Evaporation of two-dimensional black holes

An interesting two-dimensional model theory has been proposed that allows one to consider black-hole evaporation in the semiclassical approximation. The semiclassical equations will give a singularity where the dilaton field reaches a certain critical value. This singularity will be hidden behind a horizon. As the evaporation proceeds, the dilaton field on the horizon will approach the critical value but the temperature and rate of emission will remain finite. These results indicate either that there is a naked singularity, or (more likely) that the semiclassical approximation breaks down