So, in quantum electrodynamics (at least to my rudimentary knowledge), the electromagnetic force is mediated by photons.
On the other hand, in classical general relativity, the Kerr Black Hole solutions, are a family parametrized by 3 numbers, one of which is $Q$, which is interpreted as the charge of the body.
Now, light cannot escape from a black hole, so if a charged particle enters the black hole, how could a particle outside of the black hole sense the charge (since no exchange of photons can occur)?
One possibility is that the charge (or at least the information about it) remains on the surface of the black hole. But matter is supposed to reach the singularity at the center of the black hole in finite proper time.
So, what actually happens? It is hard for me to imagine that, say, a proton that enters the black hole "separates" from its charge while the "rest" of it continues moving to the singularity. If this was to happen, something far more interesting than spaghettification would occur! Indeed, moving past the event horizon of a super massive black hole would be impossible, since the electostatic forces holding us together would disappear.
Or it could be that this is not a well posed question. After all, quantum field theories deal with fields not "particles".
I'm in the math department, so I was just curious what the physicists thought of this situation, and if there is some standard explanation given for this.