  The SL(2,R)/U(1) gauged Wess-Zumino-Witten model is an exact conformal field
theory describing a black hole in two-dimensional space-time. The free field
approach of Bershadsky and Kutasov is a suitable formulation of this CFT in
order to compute physically interesting quantities of this black hole. We find
the space-time interpretation of this model for k=9/4 and show that it
reproduces the metric and the dilaton found by Dijkgraaf, E. Verlinde and H.
Verlinde in the mini-superspace approximation. We compute the two- and
three-point functions of tachyons interacting in the black hole background and
analyse in detail the form of the four-point tachyon scattering amplitude. We
discuss the connection to the c=1 matrix model and the deformed matrix model of
Jevicki and Yoneya.
