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

Christian Fidler, Cornelius Rampf, Thomas Tram, Robert Crittenden, Kazuya Koyama, David Wands

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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.
Original languageEnglish
Article number123517
JournalPhysical Review D
Publication statusPublished - 18 May 2015


  • astro-ph.CO
  • gr-qc
  • ST/K00090X/1
  • ST/ L005573/1
  • STFC
  • RCUK


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