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Stochastic Gravity: Theory and Applications.

Bei Lok Hu¹, Enric Verdaguer²

¹Department of Physics, University of Maryland, College Park, 20742-4111 Maryland USA.

Living Reviews in Relativity

|November 17, 2017

Summary

This summary is machine-generated.

Stochastic gravity introduces the Einstein-Langevin equation, incorporating quantum field fluctuations via a noise kernel. This theory explains phenomena like structure formation and Hawking radiation backreaction.

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Area of Science:

Theoretical Physics
Quantum Gravity
Cosmology

Background:

Semiclassical gravity uses the semiclassical Einstein equation with quantum field expectation values.
Stochastic gravity extends this with the Einstein-Langevin equation, including quantum noise.
The noise kernel quantifies fluctuations of quantum matter fields in curved spacetimes.

Purpose of the Study:

To establish the fundamentals of stochastic gravity theory.
To derive a general expression for the noise kernel.
To explore applications of stochastic gravity in cosmology and black hole physics.

Main Methods:

Axiomatic approach: Linking mean values to correlation functions.
Functional approach: Employing Feynman-Vernon influence functional and Schwinger-Keldysh methods.
Derivation of the noise kernel for quantum fields in curved spacetimes.

Main Results:

A general expression for the noise kernel was obtained.
Analytical solutions for metric perturbations in Minkowski spacetime were computed.
The theory was applied to structure formation and Hawking radiation backreaction.

Conclusions:

Stochastic gravity provides a framework for understanding quantum effects in gravity.
The theory offers insights into structure formation and black hole thermodynamics.
Fluctuation-dissipation relations were derived for black hole systems.