Do Newtonian large-scale structure simulations fail to include relativistic effects?

TL;DR

This paper investigates whether Newtonian large-scale structure simulations neglect significant relativistic effects, proposing a new energy-splitting approach that shows Newtonian effects dominate over relativistic ones over time.

Contribution

It introduces a novel energy-splitting method to assess relativistic effects in Newtonian simulations of cosmic structure formation.

Findings

Newtonian energy dominates over relativistic energy as time progresses

Supports the continued use of Newtonian simulations for large-scale structure formation

Relativistic effects are found to be negligible in the long-term evolution

Abstract

The Newtonian simulations describing the formation of large-scale structures do not include relativistic effects. A new approach to this problem is proposed, which consists of splitting the Hawking-Hayward quasi-local energy of a closed spacelike 2-surface into a "Newtonian" part due to local perturbations and a "relativistic" part due to the cosmology. It is found that the Newtonian part dominates over the relativistic one as time evolves, lending support to the validity of Newtonian simulations.