Inhomogeneity effect in Wainwright-Marshman space-times

Abstract

Green and Wald have presented a mathematically rigorous framework to study, within general relativity, the effect of small-scale inhomogeneities on the global structure of space-time. The framework relies on the existence of a one-parameter family of metrics that approaches the effective background metric in a certain way. Although it is not necessary to know this family in an exact form to predict properties of the backreaction effect, it would be instructive to find explicit examples. In this paper, we provide the first example of such a family of exact nonvacuum solutions to the Einstein equations. It belongs to the Wainwright-Marshman class and satisfies all of the assumptions of the Green-Wald framework.

Inhomogeneous cosmology and backreaction: Current status and future prospects

“…32,33 Therefore, more effort should be put towards exploring the known solutions and testing the backreaction within these solutions. 72,[157][158][159][160][161] Another important issue is to analyse cosmological observations within these models, 162,163 as well as trying to develop and find new solutions with lesser symmetries. 32 Collaboration with the observers: Observational data are not only analysed within the framework of FLRW model, but often assumptions and equations of the FLRW models are used to process the raw data and derive the "observables".…”

Backreaction for Einstein-Rosen waves coupled to a massless scalar field

“…The exact solution presented in this paper provides such an opportunity. Some time ago we 2 presented a one-parameter family of exact solutions to Einstein's equations that was used to test the Green-Wald backreaction framework [9]. This was the first nonvacuum example of a family of exact solutions that satisfies the Green-Wald assumptions.…”

Averaging the Schwarzschild spacetime

“…The expressions for the Einstein tensor's eigenvalues (20) and (21) also hold true but due to the γ 2 + γ 3 factor in γ 1 , all the eigenvalues are finite for any r > R. The behavior of the eigenvalues near the center is given by the series…”

“…It has recently been widely discussed [19][20][21][22] because of the restrictive conclusion on possible backreaction. The method generalizes the approach of Burnett [23] and Isaacson [24] for gravitationally radiating systems and defines the average metric as the limit of a one-parameter family of metrics without the usual integration over a finite volume.…”