Living Reviews in Relativity

"Stochastic Gravity:
Theory and Applications"
Bei Lok Hu and Enric Verdaguer  

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1 Overview
2 From Semiclassical to Stochastic Gravity
2.1 The importance of quantum fluctuations
3 The Einstein–Langevin Equation: Axiomatic Approach
3.1 Semiclassical gravity
3.2 Stochastic gravity
4 The Einstein–Langevin Equation: Functional Approach
4.1 Influence action for semiclassical gravity
4.2 Influence action for stochastic gravity
4.3 Explicit form of the Einstein–Langevin equation
5 Noise Kernel and Point-Separation
5.1 Point separation
5.2 Stress-energy bi-tensor operator and noise kernel
6 Metric Fluctuations in Minkowski Spacetime
6.1 Perturbations around Minkowski spacetime
6.2 The kernels in the Minkowski background
6.3 The Einstein–Langevin equation
6.4 Correlation functions for gravitational perturbations
6.5 Discussion
7 Structure Formation
7.1 The model
7.2 The Einstein–Langevin equation for scalar metric perturbations
7.3 Correlation functions for scalar metric perturbations
7.4 Discussion
8 Black Hole Backreaction
8.1 The model
8.2 CTP effective action for the black hole
8.3 Near flat case
8.4 Near horizon case
8.5 The Einstein–Langevin equation
8.6 Discussions
9 Concluding Remarks
10 Acknowledgements
Open References References