Stochastic semiclassical gravity - art. no. 084008

In the first part of this paper, we show that the semiclassical Einstein-La ngevin equation, introduced in the framework of a stochastic generalization of semiclassical gravity to describe the back reaction of matter stress-en ergy fluctuations, can be formally derived from a functional method based o n the influence functional of Feynman and Vernon. In the second part, we de rive a number of results for background solutions of semiclassical gravity consisting of stationary and conformally stationary spacetimes and scalar f ields in thermal equilibrium states. For these cases, fluctuation-dissipati on relations are derived. We also show that particle creation is related to the vacuum stress-energy fluctuations and that it is enhanced by the prese nce of stochastic metric fluctuations. [S0556-2821(99)02318-8].