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.

  • $\begingroup$ See math.ucr.edu/home/baez/physics/Relativity/BlackHoles/… $\endgroup$ – PM 2Ring Apr 26 '17 at 3:30
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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/937/2451 , physics.stackexchange.com/q/149581/2451 , physics.stackexchange.com/q/166033/2451 and links therein. $\endgroup$ – Qmechanic Apr 26 '17 at 3:42
  • $\begingroup$ From what I've heard, the "virtual particles" used in quantum field theory can do all sorts of things that seem to break the laws of physics, including move faster than light. Also, I think adding up all of the possible "paths" which include these "virtual particles" in the Feynman Path Integral, which is somehow related to how quantum particles are waves of probability, leads to continuous fields of electrical potential and probability. Maybe something relating to these ideas can explain how both the particle and field explanations would allow electromagnetic fields to leave the black hole. $\endgroup$ – H. H. Jul 27 '20 at 22:44

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.

This particle physicist ( experimental) knows that quantization of gravity and unification of all four forces is still in the future. One needs to be able to write down rigorously the feynman diagrams of the interaction of a photon ( quantum mechanics) and a black hole ( classical general relativity) and that can only be guesses till a definitive model is found.

String theories are attractive candidates but at the moment there is no phenomenological validation for choosing one as a standard model where such questions can be answered. There are guesses as Fuzzball(string theory) :

Fuzzball theory replaces the singularity at the heart of a black hole by positing that the entire region within the black hole’s event horizon is actually a ball of strings, which are advanced as the ultimate building blocks of matter and energy. Strings are thought to be bundles of energy vibrating in complex ways in both the three physical dimensions of space as well as in compact directions—extra dimensions interwoven in the quantum foam (also known as spacetime foam).

This link may give an insight to the research going on in the unification of forces through string theories. As an example of research , this was written in 1996 by a now well known string theory physicist ( the mills of God grind slowly). String theorists are working on charged black holes .

Until the holy grail of unification is reached one uses effective field theories for specific problems, as the Big Bang model of the history of the universe,which has a fuzzy region in the place of the original singularity so that the framework of quantum mechanics can fit the astrophysical observations ( cosmic microwave background for one).

  • $\begingroup$ TOE and quantum gravity are overkill for this question. You can tackle it semiclassically, through QFT in curved space. facultystaff.richmond.edu/~ebunn/ajpans/ajpans.html $\endgroup$ – Mitchell Porter Apr 26 '17 at 5:00
  • $\begingroup$ @MitchellPorter will you write an answer? I did not find the link in my searches. thanks. I read it, it is too handwaving for me, too many guesses. The question is from a mathematician . I will edit in your comment if you are not going to answer yourself. $\endgroup$ – anna v Apr 26 '17 at 5:52
  • $\begingroup$ I will write something, unless someone beats me to it. $\endgroup$ – Mitchell Porter Apr 26 '17 at 6:16

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