Electron falling into an extreme black hole and Cosmic Censorship Hypothesis [duplicate]

Question

This question already has an answer here:

• What prevents the accumulation of charge in a black hole? 6 answers

It is argued that a black hole with Q>M cannot be formed as the formation of such a black hole leaves a naked singularity which is against the Cosmic Censorship Hypothesis.

But, consider an extreme black hole (Q=M) and consider a particle falling into the black hole. If the particle has Q>M (like an electron) then the black hole at the end becomes one with Q>M. Does this lead to a contradiction with Cosmic Censorship Hypothesis?

A particle like an electron could cause concerns about the quantum effects that we are ignoring in this problem. So rather consider a really heavy particle but again with a charge greater than its mass.

The formula for the temperature of a charged black hole has in it the expression (for the Reissner-Nordstrom black hole) $$\sqrt{M^2-Q^2}$$ Hence, if Q>M we get complex valued temperature which doesn't make sense. How do we make sense of all these together?

Answer 1

The point is that if the black hole is extremal the electric repulsion of a particle with $Q>M$ will be greater than its gravitational attraction. Consequently, it cannot fall into the black hole.

A general proof that creating over-extremal black hole this way (covering all the what ifs you can come up with) was recently provided by Sorce and Wald: https://arxiv.org/abs/1707.05862. (See reference in that paper for various previous arguments about this in the literature).