If hawking radiation simply reduces the mass and emits electromagnetic radiation, how can the balance of matter / antimatter be maintained? Couldn't you use some of that $E = mc^2$ energy you would get to create antimatter and matter, effectively transforming one into the other? What am I missing here?
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1$\begingroup$ how can the balance of matter / antimatter be maintained? What balance? The universe has a massive imbalance. $\endgroup$– G. SmithCommented Apr 7, 2021 at 20:17
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$\begingroup$ @G.Smith that's a completely different problem. Antimatter annihilates with matter because every property it has is exactly the inverse of matter, except for mass. When the two cancel each other out, all that's left is mass, so pure energy is what's left (photons). These traits (like charge, for example) are always conserved as far as we know. My question has to do with seemingly transforming an atom with charge, spin, etc. and removing all of those traits except mass. $\endgroup$– Wesley AdamsCommented Apr 7, 2021 at 20:26
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$\begingroup$ That’s really the issue of what happens to all the details of the stuff that falls into a black hole, since in classical GR the black hole is an object with only three parameters. You have that problem without Hawking radiation. $\endgroup$– G. SmithCommented Apr 7, 2021 at 20:36
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1$\begingroup$ @safesphere: Yes, baryon number vanishes even without Hawking, but my point was that with the technical term “baryon number” there are already several questions on this site like this, or that (this considered a duplicate of the first by more in spirit like this one). $\endgroup$– A.V.S.Commented Apr 8, 2021 at 5:59
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1$\begingroup$ @A.V.S. You should put that into an answer! First, though, it would nice to know why the baryon number is canceled within a black hole. Thanks! $\endgroup$– Wesley AdamsCommented Apr 8, 2021 at 22:06
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1 Answer
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Black holes don't preserve an matter/antimatter balance. You can in principle toss some protons into a black hole, collect some positrons from the Hawking radiation, and thereby "turn matter into antimatter".
This doesn't violate any physical law because there just isn't any law saying that the total "antiness" of the particles in the universe must be conserved. The reason it seems that there might be such a law is that most processes in the Standard Model conserve the baryon and lepton numbers, i.e. the number of quarks/leptons minus the number of antiquarks/antileptons. But this property of the SM is "accidental" and there's no known reason why it should hold in any extension of the SM. (In fact it doesn't quite hold even in the SM, but the processes that theoretically violate it are unobservably rare.)
I don't particularly like the statements in the comments that the baryon number "vanishes" or is "canceled" since that suggests that it's somehow forced to zero. There is, rather, just no known mechanism that would relate the total baryon number of matter falling in to the total baryon number of the Hawking radiation (and you can argue that it's impossible to preserve it in general: see this comment).
You should rather ask why any properties of the infalling matter are preserved, and the reason is that certain properties are encoded in fields outside the event horizon, and can't change for geometric reasons. Rather than saying that black holes have no hair, it would probably be better to say that they have no hair other than those fields.
