N-body simulations are of great importance for our current understanding of the evolution of non-linear structures like clusters or galaxies. The treatment of complex phenomena such as feedback from active galactic nuclei or star formation has been continuously refined while the gravitational interaction has barely ever been taken beyond the Newtonian approximation. In general one needs to make some assumption about the nature of the "dark" components of our universe in order to ensure that the Newtonian approximation remains justified. The true nature of these components is, however, poorly understood, and it is indeed hoped that one can learn some important clues from their subtle effects on the evolution of structure. It is therefore a great advantage if one can overcome the limitations imposed by the use of the Newtonian approximation.
I will present a significant conceptual advancement in this direction, making it possible for the first time to carry out cosmological simulations within a truly dynamical space-time. On the scales of interest the gravitational fields will generally remain weak, allowing for a set of controlled approximations which nonetheless go beyond the Newtonian limit and encompass the full dynamical content of general relativity. I will discuss the logical structure of the framework and shall be able to show preliminary results from its first numerical implementation within a fully-fledged and parallelized N-body code.