by their Nilpotent Subgroups

We consider the gauging of SL(2, R) and SL(2, R) × U(1) WZNW model by their nilpotent subgroups. The resulting space-times of the corresponding sigma models are seen to collapse to the one dimensional Liouville theory in the first case, and lead to an extremal three dimensional black string in the second case. We show that these results are also obtained by boosting the Witten black hole solution and Horne and Horowitz black string solution respectively. 0