# Do semiclassical GR and charge quantisation imply magnetic monopoles?

Assuming charge quantisation and semiclassical gravity, would the absence of magnetically charged black holes lead to a violation of locality, or some other inconsistency? If so, how?

(I am not asking about how magnetic monopoles explain charge quantisation.)

I am looking to fill in the blanks in the claims found in this answer to "Is it possible to separate the poles of a magnet?" according to which "magnetic monopoles certainly exist [assuming] charge is quantized. This follows only from the semiclassical behavior of black hole decay, and so does not require unknown physics ... you can't forbid them, at least not for macroscopically sized black holes, without ruining the theory [of General Relativity]."

Related claims are found in this answer to "Why do physicists believe that there exist magnetic monopoles?" according to which, if a black hole cannot carry magnetic charge, it would result in a "violation of the laws of locality". (This refers to "any consistent theory of quantum gravity", which may or may not require more assumptions than the other claim.)

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Yes, magnetic monopoles are theoretically expectected to exist and to be quantized due to the electro-magnetic duality, which is an example of a strong-weak or S-duality. The relationship between magnetic an electric charges, discovered by Dirac, is $me = 2\pi n$. This means that if electric charges exist, magnetic charges m are quantized in units of $2\pi / e$. –  Dilaton Apr 5 '13 at 21:47
In addition, since the electrically charged particles are light, the magnetically charged particles are expected to be (at present) unobservably heavy in the current regime where QED is weakly coupled such that it can be calculated perturbatively. –  Dilaton Apr 5 '13 at 21:48
@Dilaton: I'm asking about GR or semiclassical extensions thereof -- and judging from the linked claims, I think this extension is really only needed for Hawking radiation. I don't think S-duality is relevant here, though I could be missing something. –  Retarded Potential Apr 10 '13 at 17:02
Hm, maybe I do not understand your question well enough. Reading the linked answers there is nothing theirin which conflicts with what I think I understand, so I agree with them. And I am not sure if gravity is absolutely needed to see why theoretically inclinded people expect magnetic monopoles to exist in principle. To me the relation discovered by dirac following just from the plain ordinary electro-magnetic duality should is enough (you do not have to call it S-duality if you dont like this term ;-) ...). It would be best if Ron could write an answer ... –  Dilaton Apr 10 '13 at 18:01
@Dilaton - I am reading it quite differently from you then. They are not talking about the expectation due to some standard duality argument (which is well covered in other questions on this site), but necessity due to some thought experiment(s) specifically involving black holes. (Yes, I for one would appreciate hearing from Ron Maimon.) –  Retarded Potential Apr 10 '13 at 21:47