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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?


marked as duplicate by StephenG, Kyle Kanos, Chris, Jon Custer, CR Drost Feb 11 '18 at 20:00

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  • $\begingroup$ All black holes are extreme--but not all are extremal. $\endgroup$ – JEB Feb 7 '18 at 14:32

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).


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