Non-commutative black hole algebra and string theory from gravity

Abstract

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 mec hanism for reco vering information about the momen tumof the incoming particles. The new action also describes particles with transverse momen ta 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 b y 't Hooft, we also find an antisymmetri c tensor, which is here related to the momentum of the particles. At the quantum level, the identification between position and momen tum operators leads to four non-comm uting coordinates. A certain relation to M(atrix) theory is proposed.