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

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 DrostFeb 11 '18 at 20:00

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.