Abstract

Cosmologists routinely use Newtonian N-body simulations to simulate the complex nonlinear processes of structure formation, which we believe approximates the “true” relativistic behaviour in general relativity. I will show first how we can make a consistent GR interpretation of the Newtonian solutions in the simplest case of linear perturbations with zero pressure, and then how this can be extended to include (a) non-zero pressure and (b) non-linear perturbations, in a weak-field limit. I will advocate an computationally efficient approach that uses unmodified Newtonian simulations to simulate non-linear structures and embeds them in a perturbative relativistic spacetime, including radiation perturbations, calculated using standard Einstein-Boltzmann codes. I will discuss existing approaches to incorporating radiation in Newtonian simulations and how they can be interpreted in a relativistic framework. An outstanding challenge remains how to incorporate nonlinear metric perturbations and initial conditions.