  We study propagation of D0-brane in two-dimensional Lorentzian black hole
backgrounds by the method of boundary conformal field theory of SL(2,R)/U(1)
supercoset at level k. Typically, such backgrounds arise as near-horizon
geometries of k coincident non-extremal NS5-branes, where 1/k measures
curvature of the backgrounds in string unit and hence size of string worldsheet
effects. At classical level, string worldsheet effects are suppressed and
D0-brane propagation in the Lorentzian black hole geometry is simply given by
the Wick rotation of D1-brane contour in the Euclidean black hole geometry.
Taking account of string worldsheet effects, boundary state of the Lorentzian
D0-brane is formally constructible via Wick rotation from that of the Euclidean
D1-brane. However, the construction is subject to ambiguities in boundary
conditions. We propose exact boundary states describing the D0-brane, and
clarify physical interpretations of various boundary states constructed from
different boundary conditions. As it falls into the black hole, the D0-brane
radiates off to the horizon and to the infinity. From the boundary states
constructed, we compute physical observables of such radiative process. We find
that part of the radiation to infinity is in effective thermal distribution at
the Hawking temperature. We also find that part of the radiation to horizon is
in the Hagedorn distribution, dominated by massive, highly non-relativistic
closed string states, much like the tachyon matter. Remarkably, such
distribution emerges only after string worldsheet effects are taken exactly
into account. From these results, we observe that nature of the radiation
distribution changes dramatically across the conifold geometry k=1 (k=3 for the
bosonic case), exposing the `string - black hole transition' therein.
