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

Fidler, Christian;et.al.
(2015) Physical review. D, Particles and fields — Vol. D92, p. 123517 (2015)

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  • Fidler, ChristianUCLouvain
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  • et. al.
Abstract
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 of density fluctuations generated by an Einstein-Boltzmann solver. We show that in most gauges the initial displacements generated in this way receive a first-order relativistic correction. We define a new gauge, the $N$-body gauge, in which this relativistic correction vanishes and show that a conventional Newtonian $N$-body simulation includes all first-order relativistic contributions (in the absence of radiation) if we identify the coordinates in Newtonian simulations with those in the relativistic $N$-body gauge.
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Fidler, C., & et al. (2015). General relativistic corrections to $N$-body simulations and the Zel’dovich approximation. Physical review. D, Particles and fields, D92, 123517. https://doi.org/10.1103/PhysRevD.92.123517 (Original work published 2015)