Einstein-Langevin equation: semiclassical gravity with quantum noise source
Stochastic gravity extends semiclassical gravity by including fluctuations of the stress-energy tensor as a stochastic source in the Einstein-Langevin equation: G_{μν} + Λg_{μν} = 8πG(⟨T_{μν}⟩ + ξ_{μν}), where ξ is the Gaussian noise kernel from the quantum vacuum. The metric fluctuates around the semiclassical background, with noise amplitude ~ ℏ.