Nonthermal nature of incipient extremal black holes - art. no. 024005

We examine particle production from spherical bodies collapsing into extrem al Reissner-Nordstrom black holes. Kruskal coordinates become ill defined i n the extremal case, but we are able to find a simple generalization of the m that is good in this Limit. The extension allows us to calculate the late -time world Line of the center of the collapsing star, thus establishing a correspondence with a uniformly accelerated mirror in Minkowski spacetime. The spectrum of created particles associated with such uniform acceleration is nonthermal, indicating that a temperature is not defined. Moreover, the spectrum contains a constant that depends on the history of the collapsing object. At first sight this points to a violation of the no-hair theorems; however, the expectation value of the stress-energy-momentum tensor is zer o and its variance vanishes as a power law at late times. Hence, both the n o-hair theorems and the cosmic censorship conjecture are preserved. The pow er-law decay of the variance is in distinction to the exponential falloff o f a nonextremal black hole. Therefore, although the vanishing of the stress tenser's expectation value is consistent with a thermal state at zero temp erature, the incipient black hole does not behave as a thermal object at an y time and cannot be regarded as the thermodynamic limit of a nonextremal b lack hole, regardless of the fact that the final product of collapse is qui escent.