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I recently read that, if the mass of a charged black hole is small (compared to its squared charge times some constant), than there is no event horizon, but there is still a (naked) singularity. My doubt is the following:

The presence of a singularity means that the curvature diverges; in other words, gravity tends to infinity as we approach the central mass. So, as we approach the mass, gravity grows and grows unlimitlessly so, at a certain distance, it should become so strong that the escape velocity would be $>c$ (hence, at that distance, we would have an horizon).

What mechanism prevents the formation of an event horizon in the presence of a (relatively small) charged mass?

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  • $\begingroup$ What happens if you actually insert real numbers? The lowest mass black hole with the largest possible charge would be made of nothing but electrons for all I can tell. Would this black hole be a naked singularity? (Neglect for a moment that this is not a stable state of the vacuum and that tons of other "particles" would pop up very quickly if we actually tried to build such a black hole in an accelerator.). $\endgroup$ Jun 11, 2023 at 2:48
  • $\begingroup$ Does this answer your question? Physical interpretation of the Reissner-Nordstrom metric $\endgroup$ Jun 11, 2023 at 4:09
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    $\begingroup$ @JohnRennie I don't think this is a duplicate of that question. $\endgroup$
    – benrg
    Jun 11, 2023 at 4:50
  • $\begingroup$ @FlatterMann: if you treat an electron as a point particle in general relativity, and assume there is no special quantum magic to save you, then the electron is a naked singularity $\endgroup$ Jun 11, 2023 at 5:30
  • $\begingroup$ @ZotheRelativist General relativity has nothing to say about matter and in quantum field theory an electron is merely an amount of energy, momentum, angular momentum and charge. The reason why it "exists" is because in weak gravitational fields these quantities are conserved. We do not know if they are conserved in strong gravity (based on the fact that the universe as a whole is not energy conserving we can probably guess that they are not, which makes any speculation about the innards of black holes pretty useless). Having said that, my question stands. If electrons can't do it... $\endgroup$ Jun 11, 2023 at 5:33

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There is no known mechanism to prevent this. Hawking and Penrose proposed the Cosmic Censorship Hypothesis as basically a assertion that 'well behaved spacetimes don't have end states that have naked singularities'.

It's also worth noting that if you believe that Black hole thermodynamics corresponds to real thermodynamics, as most theoretical physicists do for various good reasons that are slightly short of real proofs, then if you start out with a "normal" black hole, then the naked singularity states are not reachable through a continuous process, because they will require reaching, and then going "beyond" a state where the temperature of the black hole is absolute zero, which would violate the third law of thermodynaics.

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