  We show how standard Newtonian N-body simulations can be interpreted in terms
of the weak-field limit of general relativity by employing the recently
developed Newtonian motion gauge. Our framework allows the inclusion of
radiation perturbations and the non-linear evolution of matter. We show how to
construct the weak-field metric by combining Newtonian simulations with results
from Einstein-Boltzmann codes. We discuss observational effects on weak lensing
and ray tracing, identifying important relativistic corrections.
