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Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel....

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Autores principales: Hu, Bei Lok, Verdaguer, Enric
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2004
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5660882/
https://www.ncbi.nlm.nih.gov/pubmed/29142503
http://dx.doi.org/10.12942/lrr-2004-3
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author Hu, Bei Lok
Verdaguer, Enric
author_facet Hu, Bei Lok
Verdaguer, Enric
author_sort Hu, Bei Lok
collection PubMed
description Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operatorvalued) stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field’s Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole (enclosed in a box). We derive a fluctuation-dissipation relation between the fluctuations in the radiation and the dissipative dynamics of metric fluctuations.
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spelling pubmed-56608822017-11-13 Stochastic Gravity: Theory and Applications Hu, Bei Lok Verdaguer, Enric Living Rev Relativ Review Article Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operatorvalued) stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field’s Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole (enclosed in a box). We derive a fluctuation-dissipation relation between the fluctuations in the radiation and the dissipative dynamics of metric fluctuations. Springer International Publishing 2004-03-11 2004 /pmc/articles/PMC5660882/ /pubmed/29142503 http://dx.doi.org/10.12942/lrr-2004-3 Text en © The Author(s) 2004
spellingShingle Review Article
Hu, Bei Lok
Verdaguer, Enric
Stochastic Gravity: Theory and Applications
title Stochastic Gravity: Theory and Applications
title_full Stochastic Gravity: Theory and Applications
title_fullStr Stochastic Gravity: Theory and Applications
title_full_unstemmed Stochastic Gravity: Theory and Applications
title_short Stochastic Gravity: Theory and Applications
title_sort stochastic gravity: theory and applications
topic Review Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5660882/
https://www.ncbi.nlm.nih.gov/pubmed/29142503
http://dx.doi.org/10.12942/lrr-2004-3
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