N-body simulations of gravitational redshifts and other relativistic
  distortions of galaxy clustering
  Large redshift surveys of galaxies and clusters are providing the first
opportunities to search for distortions in the observed pattern of large-scale
structure due to such effects as gravitational redshift. We focus on non-linear
scales and apply a quasi-Newtonian approach using N-body simulations to predict
the small asymmetries in the cross-correlation function of two galaxy different
populations. Following recent work by Bonvin et al., Zhao and Peacock and
Kaiser on galaxy clusters, we include effects which enter at the same order as
gravitational redshift: the transverse Doppler effect, light-cone effects,
relativistic beaming, luminosity distance perturbation and wide-angle effects.
We find that all these effects cause asymmetries in the cross-correlation
functions. Quantifying these asymmetries, we find that the total effect is
dominated by the gravitational redshift and luminosity distance perturbation at
small and large scales, respectively. By adding additional subresolution
modelling of galaxy structure to the large-scale structure information, we find
that the signal is significantly increased, indicating that structure on the
smallest scales is important and should be included. We report on comparison of
our simulation results with measurements from the SDSS/BOSS galaxy redshift
survey in a companion paper.
