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Under General Relativity, nothing can escape a black hole's event horizon, not even light, which is of course made of photons.

However, it is said that black holes can have charge. This presents a problem when the Standard Model is included in describing a black hole.

The Standard Model requires the exchange of force carrier particles, which exchange momentum and thus impart a force between particles. The force carrier particle for the electromagnetic force is the photon, which we have just stated is incapable of escaping a black hole's event horizon.

How then, is it possible for a black hole to have an electric charge, if for that charge to exert a force, it requires the exchange of photons?

It seems like if a black hole could have a charge, then you could send information across its event horizon, for example by sending a charge across the event horizon and triangulating its position inside the horizon by looking at its effects on the EM field outside of the horizon. You could then move this charge inside the horizon and look at the "wobbling" as a means of sending bits.

How is this scenario prevented while still allowing black holes to have charge?

Edit: Most of the suggested answers treat the problem classically and sweep it under the rug, usually by treating the observer at infinity, or by saying the charge never crosses the horizon from an external observer's view, which doesn't provide an answer for how matter inside the horizon can affect the EM field outside it. Some of the ones that do attempt to provide an answer within QM even imply the virtual photons exchanging the forces of the charges travel at infinite speed, or that information can even pass the event horizon under QM, which doesn't erase the information passing problem at all nor provide an answer of how it is that a black hole can have a charge.

I understand that QM and GR are far from being unified into a coherent framework, but we seem pretty convinced that black holes can have a charge under classical GR treatment, but QM seems to imply that either can't be possible (the photons that exchange the force cannot cross the horizon, and thus black holes should not be able to have a charge classically), or that information can be exchanged across the horizon under QM, which clearly breaks GR.

stix
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    "Under General Relativity, nothing can escape a black hole's event horizon, not even light, which is of course made of photons." -- No, light is not made of photons under general relativity. –  Apr 01 '21 at 19:38
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    Did you first search for similar questions? For example, this or this? – G. Smith Apr 01 '21 at 19:42
  • As a charge approaches the horizon, the electric field outside becomes more and more spherically symmetric around the hole. Once inside, its exterior field is completely symmetric and you can’t tell where it is. (I have seen the math for a charge at rest and I believe a falling charge is similar.) – G. Smith Apr 01 '21 at 19:47
  • @G.Smith Neither of those provide actual answers as to how the exchange of force carrier particles can cross the event horizon. Per GR, there's nothing "special" about the space inside the horizon, nor the horizon itself. It doesn't explain how you can't detect the position of a charge inside the horizon, nor how static charges are able to exchange forces across an event horizon in the Standard Model. – stix Apr 01 '21 at 19:48
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    You are presuming that we have a theory combining General Relativity and virtual photons. There is no such accepted theory. GR is a classical theory in which electromagnetic fields are classical. That said, I don’t know of any physicist who thinks charged black holes can’t exist, including when the EM field is quantized. – G. Smith Apr 01 '21 at 19:49
  • @G.Smith In such a case, how can we say with certainty that black holes have electric charge? Classically and quantumly(?) moving electric charges are detectable, and can thus send information. How do you prevent a moving electric charge inside an event horizon from being detected outside the horizon? – stix Apr 01 '21 at 19:52
  • I already explained what I believe happens with the field of the moving charge inside. – G. Smith Apr 01 '21 at 19:53
  • @DvijD.C. Your comment is both condescending and irrelevant. I wasn't implying that light was made of photons under GR, only that GR states that a photon cannot escape a black hole's event horizon. Are you suggesting GR doesn't state this? – stix Apr 01 '21 at 19:53
  • @safesphere Did you not just say that it can’t cross? – G. Smith Apr 01 '21 at 20:01
  • A.V.S.’s answer is similar to my second comment. There is an exact solution for the field of a charge at rest outside the horizon. – G. Smith Apr 01 '21 at 20:03
  • Which is what I said it did, in the first sentence of my second comment. – G. Smith Apr 01 '21 at 20:12
  • A.V.S. writes “falling into the black hole”, not “falling closer and closer toward the horizon”. – G. Smith Apr 01 '21 at 20:14
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    @stix Yes, because GR does not deal with photons at all. You would have to go to semi-classical GR or QFT in curved spacetime to make any statement about the implications of GR for quantum mechanical entities. –  Apr 01 '21 at 20:24
  • @stix In my opinion, you should consider this a challenge. Perhaps a future theory will be completely clear on how Feynman diagrams with virtual particles crossing horizons are evaluated. Or perhaps there will be a completely different formalism for understanding the force of a charged hole on an charge outside the horizon, either using QFT or something beyond. Maybe string theory already explains this? – G. Smith Apr 01 '21 at 20:30
  • @DvijD.C. Considering GR was "proven" through looking at the deflection of photon paths, is such a distinction relevant to the question, or is this a mere matter of pedantry? – stix Apr 01 '21 at 20:34
  • @G.Smith It's sounding like you're saying the problem of how a black hole can have charge under the Standard Model is an open and unsolved question? If that is the case, it begs the question of how we can accept classical explanations since we know classically GR can't be fully correct. Most of the classical explanations I've seen here seem to treat the event horizon like a charged sphere, which would make horizons "special," which itself seems to be in conflict with a classical description of them. – stix Apr 01 '21 at 20:36
  • The distinction between GR and quantum mechanics is crucially relevant to your question. The "exchange of photons" description of the electromagnetic force is characteristically quantum and cannot be dealt with in any classical model. –  Apr 01 '21 at 20:36
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    There are no black holes in the Standard Model. Any question that combines “black hole” and “Standard Model” has no widely-accepted answer. Physicists are not particularly worried about virtual photons and black holes for the same reason that they are not worried about virtual gravitons and black holes. Black holes exert gravitational forces and there is no reason to think they don’t exert EM forces. Eventually we will have a good theory of the quantum mechanics of both. It would be bizarre if an eventual quantum theory did not reproduce classical results. For now, we are still speculating. – G. Smith Apr 01 '21 at 20:46
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    Most of the classical explanations I've seen here seem to treat the event horizon like a charged sphere. I’m not sure how you got that impression, but it’s not correct. The discussion has gotten too long, and I’ve made my points, so I’m done. – G. Smith Apr 01 '21 at 20:52

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