The detection of relativistic corrections in cosmological N-body simulations

TL;DR

This paper investigates the feasibility of detecting relativistic effects, like perihelion advance, in cosmological N-body simulations using current computational methods and identifies specific parameter ranges where such effects could be observed.

Contribution

It provides an analysis of the conditions under which relativistic corrections can be numerically detected in N-body simulations, considering integration methods and force interpolation techniques.

Findings

Relativistic perihelion advance can be detected within small parameter windows.

Detection depends on eccentricity, distance, and Schwarzschild radius.

Certain simulation parameters enable the observation of relativistic effects.

Abstract

Cosmological N-body simulations are done on massively parallel computers. This necessitates the use of simple time integrators, and, additionally, of mesh-grid approximations of the potentials. Recently, Adamek et al. (2015); Barrera-Hinojosa et al. (2019) have developed general relativistic N-body simulations to capture relativistic effects mainly for cosmological purposes. We therefore ask whether, with the available technology, relativistic effects like perihelion advance can be detected numerically to a relevant precision. We first study the spurious perihelion shift in the Kepler problem, as a function of the integration method used, and then as a function of an additional interpolation of forces on a 2-dimensional lattice. This is done for several choices of eccentricities and semi-major axes. Using these results, we can predict which precisions and lattice constants allow for a detection of the relativistic perihelion advance in N-body simulation. We find that there are only small windows of parameters -- such as eccentricity, distance from the central object and the Schwarzschild radius -- for which the corrections can be detected in the numerics.