General relativistic weak-field limit and Newtonian N-body simulations

TL;DR

This paper demonstrates how Newtonian N-body simulations can be understood within general relativity's weak-field limit, incorporating radiation effects and relativistic corrections for improved cosmological modeling.

Contribution

It introduces a framework using the Newtonian motion gauge to interpret Newtonian simulations in relativistic terms, including radiation and non-linear matter evolution.

Findings

Framework for interpreting Newtonian simulations in GR

Method to incorporate radiation perturbations

Identification of relativistic corrections in weak lensing

Abstract

We show how standard Newtonian N-body simulations can be interpreted in terms of the weak-field limit of general relativity by employing the recently developed Newtonian motion gauge. Our framework allows the inclusion of radiation perturbations and the non-linear evolution of matter. We show how to construct the weak-field metric by combining Newtonian simulations with results from Einstein-Boltzmann codes. We discuss observational effects on weak lensing and ray tracing, identifying important relativistic corrections.