Averaging in LRS class II spacetimes

TL;DR

This paper extends Buchert's averaging method to LRS class II dust spacetimes, deriving new averaged equations and exploring backreaction effects on expansion and shear, with a proposed closure scheme for the system.

Contribution

It generalizes Buchert's averaging to all Einstein equations in LRS class II dust models and introduces a closure method for the averaged system.

Findings

Derived new averaged equations for LRS class II dust spacetimes.

Analyzed backreaction effects on expansion and shear scalars.

Proposed a closure scheme for the averaged equations.

Abstract

We generalize Buchert's averaged equations [Gen. Rel. Grav. 32, 105 (2000); Gen. Rel. Grav. 33, 1381 (2001)] to LRS class II dust model in the sense that all Einstein equations are averaged, not only the trace part. We derive the relevant averaged equations and we investigate backreaction on expansion and shear scalars in an approximate LTB model. Finally we propose a way to close the system of averaged equations.