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The string propagation in the two-dimensional stringy black-hole isinvestigated from a new approach. We completely solve the classical and quantumstring dynamics in the lorentzian and euclidean regimes. In the lorentzian caseall the physics reduces to a massless scalar particle described by aKlein-Gordon type equation with a singular effective potential. The scatteringmatrix is found and it reproduces the results obtained by coset CFT techniques.It factorizes into two pieces : an elastic coulombian amplitude and anabsorption part. In both parts, an infinite sequence of imaginary poles in theenergy appear. The generic features of string propagation in curvedD-dimensional backgrounds (string stretching, fall into spacetimesingularities) are analyzed in the present case. A new physical phenomenonspecific to the present black-hole is found : the quantum renormalization ofthe speed of light. We find $c_{quantum} = \sqrt{{k\o{k-2}}}~c_{classical}$,where $k$ is the integer in front of the WZW action. This feature is, however,a pathology. Only for $ k \to \infty$ the pathology disappears (although theconformal anomaly is present). We analyze all the classical euclidean stringsolutions and exactly compute the quantum partition function. No criticalHagedorn temperature appears here.Comment: 32 pages, uses phyzz

THE TWO-DIMENSIONAL STRINGY BLACK HOLE: A NEW APPROACH AND A NEW EFFECT