Connection between Newtonian simulations and general relativity
  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 solve for the metric,
densities and velocities in a specific coordinate system or gauge. The method
of choice for simulating large-scale structure is numerical N-body simulations
which are performed in the Newtonian limit. Even though one might worry that
the use of the Newtonian approximation would make it impossible to use these
simulations to compute properties on very large-scales, we show that the
simulations are still solving the dynamics correctly even for long modes and we
give formulas to obtain the position of particles in the conformal Newtonian
gauge given the positions computed in the simulation. We also give formulas to
convert from the output coordinates of N-body simulations to the observable
coordinates of the particles.
