Martín Menéndez, RosarioVerdaguer Oms, Enric, 1950-2010-05-062010-05-0619990556-2821https://hdl.handle.net/2445/12310In the first part of this paper, we show that the semiclassical Einstein-Langevin equation, introduced in the framework of a stochastic generalization of semiclassical gravity to describe the back reaction of matter stress-energy fluctuations, can be formally derived from a functional method based on the influence functional of Feynman and Vernon. In the second part, we derive a number of results for background solutions of semiclassical gravity consisting of stationary and conformally stationary spacetimes and scalar fields in thermal equilibrium states. For these cases, fluctuation-dissipation relations are derived. We also show that particle creation is related to the vacuum stress-energy fluctuations and that it is enhanced by the presence of stochastic metric fluctuations.24 p.application/pdfeng(c) The American Physical Society, 1999Gravetat quànticaQuantum gravityinfo:eu-repo/semantics/article145499info:eu-repo/semantics/openAccess