Wave propagation in stringy black hole

We further study the non-perturbative formulation of two-dimensional black holes. We find a nonlinear differential equation satisfied by the tachyon in the black hole background. We show that singularities in the tachyon field configurations are always associated with divergent semiclassical expansions and are absent in the exact theory. We also discuss how the Euclidean black hole emerges from an analytically continued fermion theory that corresponds to the right side up harmonic oscillator potential