  We study cosmic censorship in the Reissner-Nordstrom charged black hole by
means of quantum gravity holding near the apparent horizons. We consider a
gedanken experiment whether or not a black hole with the electric charge $Q$
less than the mass $M$ ($Q < M$) could increase its charge to go beyond the
extremal limit $Q = M$ by absorbing the external charged matters. If the black
hole charge could exceed the extremal value, a naked singularity would be
liberated from the protection of the outer horizon and visible to distant
observers, which means weak cosmic censorship to be violated in this process.
It is shown that the black hole never exceeds the extremal black hole this way
in quantum gravity as in classical general gravity. An increment of the trapped
external charged matters by the black hole certainly causes the inner Cauchy
horizon to approach the outer horizon, but its relative approaching speed
gradually slows down and stops precisely at the extremal limit. It is quite
remarkable that cosmic censorship remains true even in quantum gravity. This
study is the first attempt of examining weak cosmic censorship beyond the
classical analysis.
