BRST analysis of physical states in a two-dimensional black hole

We study the BRST cohomology for an $\frac{\mathrm{SL}(2, R)}{\mathrm{U}\mathrm{}\left(1\right)\mathrm{}}$ coset model, which describes an exact string black hole solution. It is shown that the physical spectrum could contain not only the extra discrete states corresponding to those in $c=1\mathrm{}$ two-dimensional gravity but also many additional new states with a ghost number $N_{\mathrm{EP}}=-1\mathrm{} \mathrm{to} 2$. We also discuss characters for nonunitary representations and the relation of our results to other approaches.