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

Abstract

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 relativistic corrections.

22 pages, 3 figures; accepted for publication at JCAP

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• Cosmological $N$-body simulations including radiation perturbations
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• Perturbed redshifts from N-body simulations