N-body simulations normally use equations of Newtonian dynamics to evolve
particles and fields forward in time. On galactic scales and at times late
enough for velocities and gradients of fields to be small this turns out to
be an extremely good approximation. However, in modified gravity models, at
earlier times when neutrinos are relativistic, or on much larger scales,
evolving relativistic sources become important. Therefore, nonlinear
evolution of cosmic structure requires a more sophisticated modelling of
dynamics. We model general relativity numerically with a weak-field
approximation, but still allow for large gradients of the fields and
relativistic velocities for the particles. This makes the system much more
complicated. In this work, we therefore simplify the system by considering
a one-dimensional, spherically symmetric setup. Apart from just reducing
the complexity, this setup also allows us to model spherically symmetric
fluctuations such as a void or a spherical halo.