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11 - Metric Fluctuations in Minkowski Spacetime

from Part III - Stochastic Gravity

Published online by Cambridge University Press:  20 January 2020

Bei-Lok B. Hu
Affiliation:
University of Maryland, College Park
Enric Verdaguer
Affiliation:
Universitat de Barcelona
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Summary

In this chapter we describe an important application of stochastic gravity: we derive the Einstein–Langevin equation for the metric perturbations in a Minkowski background. We solve this equation for the linearized Einstein tensor and compute the associated two-point correlation functions, as well as the two-point correlation functions for the metric perturbations. The results of this calculation show that gravitational fluctuations are negligible at length scales larger than the Planck length and predict that the fluctuations are strongly suppressed at small scales. These results also reveal an important connection between stochastic gravity and the 1/N expansion of quantum gravity. In addition, they are used to study the stability of the Minkowski metric as a solution of semiclassical gravity, which constitutes an application of the validity criterion introduced in the previous chapter. This calculation requires a discussion of the problems posed by the so-called runaway solutions and some of the methods of dealing with them.

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Chapter
Information
Semiclassical and Stochastic Gravity
Quantum Field Effects on Curved Spacetime
, pp. 364 - 388
Publisher: Cambridge University Press
Print publication year: 2020

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