  Recently, 't Hooft's S-matrix for black hole evaporation, obtained from the
gravitational interactions between the in-falling particles and Hawking
radiation, has been generalised to include transverse effects. The action
describing the collision turned out to be a string theory action with an
antisymmetric tensor background. In this article we show that the model
reproduces both the correct longitudinal and transverse dynamics, even when one
goes beyond the eikonal approximation or particles collide at nonvanishing
incidence angles. It also gives the correct momentum tranfer that takes place
in the process. Including a curvature on the horizon provides the action with
an extra term, which can be interpreted as a dilaton contribution. The
amplitude of the scattering is seen to reproduce the Veneziano amplitude in a
certain limit, as in earlier work by 't Hooft. The theory resembles a
"holographic" field theory, in the sense that it only depends on the horizon
degrees of freedom, and the in- and out-Hilbert spaces are the same. The
operators representing the coordinates of in- and out-going particles are
non-commuting, and Heisenberg's uncertainty principle must be corrected by a
term proportional to the ratio of the ingoing momentum to the impact parameter,
times Newton's constant. Reducing to 2+1 dimensions, we find that the
coordinates satisfy an SO(2,1) algebra.
