On the semiclassical Einstein-Langevin equation

We introduce a semiclassical Einstein-Langevin equation as a consistent dyn amical equation for a first order perturbative correction to semiclassical gravity. This equation includes the lowest order quantum stress-energy fluc tuations of matter fields as a source of classical stochastic fluctuations of the gravitational field. The Einstein-Langevin equation is explicitly so lved around one of the simplest solutions of semiclassical gravity: Minkows ki spacetime with a conformal scalar field in its vacuum state. We compute the two-point correlation function of the linearized Einstein tensor. This calculation illustrates the possibility of obtaining some "non-perturbative '' behavior for the induced gravitational fluctuations. (C) 1999 Published by Elsevier Science B.V. All rights reserved.