Semiclassical S-matrix and black hole entropy in dilaton gravity

We use complex semiclassical method to compute scattering amplitudes of a point particle in dilaton gravity with a boundary. This model has nonzero minimal black hole mass Mcr. We find that at energies below Mcr the particle trivially scatters off the boundary with unit probability. At higher energies the scattering amplitude is exponentially suppressed. The corresponding semiclassical solution is interpreted as formation of an intermediate …