Computing General Relativistic effects from Newtonian N-body simulations: Frame dragging in the post-Friedmann approach

TL;DR

This paper introduces a method to compute relativistic frame dragging effects from standard Newtonian N-body simulations in cosmology, enabling the study of relativistic phenomena within a non-linear structure formation framework.

Contribution

It presents the first calculation of a relativistic quantity, the gravito-magnetic vector potential, from Newtonian simulations in a fully non-linear cosmological context.

Findings

The vector potential can be derived from Newtonian simulations without affecting matter dynamics.

The magnitude of the vector potential is quantified relative to the scalar potential.

Potential observable effects of frame dragging in large-scale structures are discussed.

Abstract

We present the first calculation of an intrinsically relativistic quantity in fully non-linear cosmolog- ical large-scale structure studies. Traditionally, non-linear structure formation in standard {\Lambda}CDM cosmology is studied using N-body simulations, based on Newtonian gravitational dynamics on an expanding background. When one derives the Newtonian regime in a way that is a consistent ap- proximation to the Einstein equations, a gravito-magnetic vector potential - giving rise to frame dragging - is present in the metric in addition to the usual Newtonian scalar potential. At leading order, this vector potential does not affect the matter dynamics, thus it can be computed from Newtonian N-body simulations. We explain how we compute the vector potential from simulations in {\Lambda}CDM and examine its magnitude relative to the scalar potential. We also discuss some possible observable effects.