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

@article{Fidler2017GeneralRW, title={General relativistic weak-field limit and Newtonian N-body simulations}, author={Christian Fidler and Thomas Tram and Cornelius Rampf and Robert G. Crittenden and Kazuya Koyama and David I F Wands}, journal={arXiv: Cosmology and Nongalactic Astrophysics}, year={2017} }

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… Expand

#### 54 Citations

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#### References

SHOWING 1-10 OF 43 REFERENCES

General relativistic N -body simulations in the weak field limit

- Physics
- 2013

We develop a formalism for general relativistic $N$-body simulations in the weak field regime, suitable for cosmological applications. The problem is kept tractable by retaining the metric… Expand

Relativistic Interpretation of Newtonian Simulations for Cosmic Structure Formation

- Physics
- 2016

The standard numerical tools for studying non-linear collapse of matter are Newtonian $N$-body simulations. Previous work has shown that these simulations are in accordance with General Relativity… Expand

Connection between Newtonian simulations and general relativity

- Physics
- 2011

On large scales, comparable to the horizon, the observable clustering properties of galaxies are affected by various general relativistic effects. To calculate these effects one needs to consistently… Expand

General relativistic corrections to $N$-body simulations and the Zel'dovich approximation

- Physics
- 2015

The initial conditions for Newtonian $N$-body simulations are usually generated by applying the Zel'dovich approximation to the initial displacements of the particles using an initial power spectrum… Expand

Cosmological N -body simulations including radiation perturbations

- Physics
- 2017

Cosmological $N$-body simulations are the standard tool to study the emergence of the observed large-scale structure of the Universe. Such simulations usually solve for the gravitational dynamics of… Expand

Relativistic initial conditions for N-body simulations

- Physics
- 2017

Initial conditions for (Newtonian) cosmological N-body simulations are usually set by re-scaling the present-day power spectrum obtained from linear (relativistic) Boltzmann codes to the desired… Expand

Second-order Cosmological Perturbations Engendered by Point-like Masses

- Physics
- 2017

In the $\Lambda$CDM framework, presenting nonrelativistic matter inhomogeneities as discrete massive particles, we develop the second-order cosmological perturbation theory. Our approach relies on… Expand

The effect of early radiation in N-body simulations of cosmic structure formation

- Physics
- 2017

Newtonian N-body simulations have been employed successfully over the past decades for the simulation of the cosmological large-scale structure. Such simulations usually ignore radiation… Expand

Newtonian and relativistic cosmologies

- Physics
- 2012

Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in… Expand

Large-Scale Structure Observables in General Relativity

- Physics
- 2014

We review recent studies that rigorously define several key observables of the large-scale structure of the Universe in a general relativistic context. Specifically, we consider (i) redshift… Expand