# How can there be a naked singularity in the Reissner-Nordström (RN) geometry? [duplicate]

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?

• 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.). Commented Jun 11, 2023 at 2:48
• Does this answer your question? Physical interpretation of the Reissner-Nordstrom metric Commented Jun 11, 2023 at 4:09
• @JohnRennie I don't think this is a duplicate of that question. Commented Jun 11, 2023 at 4:50
• @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 Commented Jun 11, 2023 at 5:30
• @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... Commented Jun 11, 2023 at 5:33