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
3.3 Validity of semiclassical 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 bitensor 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 Stability of Minkowski spacetime
7 Structure Formation in the Early Universe
7.1 The model
7.2 Einstein–Langevin equation for scalar metric perturbations
7.3 Correlation functions for scalar metric perturbations
7.4 Summary and outlook
8 Black Hole Backreaction and Fluctuations
8.1 General issues of backreaction
8.2 Backreaction on black holes under quasi-static conditions
8.3 Metric fluctuations of an evaporating black hole
8.4 Other work on metric fluctuations but without backreaction
9 Concluding Remarks
10 Acknowledgements
Open References References