LIMITATIONS ON THE STATISTICAL DESCRIPTION OF BLACK-HOLES

We argue that the description of a black hole as a statistical (thermal) object must break down as the extreme (zero-temperature) limit is approached, due to uncontrollable thermodynamic fluctuations. For the recently discovered charged dilaton black holes, the analysis is significantly different, but again indicates that a statistical description of the extreme hole is inappropriate. These holes invite a more normal elementary particle interpretation than is possible for Reissner-Nordstrom holes.