String Propagation in a Black Hole

We consider string theory in the background of the two-dimensional black hole as described by the SL(2; R)=U(1) coset theory recently introduced by Witten. We study the spectrum of this conformal eld theory, and give explicit representations for the tachyon vertex operators in terms of SL(2; R) matrix elements. This is used to compute the scattering of strings oo the black hole and to show that the string propagator exhibits Hawking radiation. We further discuss the role of winding states and the appearance of bound states in the Euclidean solution. We nd that target space duality in the Lorentzian theory interchanges the black hole horizon with the space-time singularity. We conclude with a comparison with the non-critical c = 1 string and its formulation as a gauged SL(2; R) WZW model.