relating to identical particles is wrong if the particles being emitted are fermions, but basically I think the shape of the high-energy tail of Planck's law just follows from the partition function. So the intensity of a given type of massive particle would fall off like exp(-mc^2/kT), but it would never vanish, even at very low temperatures. It would be interesting to estimate how much of an astrophysical black hole's mass is destined to be emitted as neutrinos, etc.
The freaky thing about Hawking radiation is that it includes all particles, so it violates all the usual conservation laws of particle physics, such as baryon number, lepton number, etc.
How does a black hole emit massive particles?
If it can, doesn't this thwart Penrose CCC which was just discussed in another thread. There, no one questioned the emission of radiation only from black holes at the end of this eon...no massive particles were claimed to be emitted.
"The freaky thing about Hawking radiation is that it includes all particles, so it violates all the usual conservation laws of particle physics..."
I did not realize that.....I thought Hawking radiation was black body radiation...electromagnetic, thermal, radiation....thermal radiation has massive particles??
Hawking radiation includes particles of all types, in thermal equilibrium with themselves, and with each other.
The fermions emitted, of course, will follow a Fermi-Dirac distribution instead of Planck.
While the answer seems clear, no, the details don't.
Quoting Birrell & Davies,
Page has estimated the total luminosity L = (3.4 x 1048)(M/1 gm)-2 ergs-1 for a Schwarzschild black hole of mass >> 1017 gm, which consists of 81% neutrinos, 17% photons and 2% gravitons. The temperature may be written T = (1.2 x 1026 K)(gm/M), which for a solar mass object gives 6 x 10-8 K. For such an object, only massless quantum emission is relevant. However, for M < 1017 gm, T > 109 K, and the creation of thermal electron-positron pairs becomes possible. At lower masses, other species of elementary particles will be emitted."
BillK...did you print the right Temperatures??
the solar mass at T = 10-8 is unsurprising......but
A black hole hotter than 109K would seem really unusual....really small....
Is this saying as BH get smaller, hotter, they emit larger proportions of massive particles??
Am I misreading something that makes my earlier comment invalid:
Yes indeed! The book points out that the diameter of such a black hole would be about a fermi.
Hawking radiation is very much a quantum effect - the typical wavelength of the emission is comparable to the size of the hole. The Compton wavelength of an electron is what, 400 fermis, and for a proton it's a fraction of a fermi. So this is why the radiation from the hole is almost entirely massless until its last dying gasp.
"the typical wavelength of the emission is comparable to the size of the hole.."
yes, have seen that in several sources....a good point!
First of all I had not been aware if that is in fact accurate; if it is accurate, it was entirely missed in the Penrose CCC discussion by several forum experts and apparently by Penrose himself.
I listened to the entire Penrose lecture about his CCC theory at Perimeter online a few days ago and if he said anything about partile emission from BH at the end of the universe, when he appears to claim all is radiation, I'd be really surprised....
Penrose's theory seems to involve a lot of wishful thinking...
I don't think he missed it. I think he just realized that it was an unimportant side issue.
Regardless of whether black holes emit some fraction of their Hawking radiation as neutrinos, etc., there is a much bigger issue with CCC, which is that many massive particles never get recycled through black holes at all. We know that these particles will exist, so if their numbers are augmented somewhat by Hawking radiation, it doesn't change anything fundamental. The real problem with CCC is that he needs nonstandard particle physics to get all his massive particles to decay into photons. He originally portrayed this as a prediction of CCC (massless charged particles). Then when it became clear that it was inconsistent with previously established experimental facts about particle physics, he backed off from it.
I cannot derive the conclusion that ALL massive particles must disappear. Nor can I tell how important it is that ALL do.
In places Penrose sounds like it is a requirement, in others [the Batchlor radio interview notes of mine and the Penrose paper here to which which BenCrowell linked, it seems some
[insignificant] mass is allowed....
where, for example, Penrose says....
One thing I don't recall being discussed in our threads is dark matter and the Higgs field. In his radio interview he says a requirement is that dark matter disappears and hypothesizes it reappears when the Higgs field does....
AH HA: does a conformal geometry say anything about the demise of the Higgs field which provides mass to particles???
Naty1 - The quote in your #13 is talking about the early universe, not the far future. I don't see the relevance of the Higgs boson. He wants dark matter to disappear, because he wants all massive particles to disappear.
I assume no Higgs, no 'matter'...thats a potentially slick way to eliminate mass....
and Penrose mentions the Higgs field reappearing in the early universe.....he did not make clear when it 'disappeared' in his view.....
I'm wondering if the Higgs field can exist in a conformally geometric universe...if not, no mass!!
Sorry, but this verbal description is a little too vague for me. What would be optimal would be if you could find a published paper by Penrose, preferably one that's freely available on the web, that discusses what you're describing. Then we'd all see a clearly formulation expression of this. Did Penrose say something about the Higgs in the radio interview? It's just going to be way too hard to decode all of this based on a second-hand description of a verbal popularization. Have you tried, for example, searching on arxiv.org for Penrose's name, to see what is the most recent thing he's published on CCC? My impression is that the theory was rapidly changing ca. 2009-2010, and that ca. 2011-2012 it basically was found not to be viable, both because the nonstandard particle physics was incompatible with observation and because the claim of confirmation from the CMB turned out to be completely wrong.
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