Inhomogeneity effect in Wainwright-Marshman space-times

TL;DR

This paper provides the first explicit example of a one-parameter family of non-vacuum solutions in the Wainwright-Marshman class that fits within Green and Wald's framework for analyzing small-scale inhomogeneity effects in general relativity.

Contribution

It introduces the first explicit non-vacuum solutions that demonstrate the Green-Wald inhomogeneity framework in the Wainwright-Marshman class.

Findings

First explicit non-vacuum solutions satisfying Green-Wald assumptions

Demonstrates applicability of the framework to specific space-time models

Supports the study of inhomogeneity effects in general relativity

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 non-vacuum solutions to the Einstein's equations. It belongs to the Wainwright-Marshman class and satisfies all of the assumptions of the Green-Wald framework.