  We study the dynamics of small inhomogeneities in an expanding universe
collapsing to form bound structures using full solutions of the Einstein-Vlasov
(N-body) equations. We compare these to standard Newtonian N-body solutions
using quantities defined with respect to fiducial observers in order to bound
relativistic effects. We focus on simplified initial conditions containing a
limited range of length scales, but vary the inhomogeneities from small
magnitude, where the Newtonian and general-relativistic calculations agree
quite well, to large magnitude, where the background metric receives an order
one correction. For large inhomogeneities, we find that the collapse of
overdensities tends to happen faster in Newtonian calculations relative to
fully general-relativistic ones. Even in this extreme regime, the differences
in the spacetime evolution outside the regions of large gravitational potential
and velocity are small. For standard cosmological values, we corroborate the
robustness of Newtonian N-body simulations to model large scale perturbations
and the related cosmic variance in the local expansion rate.
