# The large-scale general-relativistic correction for Newtonian mocks

## TL;DR

This paper addresses the challenge of accurately mapping Newtonian simulations to relativistic light-cone observables at large scales, emphasizing the importance of gauge choices and proposing solutions for consistent relativistic interpretation.

## Contribution

It clarifies the gauge-related issues in translating Newtonian simulations to relativistic observables and quantifies the resulting systematic errors using perturbation theory and relativistic simulations.

## Key findings

- Gauge differences significantly affect large-scale observables.
- Systematic errors from gauge mismatch can be quantified.
- Proposed solutions improve relativistic consistency of simulations.

## Abstract

We clarify the subtle issue of finding the correct mapping of Newtonian simulations to light-cone observables at very large distance scales. A faithful general-relativistic interpretation specifies a gauge, i.e. a chart that relates the simulation data to points of the space-time manifold. It has already been pointed out that the implicit gauge choice of Newtonian simulations is indeed different from the Poisson gauge that is commonly adopted for relativistic calculations, the difference being most significant at large scales. It is therefore inconsistent, for example, to predict weak-lensing observables from simulations unless this gauge issue is properly accounted for. Using perturbation theory as well as fully relativistic N-body simulations we quantify the systematic error introduced this way, and we discuss several solutions that would render the calculations relativistically self-consistent.