  We generalize the action found by 't Hooft, which describes the gravitational
interaction between ingoing and outgoing particles in the neighbourhood of a
black hole. The effect of this back-reaction is that of a shock wave, and it
provides a mechanism for recovering information about the momentum of the
incoming particles. The new action also describes particles with transverse
momenta and takes into account the transverse curvature of the hole, and has
the form of a string theory action. Apart from the Polyakov term found by 't
Hooft, we also find an antisymmetric tensor, which is here related to the
momentum of the particles. At the quantum level, the identification between
position and momentum operators leads to four non-commuting coordinates. A
certain relation to M(atrix) theory is proposed.
