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Large redshift surveys of galaxies and clusters are providing the firstopportunities to search for distortions in the observed pattern of large-scalestructure due to such effects as gravitational redshift. We focus on non-linearscales and apply a quasi-Newtonian approach using N-body simulations to predictthe small asymmetries in the cross-correlation function of two galaxy differentpopulations. Following recent work by Bonvin et al., Zhao and Peacock andKaiser on galaxy clusters, we include effects which enter at the same order asgravitational 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-correlationfunctions. Quantifying these asymmetries, we find that the total effect isdominated by the gravitational redshift and luminosity distance perturbation atsmall and large scales, respectively. By adding additional subresolutionmodelling of galaxy structure to the large-scale structure information, we findthat the signal is significantly increased, indicating that structure on thesmallest scales is important and should be included. We report on comparison ofour simulation results with measurements from the SDSS/BOSS galaxy redshiftsurvey in a companion paper.

N-body simulations of gravitational redshifts and other relativistic distortions of galaxy clustering