QUANTUM SPACE-TIME AND CLASSICAL GRAVITY

A method has been recently proposed for defining an arbitrary number o f differential calculi over a given noncommutative associative algebra . As an example a version of quantized space-time is considered here. It is found that there is a natural differential calculus over this ve rsion of quantized space-time using which the only possible torsion-fr ee, metric-compatible, linear connection has zero curvature. It is the n the noncummutative version of Minkowski space-time. Perturbations of this calculus are shown to give rise to nontrivial gravitational fiel ds. (C) 1998 American Institute of Physics.