4-DIMENSIONAL AND 2-DIMENSIONAL EVAPORATING DILATONIC BLACK-HOLES

The picture of S-wave scattering from a 4-D extremal dilatonic black hole is examined. Classically, a small matter shock wave will form a non-extremal black hole. The 4-D Hawking radiation (in this classical background) gives the 2-D Hawking radiation exactly in the throat region. The 4-D geometry outside the throat region is almost the external one, and the deviations can be calculated using a linear approximation. Inclusion of the back-reaction changes this picture: the linear approximation is valid only at the beginning of the evaporating process. We give (explicitly) that linear 4-D solution. The linear approximation breaks down even before an apparent horizon is formed, which suggests that the 4-D semiclassical solution may be quite different from the 2-D one.