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Stochastic semiclassical gravity
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In 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.
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MARTÍN MENÉNDEZ, Rosario and VERDAGUER OMS, Enric. Stochastic semiclassical gravity. Physical Review D. 1999. Vol. 60, num. 8, pags. 084008-1-084008-24. ISSN 0556-2821. [consulted: 10 of June of 2026]. Available at: https://hdl.handle.net/2445/12310