Coarse-graining of inhomogeneous dust flow in General Relativity via isometric embeddings

TL;DR

This paper introduces a coordinate-independent method for coarse-graining tensorial dust flow variables in General Relativity using isometric embeddings, aiding in the analysis of inhomogeneous cosmological models.

Contribution

It develops a novel approach based on isometric embeddings to coarse-grain tensor quantities in GR, unlike previous schemes.

Findings

Allows coordinate-independent coarse-graining of shear, twist, and expansion.

Provides a framework to estimate backreaction effects in inhomogeneous cosmology.

Enables analysis of dust flow in complex spacetime geometries.

Abstract

We present a new approach to coarse-graining of variables describing dust flow in GR. It is based on assigning quasi-local shear, twist and expansion to 2-dimensional surfaces with the help of isometric embeddings into the 3-dimensional Euclidean space and deriving the time evolution equations for them. In contrast to the popular Buchert's scheme it allows to coarse-grain tensorial quantities in a coordinate-independent way. The framework can be used to estimate backreaction in inhomogeneous cosmological models.