String propagation in black hole geometry

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 untroduced by Witten. We study the spectrum of this conformal field 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 of the black hole and to show that the string propagator exhibits Hawking radiation. We further discuss the role of winding state and the appearance of bound states in the euclidean solution. We find that target-space duality in the lorentzian theory interchanges the black hole horizon with the space-time singulartty. We conclude with a comparison a non-critical c = 1 string and its formulation as a gauged SL2,R WZW model.