Moving mirrors, black holes, and cosmic censorship

We examine negative-energy fluxes produced by mirrors moving in two-dimensional charged-black-hole backgrounds. If there exist no constraints on such fluxes, then one might be able to manipulate them to achieve a violation of cosmic censorship by shooting a negative-energy flux into an extreme $Q=M$ or near-extreme Reissner-Nordström black hole. However, if the magnitude of the change in the mass of the hole $\Delta M$, resulting from the absorption of this flux, is small compared to the normal quantum uncertainty in the mass expected from the uncertainty principle $\Delta E\Delta T\ge 1$, then such changes should not be macroscopically observable. We argue that, given certain (physically reasonable) restrictions on the trajectory of the mirror, this indeed seems to be the case. More specifically, we show that $\left|\Delta M\right|$ and $\Delta T$, the "effective lifetime" of any naked singularity thus produced, are limited by an inequality of the form $\left|\Delta M\right|\Delta T<\mathrm{}1\mathrm{}$. We then conclude that the negative-energy fluxes produced by two-dimensional moving mirrors do not lead to a classically observable violation of cosmic censorship.