  Distance measurements are usually thought to probe the background metric of
the universe, but in reality the presence of perturbations will lead to
deviations from the result expected in an exactly homogeneous and isotropic
universe. At least in principle the presence of perturbations could even
explain the observed distance-redshift relation without the need for dark
energy. In this paper we re-investigate a toy model where perturbations are
plane symmetric, and for which exact solutions are known in the fluid limit.
However, if perturbations are large, shell-crossing occurs and the fluid
approximation breaks down. This prevents the study of the most interesting
cases. Here we use a general-relativistic N-body simulation that does not
suffer from this problem and which allows us to go beyond previous works. We
show that even for very large plane-symmetric perturbations we are not able to
mimic the observed distance-redshift relation. We also discuss how the
synchronous comoving gauge breaks down when shell-crossing occurs, while metric
perturbations in the longitudinal gauge remain small. For this reason the
longitudinal (Newtonian) gauge appears superior for relativistic N-body
simulations of large-scale structure formation.
