Black holes violate the conservation of baryon number. Is that true?
A more general question is: Is information lost "down" a black hole?
The answer to this question is "observer dependent", i.e., it depends on to whom you talk. Many people in the high energy crowd answer this question with "no," while many people in the GR crowd, including Wald and Penrose, answer this question with "yes."
Fairly recently, there was a famous defection - after decades of being a "yes," Hawking switched camps to "no."
It probably will take an accepted quantum treatment of what happens inside, and (because of the so-called transplanckian modes) maybe even around, black holes before there is a general consensus within the physics community as the the answer of your question.
George I have to compliment you on making a generalization that wasnt obvious to me (although it perhaps should have been) and puts a new light on the question.
Intuitively, if some number of baryons fall into a BH then that number (or the net excess of ordinary versus antimatter) is lost
to the universe OUTSIDE the BH
So I guess I would have said "yes, baryon number is not conserved" in the part of the U outside.
But I was forgetting that recent Loop Gravity results point to spacetime continuing and re-expanding from the pit of a BH----they indicate "Black Hole Bounce". So maybe the information represented by the baryon number is somehow reflected in the new big bang and inflation resulting from the bounce---and somehow present in the new branch of the universe that sprouts off of ours.
It seems too speculative to think about---when I say it that way. But what you asked is more general and it is a mainstream question that plenty of people think about. And the recent Loop Gravity papers about spacetime extending to a new expanding region do seem to have some bearing on the "BH information paradox". I'd say it hasn't been settled yet, and in particular Hawking changing his mind did not settle it.
I think I understand what George and marcus say. So, now I'll tell myself that this is still an open question.
But my next question: Why is EM charge conserved (no-hair theorem) even to an observer outside a BH, but all other elementary particle physics conservation law violated? I'm abit intrigued.
It seems that EM charge conservation is a more robust conservation than even baryon number. Before this, I would have thought otherwise.
Now, I have one more thing in my mind. We know that all elementary particles have their own specific mass. Supposing we have a BH with a specific mass, say M. Then, we can express M in terms of the masses of possible elementary particles. And from there, reconstruct, the number of elementary particles and identify the particles, and hence, we have no violation of any conservations?
Conservation of charge is conservation of a Gaugefield charge. The Gaugefield outside of the BH "knows" about it.
The same goes for everything else.
In terms of conversation laws, it doesn't come much better then charge. The only thing that trumps it would be energy and momentum.
"Conversation Law Idol" ?
Baryon number is not a very strong symmetry, its accidental in the SM, in fact its violated even there (though such violation is suppressed by inverse powers of a heavy mass scale).
B-L is stronger otoh.
As far as blackhole information loss, this has been studied in the past, possibly as a mechanism for generating observed antimater-matter relations, but the problem is there again its way too symmetric and cannot lead to the observed discrepancies, at least through all known mechanisms.
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