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In this paper we investigate in more detail our previous formulation of thedilaton-gravity theory by Bilal--Callan--de~Alwis as a $SL_2$-conformal affineToda (CAT) theory. Our main results are: i) a field redefinition of theCAT-basis in terms of which it is possible to get the black hole solutionsalready known in the literature; ii) an investigation the scattering matrixproblem for the quantum black hole states. It turns out that there is a rangeof values of the $N$ free-falling shock matter fields forming the black holesolution, in which the end-point state of the black hole evaporation is a zerotemperature regular remnant geometry. It seems that the quantum evolution tothis final state is non-unitary, in agreement with Hawking's scenario for theblack hole evaporation.Comment: ROM2F-93-03, 27 pages, phyzz

Conformal affine Toda model of two-dimensional black holes: The end-point state and theSmatrix