Relativistic structure formation models and gravitoelectromagnetism

TL;DR

This paper explores a relativistic approach to structure formation by decomposing Einstein's equations into gravitoelectric and gravitomagnetic components, linking Newtonian and non-Newtonian gravitational phenomena.

Contribution

It introduces a method to split Einstein's equations into gravitoelectric and gravitomagnetic parts using Cartan coframes, highlighting the inclusion of gravitational waves.

Findings

Reproduces Newtonian perturbation hierarchy

Identifies non-Newtonian gravitational waves

Provides a unique split via Hodge decomposition

Abstract

In the framework of Lagrangian perturbation theory in general relativity we discuss the possibility to split the Einstein equations, written in terms of spatial Cartan coframes within a 3+1 foliation of spacetime, into gravitoelectric and gravitomagnetic parts. While the former reproduces the full hierarchy of the Newtonian perturbation solutions, the latter contains non-Newtonian aspects like gravitational waves. This split can be understood and made unique through the Hodge decomposition of Cartan coframe fields.